<p><b>kavulich@ucar.edu</b> 2013-05-16 13:09:45 -0600 (Thu, 16 May 2013)</p><p>-Add appendix about tutorial case<br>
-Finish rough quick-start guide<br>
-Various edits to other chapters, adding more sections; much of this needs consolidation<br>
</p><hr noshade><pre><font color="gray">Modified: trunk/wrfvar/3DVAR_technote/3dvar.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/3dvar.tex 2013-05-10 02:52:55 UTC (rev 431)
+++ trunk/wrfvar/3DVAR_technote/3dvar.tex 2013-05-16 19:09:45 UTC (rev 432)
@@ -117,8 +117,3 @@
\label{update_bc}
Boundary conditions are 5-gridpoints deep, nudge the interior 4 gridpoints
-
-\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/acknow.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/acknow.tex 2013-05-10 02:52:55 UTC (rev 431)
+++ trunk/wrfvar/3DVAR_technote/acknow.tex 2013-05-16 19:09:45 UTC (rev 432)
@@ -14,25 +14,10 @@
\end{itemize}
\vskip 10pt
-NCAR scientists (Dale)
+The development of WRFDA has been (and continues to be) an international team effort. We would like to acknowledge the following people for their contributions to the WRFDA 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
-SE acknowledgements (Zhang)
+Tech note reviewers (???)
\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,
-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
-Meteorological Bureau.
+The WRFDA 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.
Deleted: trunk/wrfvar/3DVAR_technote/appena.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/appena.tex 2013-05-10 02:52:55 UTC (rev 431)
+++ trunk/wrfvar/3DVAR_technote/appena.tex 2013-05-16 19:09:45 UTC (rev 432)
@@ -1,31 +0,0 @@
-\chapter{Physical Constants}
-\label{physical_constants}
-
-This is the WRF version. Needs to be updated for WRF-VAR!!!!!!!
-
-The following is a list of physical constants used in the model.
-\\[3ex]
-
-\begin{eqnarray*}
-\begin{array}{lcll}
-\pi & = & 3.1415926 & \mathrm{Pi} \\
-k & = & 0.4 & \mathrm{Von \: Karman \: constant} \\
-r_e & = & 6.370 \times 10^{6} \quad\mathrm{m} & \mathrm{ Radius \: of \: earth} \\
-g & = & 9.81 \quad\mathrm{m \: s^{-2}} & \mathrm{ Acceleration \: due \: to \: gravity}\\
-\Omega_{e} & = & 7.2921 \times 10^{-5} \quad\mathrm{s^{-1}} & \mathrm{ Angular \: rotation \: rate \: of \: the \: earth}\\
-\sigma_{B} & = & 5.67051 \times 10^{-8} \quad\mathrm{W \: m^{-2} \: K^{-4}} & \mathrm{ Stefan-Boltzmann \: constant}\\
-R_{d} & = & 287 \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Gas \: constant \: for \: dry \: air}\\
-R_{v} & = & 461.6 \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Gas \: constant \: for \: water \: vapor}\\
-c_{p} & = & 7 \times R_{d}/2 \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Specific \: heat \: of \: dry \: air \: at \: constant \: pressure}\\
-c_{v} & = & c_{p}-R_{d} \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Specific \: heat \: of \: dry \: air \: at \: constant \: volume}\\
-c_{pv} & = & 4 \times R_{v} \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Specific \: heat \: of \: water \: vapor \: at \: constant \: pressure}\\
-c_{vv} & = & c_{pv}-R_{v} \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Specific \: heat \: of \: water \: vapor \: at \: constant \: volume}\\
-c_{liq} & = & 4190 \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Specific \: heat \: capacity \: of \: water}\\
-c_{ice} & = & 2106 \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Specific \: heat \: capacity \: of \: ice}\\
-L_{v} & = & 2.5 \times 10^{6} \quad\mathrm{J \: kg^{-1}} & \mathrm{ Latent \: heat \: of \: vaporization}\\
-L_{s} & = & 2.85 \times 10^{6} \quad\mathrm{J \: kg^{-1}} & \mathrm{ Latent \: heat \: of \: sublimation}\\
-L_{f} & = & 3.50 \times 10^{5} \quad\mathrm{J \: kg^{-1}} & \mathrm{ Latent \: heat \: of \: fusion}\\
-\rho_{w} & = & 1.0 \times 10^{3} \quad\mathrm{kg \: m^{-3}} & \mathrm{ Density \: of \: liquid \: water}\\
-\end{array}
-\end{eqnarray*}
-
Copied: trunk/wrfvar/3DVAR_technote/constants.tex (from rev 429, trunk/wrfvar/3DVAR_technote/appena.tex)
===================================================================
--- trunk/wrfvar/3DVAR_technote/constants.tex (rev 0)
+++ trunk/wrfvar/3DVAR_technote/constants.tex 2013-05-16 19:09:45 UTC (rev 432)
@@ -0,0 +1,31 @@
+\chapter{Physical Constants}
+\label{physical_constants}
+
+This is the WRF version. Needs to be updated for WRF-VAR!!!!!!!
+
+The following is a list of physical constants used in the model.
+\\[3ex]
+
+\begin{eqnarray*}
+\begin{array}{lcll}
+\pi & = & 3.1415926 & \mathrm{Pi} \\
+k & = & 0.4 & \mathrm{Von \: Karman \: constant} \\
+r_e & = & 6.370 \times 10^{6} \quad\mathrm{m} & \mathrm{ Radius \: of \: earth} \\
+g & = & 9.81 \quad\mathrm{m \: s^{-2}} & \mathrm{ Acceleration \: due \: to \: gravity}\\
+\Omega_{e} & = & 7.2921 \times 10^{-5} \quad\mathrm{s^{-1}} & \mathrm{ Angular \: rotation \: rate \: of \: the \: earth}\\
+\sigma_{B} & = & 5.67051 \times 10^{-8} \quad\mathrm{W \: m^{-2} \: K^{-4}} & \mathrm{ Stefan-Boltzmann \: constant}\\
+R_{d} & = & 287 \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Gas \: constant \: for \: dry \: air}\\
+R_{v} & = & 461.6 \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Gas \: constant \: for \: water \: vapor}\\
+c_{p} & = & 7 \times R_{d}/2 \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Specific \: heat \: of \: dry \: air \: at \: constant \: pressure}\\
+c_{v} & = & c_{p}-R_{d} \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Specific \: heat \: of \: dry \: air \: at \: constant \: volume}\\
+c_{pv} & = & 4 \times R_{v} \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Specific \: heat \: of \: water \: vapor \: at \: constant \: pressure}\\
+c_{vv} & = & c_{pv}-R_{v} \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Specific \: heat \: of \: water \: vapor \: at \: constant \: volume}\\
+c_{liq} & = & 4190 \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Specific \: heat \: capacity \: of \: water}\\
+c_{ice} & = & 2106 \quad\mathrm{J \: kg^{-1} \: K^{-1}} & \mathrm{ Specific \: heat \: capacity \: of \: ice}\\
+L_{v} & = & 2.5 \times 10^{6} \quad\mathrm{J \: kg^{-1}} & \mathrm{ Latent \: heat \: of \: vaporization}\\
+L_{s} & = & 2.85 \times 10^{6} \quad\mathrm{J \: kg^{-1}} & \mathrm{ Latent \: heat \: of \: sublimation}\\
+L_{f} & = & 3.50 \times 10^{5} \quad\mathrm{J \: kg^{-1}} & \mathrm{ Latent \: heat \: of \: fusion}\\
+\rho_{w} & = & 1.0 \times 10^{3} \quad\mathrm{kg \: m^{-3}} & \mathrm{ Density \: of \: liquid \: water}\\
+\end{array}
+\end{eqnarray*}
+
Modified: trunk/wrfvar/3DVAR_technote/cover.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/cover.tex 2013-05-10 02:52:55 UTC (rev 431)
+++ trunk/wrfvar/3DVAR_technote/cover.tex 2013-05-16 19:09:45 UTC (rev 432)
@@ -6,7 +6,7 @@
\begin{tabular}{lr|l}
&\textsf{NCAR/TN--???+STR}&\hspace{0.5cm}{ }\\
&\textsf{\textbf{NCAR TECHNICAL NOTE}}&\\ \hline
- &February 2007&\\[1cm]
+ &June 2013&\\[1cm]
\multicolumn{2}{l|}
{\LARGE \textsf{\textbf{The WRF Data Assimilation System}}}
&\\ [5pt]
Modified: trunk/wrfvar/3DVAR_technote/description.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/description.tex 2013-05-10 02:52:55 UTC (rev 431)
+++ trunk/wrfvar/3DVAR_technote/description.tex 2013-05-16 19:09:45 UTC (rev 432)
@@ -54,6 +54,7 @@
\setlength{\headsep}{0.5in}
\setlength{\topskip}{0.0in}
\setlength{\footskip}{0.5in}
+\setlength{\tabcolsep}{0.1in}
%
% Include some coding shortcuts
\def \eg{{\emph{e.g.} }}
@@ -91,7 +92,8 @@
%
% appendices
\begin{appendices}
-\include{appena}
+\include{constants}
+\include{tutorial}
\begin{landscape}
\include{namelist}
\include{acronyms}
Modified: trunk/wrfvar/3DVAR_technote/intro.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/intro.tex 2013-05-10 02:52:55 UTC (rev 431)
+++ trunk/wrfvar/3DVAR_technote/intro.tex 2013-05-16 19:09:45 UTC (rev 432)
@@ -1,12 +1,13 @@
\chapter{Introduction}
\label{intro}
-This overview supplements the original description of the three-dimensional variational (3D-Var) algorithm found in \citet{BarkerEA2004}.
+% THIS CAVEAT IS PROBABLY UNNECESSARY, THAT ORIGINAL PAPER IS PRETTY OUTDATED
+% This overview supplements the original description of the three-dimensional variational (3D-Var) system found in \citet{BarkerEA2004}.
-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, together with their relationship with the rest of the WRF system.
+Data assimilation is the technique by which \textbf{observations} are combined with an NWP product (the \textbf{first guess} or background state) 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}). This technical note will only cover the 3DVAR portion of the WRFDA system.
+
\section{Overview of Variational Data Assimilation}
\label{overview}
@@ -28,7 +29,7 @@
As described in \citet{BarkerEA2004}, 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{BarkerEA2004}. A number of recent upgrades to the WRF-Var algorithm will be described in Section \ref{var-upgrade}.
+Figure \ref{wrfda-sketch} illustrates the relationship between WRF-Var, the various datasets, and the other components of a typical NWP system (here ARW).
%
% Figure ?.? WRFDA flowchart
@@ -36,23 +37,25 @@
\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.}
+ \caption{\label{wrfda-sketch}Sketch showing the relationship between various datasets, files, algorithms, and programs of the WRFDA system.}
\end{figure}
-The three inputs to WRF-Var are:
+There are three basic inputs needed for WRFDA--3DVAR, which are described in the following sections.
-\vspace{0.5cm}
+\subsection{Background ${\bf x^{b}}$}
+\label{fg-intro}
+In cold-start mode, the background (first guess) is typically a model output/analysis interpolated to the WRF-ARW grid (and variables) using the WRF Preprocessing System (WPS) and \texttt{real.exe}, WRF's initialization program. In cycling mode, the first guess is a short-range (typically 1--6 hour) ARW forecast.
-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.
+\subsection{Observations ${\bf y^{o}}$}
+\label{obs-intro}
-\vspace{0.5cm}
+WRFDA observations may be supplied in a number of different formats.
-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{BarkerEA2003,BarkerEA2004}.
+either in PREPBUFR format (\texttt{ob\_format=1}) or an ASCII ``little\_r'' format (\textit{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{BarkerEA2003,BarkerEA2004}.
-\vspace{0.5cm}
+\subsection{Background error covariances ${\bf B}$}
-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}.
+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{BarkerEA2003}). 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.
@@ -76,7 +79,7 @@
\subsection{System requirements}
\label{system_requirements}
-WRFDA must be installed on a Unix-based (such as Mac OS X) or Linux-based operating system; installation with Windows or other platforms is not supported. WRFDA\textendash3DVAR requires at least INSERT FIGURE HERE GB of disk spaceup to 1.5 GB of disk space depending on the configuration. We recommend at least 2GB of RAM as well.
+WRFDA must be installed on a Unix-based (such as Mac OS X) or Linux-based operating system; installation with Windows or other platforms is not supported. WRFDA--3DVAR requires at least INSERT FIGURE HERE GB of disk spaceup to 1.5 GB of disk space depending on the configuration. We recommend at least 2GB of RAM as well.
\subsubsection{Compilers}
\label{compilers}
@@ -136,7 +139,7 @@
WRF was developed based on the non-hydrostatic Fifth-Generation NCAR / Penn State Mesoscale Model (MM5), which was the fifth generation of a mesoscale model originally developed at Pennsylvania State University (Penn State) starting in 1971 \citep{Anthes_Warner1978,AnthesEA1987}. In 1984, additional resources were provided by the NCAR Acid Deposition Modeling Project\footnote{This project was moved to the Atmospheric Sciences Research Center (ASRC) of the State University of New York (SUNY) at Albany in 1987 \citep{ChangEA1990}} (ADMP), allowing for the accelerated development of the model and the eventual release of the Fourth-Generation NCAR / Penn State Mesoscale Model (MM4) in 1987 \citep{Hsie1987}. The model and its related pre- and post-processing tools underwent constant improvements throughout its existence \citep{Gill1992},
-The MM5 3D-VAR system was developed starting in early 2000 \citep{TempBarker1999}. While MM5 had a functional 4D-VAR system prior to this\textemdash indeed it had been developed and utilized in various forms since the early days of the model in the 1970s \citep{GrellEA1994}\textemdash it was proprietary and not user-friendly or portable. The MM5 3D-VAR system was built with the goal of making it efficient and stable enough for operational implementation, while remaining robust enough for research applications \citep{BarkerEA2003}. It was also built with a framework such that 4D-VAR could easily be implemented by building on the existing system. In addition, because it was developed at the same time as the WRF model, it was decided early on that the MM5 3D-VAR system should be useable as/within a prototype WRF 3DVAR system. This was important to the future development of WRFDA, reducing wasted effort on developing two independent systems.
+The MM5 3D-VAR system was developed starting in early 2000 \citep{TempBarker1999}. While MM5 had a functional 4D-VAR system prior to this---indeed it had been developed and utilized in various forms since the early days of the model in the 1970s \citep{GrellEA1994}---it was proprietary and not user-friendly or portable. The MM5 3D-VAR system was built with the goal of making it efficient and stable enough for operational implementation, while remaining robust enough for research applications \citep{BarkerEA2003}. It was also built with a framework such that 4D-VAR could easily be implemented by building on the existing system. In addition, because it was developed at the same time as the WRF model, it was decided early on that the MM5 3D-VAR system should be useable as/within a prototype WRF 3DVAR system. This was important to the future development of WRFDA, reducing wasted effort on developing two independent systems.
\subsection{WRF Data Assimilation}
\label{history-wrfda}
Modified: trunk/wrfvar/3DVAR_technote/namelist.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/namelist.tex 2013-05-10 02:52:55 UTC (rev 431)
+++ trunk/wrfvar/3DVAR_technote/namelist.tex 2013-05-16 19:09:45 UTC (rev 432)
@@ -4,7 +4,7 @@
\section{Description of namelist variables}
\label{namelist_variables}
-Options highlighted in gray (\colorbox{light-gray}{like this}) are not recommended, as they are either obsolete or for debugging purposes only.
+\textbf{Options highlighted in gray (\colorbox{light-gray}{like this}) are not recommended, as they are either obsolete or for debugging purposes only.}
%\begin{tabular}[t]{lllp{5cm}}
\begin{longtabu} to \linewidth {p{4cm}lp{1cm}p{3cm}p{13cm}}
Modified: trunk/wrfvar/3DVAR_technote/quickstart.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/quickstart.tex 2013-05-10 02:52:55 UTC (rev 431)
+++ trunk/wrfvar/3DVAR_technote/quickstart.tex 2013-05-16 19:09:45 UTC (rev 432)
@@ -4,15 +4,17 @@
This opening section will serve as a guide for users who do not care about the specific details of the WRFDA\textendash3DVAR system or data assimilation in general, but just wish to get the system up and running. WRFDA must be compiled on a Unix- or Linux-based system which has a Fortran and C compiler, as well as at least 2GB of disk space and 2GB of RAM. For a full list of system prerequisites, see the ``System Requirements'' section (\ref{system_requirements}).
-\textit{\textbf{Important note:} the example commands in this quick-start guide assume a csh or tcsh shell, using \texttt{vi} as a text editor. If you use different settings you will have to change these commands appropriately.}
+In this guide, lines in fixed-width font and preceded by a ``>'' symbol (\texttt{> like this}) indicate commands to be entered to your terminal.
+\textit{\textbf{Important note:} the example commands in this quick-start guide assume a csh or tcsh shell, using} \texttt{vi} \textit{as a text editor. If you use different settings you will have to change these commands appropriately.}
+
\section*{Installing WRFDA}
\label{quick-install}
-\subsubsection*{Obtaining the WRFDA source code and test data}
+\subsection*{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. It is also strongly recommended that users download the WRFDA test data set, available at \url{http://www.mmm.ucar.edu/wrf/users/wrfda/download/testdata.html}. This test data set will be referenced as an example throughout this quick-start guide, and contains three directories: \texttt{ob} (observation files), \texttt{be} (background error files), and \texttt{rc} (first guess and boundary condition files). For more information about this tutorial case, see the ``Tutorial Case'' section (\ref{tutorial-case}).
+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. It is also strongly recommended that users download the WRFDA test data set, available at \url{http://www.mmm.ucar.edu/wrf/users/wrfda/download/testdata.html}. This test data set will be referenced as an example throughout this quick-start guide, and contains three directories: \texttt{ob} (observation files), \texttt{be} (background error files), and \texttt{rc} (first guess and boundary condition files). For more information about this tutorial case, see Appendix \ref{tutorial-case}, ``Tutorial Case''.
You should unpack the WRFDA and test data packages in the same directory, then set this directory as the environment variable \texttt{\$WRFDA\_DIR} (this is not required, but will make the instructions in this quick-start guide easy to follow):
@@ -29,18 +31,18 @@
> setenv WRFDA_DIR `pwd`
\end{verbatim}
-\subsubsection*{Setting your system environment}
+\subsection*{Setting your system environment}
\label{quick-env}
-Before starting the configuration process, you should set some necessary environment variables so that the proper libraries will be used and/or built. The only necessary library for assimilating basic observations with WRFDA is the netCDF library. WRFDA will attempt to automatically find your netCDF build, but to make the compilation process go smoothly you should set an environment variable to indicate where your netCDF library is installed:
+Before starting the configuration process, you should set some necessary environment variables so that the proper libraries will be used and/or built. The only required library for all uses of WRFDA is the netCDF library. WRFDA will attempt to automatically find your netCDF build, but to make the compilation process go smoothly you should set an environment variable to indicate where your netCDF library is installed:
\begin{verbatim}
> setenv NETCDF your_netcdf_path
\end{verbatim}
-where ``\texttt{your\_netcdf\_path}'' is the directory containing the netCDF ``\texttt{lib}'' directory. For additional details, see the section ``netCDF'' (\ref{netcdf}).
+where ``\texttt{your\_netcdf\_path}'' is the directory containing the netCDF \texttt{lib} directory. For additional details, see the Section \ref{netcdf}, ``netCDF''.
-If you intend to use BUFR- or PREPBUFR-formatted observations, set the environment variable ``BUFR'' (additional details can be found in the section ``BUFR and PREPBUFR'' (\ref{bufr-intro}):
+If you intend to use BUFR- or PREPBUFR-formatted observations, set the environment variable ``BUFR'' (additional details can be found in Section \ref{bufr-intro}, ``BUFR and PREPBUFR''):
\begin{verbatim}
> setenv BUFR 1
@@ -52,9 +54,9 @@
> setenv CRTM 1
\end{verbatim}
-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}).
+It is also possible to use RTTOV, which is a different RTM maintained by EUMETSAT. For this and other details about RTMs see Section \ref{RTM}, ``Radiative Transfer Models''.
-\subsubsection*{Configure your installation for your machine}
+\subsection*{Configure your installation for your machine}
\label{quick-config}
Enter the \texttt{WRFDA} directory and run the configure script:
@@ -64,9 +66,11 @@
> ./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.
+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, \textbf{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, \textbf{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}
+MENTION HERE WHAT THE CONFIGURE SCRIPT WILL SAY IF SUCCESSFUL
+
+\subsection*{Compile WRFDA}
\label{quick-compile}
To compile WRFDA, run the following command:
@@ -75,20 +79,20 @@
> ./compile all_wrfvar >& compile.out
\end{verbatim}
-To check for successful compilation, run the command:
+To check for successful compilation, check to see that all executables have been created:
\begin{verbatim}
>ls -l var/build/*exe var/obsproc/src/obsproc.exe
\end{verbatim}
-If the compilation was successful, this should list 44 executables. The main WRFDA executable is \texttt{da\_wrfvar.exe}; ensure this has been created before continuing.
+If the compilation was successful, the above command should list 44 executables. If any are missing, check to make sure you have selected an appropriate configuration option.
%%OBSPROC COMMENTED OUT FOR NOW; NOT SURE IF IT SHOULD BE COVERED IN QUICKSTART GUIDE
\begin{comment}
\section*{Running OBSPROC to format conventional observations}
\label{quick-obsproc}
-The OBSPROC program reads observations in LITTLE\_R format\textemdash a text-based format in use since the MM5 era\textemdash which can be read by WRFDA. Conventional observations must be processed by OBSPROC before being used in WRFDA, though PREPBUFR, radiance, and radar data \textit{are not} processed by OBSPROC. For further details about OBSPROC and LITTLE\_R format, see the section ``Observation Preprocessing'' (\ref{obsproc}).
+The OBSPROC program reads observations in LITTLE\_R format---a text-based format in use since the MM5 era---which can be read by WRFDA. Conventional observations must be processed by OBSPROC before being used in WRFDA, though PREPBUFR, radiance, and radar data \textit{are not} processed by OBSPROC. For further details about OBSPROC and LITTLE\_R format, see the section ``Observation Preprocessing'' (\ref{obsproc}).
OBSPROC requires at least 3 files to run successfully:
\begin{itemize}
@@ -114,20 +118,19 @@
\end{comment}
-\section*{Running WRFDA}
-\label{quick-run}
+\section*{Preparing input files}
+\label{quick-input}
-The standard input format for WRFDA is a record-based ASCII format produced by OBSPROC, the WRFDA Observation Preprocessor. Information on using OBSPROC can be found in the ``Observation Preprocessing'' section (\ref{obsproc}). Other data formats are allowed however, including observations in PREPBUFR format (see \ref{prepbufr}), radiance observations in BUFR format (see \ref{bufr}), and radar data in a different text-based format (see \ref{radar}). Some of these sets of observations can be assimilated concurrently (ASCII and PREPBUFR are mutually exclusive).
+The standard input format for WRFDA is a record-based ASCII format produced by OBSPROC, the WRFDA Observation Preprocessor. Information on using OBSPROC can be found in the ``Observation Preprocessing'' section (\ref{obsproc}). Other data formats are allowed however, including observations in PREPBUFR format (Section \ref{prepbufr}), radiance observations in BUFR format (Section \ref{radiance}), and radar data in a different text-based format (Chapter \ref{radar}). Some of these sets of observations can be assimilated concurrently, but \textbf{ASCII and PREPBUFR are mutually exclusive}.
-\section*{ASCII formatted observations}
-\label{quick-littler}
+\subsection*{ASCII-formatted observations}
+\label{quick-ascii}
-WRFDA requires several files to run with conventional data in OBSPROC format:
+WRFDA requires several files to run with data in OBSPROC format:
\begin{table}[h]
\begin{center}
-\vspace*{2mm}
\caption{
-Required files for assimilation in conventional OBSPROC format
+Required files for assimilation in text-based OBSPROC format
}
\label{tab:req-files-conv}
\vspace*{3mm}
@@ -137,7 +140,7 @@
First Guess & \texttt{fg} & netCDF & \textit{or} \\
& & & WRF Forecast \\
\hline Observations & \texttt{ob.ascii} & ASCII & OBSPROC \\
-\hline & & & WRFDA\textendash GEN\_BE utility (CV5) \\
+\hline & & & WRFDA--GEN\_BE utility (CV5) \\
Background Error & \texttt{be.dat} & Binary & \textit{or} \\
& & & Included in WRFDA package (CV3) \\
\hline Land Use Table & \texttt{LANDUSE.TBL} & ASCII & Included in WRFDA package \\
@@ -161,11 +164,108 @@
> cp $WRFDA_DIR/WRFDA/var/test/tutorial/namelist.input .
> ln -sf $WRFDA_DIR/var/run/LANDUSE.TBL .
> ln -sf $WRFDA_DIR/rc/2008020512/wrfinput_d01 ./fg
- > ln -sf $WRFDA_DIR/WRFDA/var/obsproc/obs_gts_2008-02-05_12:00:00.3DVAR ./ob.ascii
+ > ln -sf $WRFDA_DIR/ob/2008020512/obs_gts_2008-02-05_12:00:00.3DVAR ./ob.ascii
> ln -sf $WRFDA_DIR/be/be.dat .
> ln -sf $WRFDA_DIR/WRFDA/var/da/da_wrfvar.exe .
\end{verbatim}
-You should examine the \texttt{namelist.input} file and get acquainted with the available options. It should already be set up to run the tutorial case, but to run any other case you will likely have to change several values, especially those listed under \texttt{\&wrfvar18}, \texttt{\&wrfvar21}, \texttt{\&wrfvar22}, \texttt{\&time\_control}, and \texttt{\&domains}. The options included in the sample namelist are only a small fraction of those available: further information can be found in the ``Running WRFDA\textendash 3DVAR'' section (\ref{running}) as well as the namelist appendix (\ref{namelist}).
+You should examine the \texttt{namelist.input} file and get acquainted with the available options. It should already be set up to run the tutorial case, but to run any other case you will likely have to change several values, especially those listed under \texttt{\&wrfvar18}, \texttt{\&wrfvar21}, \texttt{\&wrfvar22}, \texttt{\&time\_control}, and \texttt{\&domains}. The options included in the sample namelist are only a small fraction of those available: further information can be found in the ``Running WRFDA--3DVAR'' section (\ref{running}) as well as Appendix \ref{namelist}, ``WRFDA namelist''.
-You should now be ready to run WRFDA\textendash 3DVAR. It is useful to
\ No newline at end of file
+\subsection*{PREPBUFR-formatted observations}
+\label{quick-prepbufr}
+
+WRFDA requires several files to run with data in PREPBUFR format:
+\begin{table}[h]
+\begin{center}
+\caption{
+Required files for assimilation in PREPBUFR format
+}
+\label{tab:req-files-conv}
+\vspace*{3mm}
+\begin{tabular}{|l|l|l|l|}
+\hline \textbf{Input file} & \textbf{File name} & \textbf{Format} & \textbf{Source} \\
+\hline & & & WRF Preprocessing System (WPS) and \texttt{real.exe} \\
+ First Guess & \texttt{fg} & netCDF & \textit{or} \\
+ & & & WRF Forecast \\
+\hline & & & OBSPROC \\
+ Observations & \texttt{ob.bufr} & PREPBUFR & \textit{or} \\
+ & & & Other source (see ``PREPBUFR'' section, \ref{prepbufr}) \\
+\hline & & & WRFDA--GEN\_BE utility (CV5) \\
+ Background Error & \texttt{be.dat} & Binary & \textit{or} \\
+ & & & Included in WRFDA package (CV3) \\
+\hline Land Use Table & \texttt{LANDUSE.TBL} & ASCII & Included in WRFDA package \\
+\hline WRFDA namelist & \texttt{namelist.input} & ASCII & Included in WRFDA package \\
+\hline
+\end{tabular}
+\end{center}
+\vspace*{-5mm}
+\end{table}
+
+To organize these files properly, create a new directory which will serve as your WRFDA working directory:
+
+\begin{verbatim}
+ > mkdir $WRFDA_DIR/workdir
+ > cd $WRFDA_DIR/workdir
+\end{verbatim}
+
+Next, run the following commands to copy/link all the necessary files:
+
+\begin{verbatim}
+ > cp $WRFDA_DIR/WRFDA/var/test/tutorial/namelist.input .
+ > ln -sf $WRFDA_DIR/var/run/LANDUSE.TBL .
+ > ln -sf $WRFDA_DIR/rc/2008020512/wrfinput_d01 ./fg
+ > ln -sf $WRFDA_DIR/ob/2008020512/ob.bufr .
+ > ln -sf $WRFDA_DIR/be/be.dat .
+ > ln -sf $WRFDA_DIR/WRFDA/var/da/da_wrfvar.exe .
+\end{verbatim}
+
+You should examine the \texttt{namelist.input} file and get acquainted with the available options. It should already be set up to run the tutorial case, but to run any other case you will likely have to change several values, especially those listed under \texttt{\&wrfvar18}, \texttt{\&wrfvar21}, \texttt{\&wrfvar22}, \texttt{\&time\_control}, and \texttt{\&domains}. The options included in the sample namelist are only a small fraction of those available: further information can be found in the ``Running WRFDA--3DVAR'' section (\ref{running}) as well as Appendix \ref{namelist}, ``WRFDA namelist''.
+
+\section*{Running WRFDA--3DVAR}
+\label{quick-run}
+
+You should now be ready to run WRFDA--3DVAR. Depending on whether you compiled to run in parallel (dmpar) or serial, the command to run WRFDA will be different:
+
+\begin{center}
+\begin{tabu} to \linewidth {p{3.3in}p{3.3in}}
+ \large{\textbf{For a serial run}} & \large{\textbf{For parallel run}} \\[1pt]
+ \texttt{./da\_wrfvar.exe > \& wrfda.log} & \texttt{mpirun -np 4 da\_wrfvar.exe} \\[1pt]
+ In a serial run, you just need to run the main executable directly, \texttt{da\_wrfvar.exe}. However, it is useful to redirect the output messages to a log file for later review, which is what the ``\texttt{> \& wrfda.log}'' portion of the command does. This output will contain information about the observations being assimilated, the minimization process, and any errors reported. &
+ In a parallel run, you must invoke MPI (Message Passing Interface) to run WRFDA; for most platforms this is done with the \texttt{mpirun} command. See the ``Parallelization'' section (\ref{parallelization}) for more information. \\
+ \end{tabu}
+\end{center}
+
+\section*{Output files}
+\label{quick-output}
+
+\begin{table}[h]
+\begin{center}
+\caption{
+Files created by a successful WRFDA--3DVAR run
+}
+\label{tab:req-files-conv}
+\vspace*{3mm}
+\begin{tabu} to \linewidth {|l|l|p{4in}|}
+\hline \textbf{Output file} & \textbf{Format} & \textbf{Description} \\
+\hline \texttt{namelist.output.da} & ASCII & All namelist values used in the run, including defaults from the Registry for those values
+ not specified by the user \\
+\hline \texttt{rsl.out.\#\#\#\#} & ASCII & Parallel runs only; will contain information about observations assimilated and the
+ minimization process (one file for each processor)\\
+\hline \texttt{rsl.error.\#\#\#\#} & ASCII & Parallel runs only; will contain information about any errors encountered (one file for
+ each processor\\
+\hline \texttt{wrfvar\_output} & netCDF & The analysis created by the assimilation process \\
+\hline
+\end{tabu}
+\end{center}
+\vspace*{-5mm}
+\end{table}
+
+The output from your WRFDA run will appear in rsl.out.* and rsl.error.* files, ending in a 4-digit number starting with ``0000''. There will be one \texttt{rsl.out.*} file (containing normal runtime messages) and one \texttt{rsl.error} file (containing information about any errors encountered) file for each processor used.
+
+The rest of this technical note contains a large amount of further information about the steps listed above, in addition to other useful features not covered in this quick guide. Among other subjects, the rest of this guide covers:
+
+\begin{itemize}
+ \item Using alternative background error options, including customizing it to your own case (Chapter \ref{be}, ``Background Error'')
+ \item Using WRFDA to initialize a WRF forecast
+ \item Cycling mode (Section \ref{cycling}, ``Cycling'')
+\end{itemize}
Modified: trunk/wrfvar/3DVAR_technote/radar.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/radar.tex 2013-05-10 02:52:55 UTC (rev 431)
+++ trunk/wrfvar/3DVAR_technote/radar.tex 2013-05-16 19:09:45 UTC (rev 432)
@@ -1,201 +1,62 @@
\chapter{Radar Data Assimilation}
\label{radar}
-A Doppler radar data assimilation scheme was developed within
-WRF-Var (3D-Var system). The dynamic balance between atmospheric wind
-and thermodynamic fields, based on Richardsons equation, is introduced
-to the 3D-Var system. Vertical velocity ($w$) increments are produced to
-enable the assimilation of vertical velocity component of Doppler radial
-velocity observation. In order to assimilate radar reflectivity data,
-the model total water mixing ratio is used as a control variable, and
-a warm rain process, its linear, and its adjoint are
-incorporated into the system to partition the moisture and hydrometeor
-increments. The observation operators for Doppler radial velocity and
-radar reflectivity are developed and implemented within the 3D-Var system.
-Numerical experiments indicate that the WRF-Var (3D-Var) system can
-successfully extract useful informations from multiple radar data at
-different times (via cycling) and different locations for initiation of
-mesoscale weather systems, such as squll lines, fronts, and hurricanes.
-
+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 Richardson 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.
+
+\section{Details}
+A Doppler radar data assimilation scheme was developed within WRF-Var (3D-Var system). The dynamic balance between atmospheric wind and thermodynamic fields, based on Richardson's equation, is introduced to the 3D-Var system. Vertical velocity ($w$) increments are produced to enable the assimilation of vertical velocity component of Doppler radial velocity observation. In order to assimilate radar reflectivity data, the model total water mixing ratio is used as a control variable, and a warm rain process, its linear, and its adjoint are incorporated into the system to partition the moisture and hydrometeor increments. The observation operators for Doppler radial velocity and radar reflectivity are developed and implemented within the 3D-Var system. Numerical experiments indicate that the WRF-Var (3D-Var) system can successfully extract useful information from multiple radar data at different times (via cycling) and different locations for initiation of mesoscale weather syst
ems, such as squall lines, fronts, and hurricanes.
+
\section{Introduction}
\label{radar-intro}
-Doppler radar observation is an important data source for mesoscale and
-microscale weather analysis and forecasting. Early work on Doppler radar
-data analysis mainly focused on two aspects: one is rainfall analysis
-using radar reflectivity via Z-R relation \citep{jorgenson82,fujiyoshi90},
-and the other is synthesis of two independent
-Doppler velocities \citep{ray80,ray81}. Techniques to estimate
-the velocity field by objectively determining the motion of radar echo
-patterns have also received much attention \citep{tuttle90}.
-In recent years, assimilation of Doppler radar data for short-term
-numerical weather forecasting or nowcasting has become a focal point of
-research \citep{sun01,weygandt02a,weygandt02b}.
+Doppler radar observation is an important data source for mesoscale and microscale weather analysis and forecasting. Early work on Doppler radar data analysis mainly focused on two aspects: one is rainfall analysis using radar reflectivity via Z-R relation \citep{jorgenson82,fujiyoshi90}, and the other is synthesis of two independent Doppler velocities \citep{ray80,ray81}. Techniques to estimate the velocity field by objectively determining the motion of radar echo patterns have also received much attention \citep{tuttle90}. In recent years, assimilation of Doppler radar data for short-term
+numerical weather forecasting or nowcasting has become a focal point of research \citep{sun01,weygandt02a,weygandt02b}.
-There are several technical and scientific challenges in Doppler radar
-data assimilation. First of all, the radar data are normally at the
-resolution of one km or higher. Yet, at the current stage, most
-operational or even research models have much lower resolutions than
-radar data. A technique of data thinning (with the radar observations
-at reduced resolution, compatible with the analysis system) has to be
-developed. Secondly, data quality control is a very important step
-before radar data are assimilated into WRF-Var analysis. Some undesired
-radar artifacts, such as ground clutter and anomalously
-propagated (AP) clutter, sea clutter, range folding, velocity folding,
-and other noise have to be removed or corrected. These errors are
-embedded in the normal weather returns, so properly recovering or
-removing them is essential to the success of the data assimilation.
-Thirdly, the error variance of the Doppler radar data needs to be
-determined and specified in order to assimilate the radar data
-observations effectively, together with other sources of information.
+There are several technical and scientific challenges in Doppler radar data assimilation. First of all, the radar data are normally at the resolution of one km or higher. Yet, at the current stage, most operational or even research models have much lower resolutions than radar data. A technique of data thinning (with the radar observations at reduced resolution, compatible with the analysis system) has to be developed. Secondly, data quality control is a very important step before radar data are assimilated into WRF-Var analysis. Some undesired radar artifacts, such as ground clutter and anomalously propagated (AP) clutter, sea clutter, range folding, velocity folding, and other noise have to be removed or corrected. These errors are
+embedded in the normal weather returns, so properly recovering or removing them is essential to the success of the data assimilation. Thirdly, the error variance of the Doppler radar data needs to be determined and specified in order to assimilate the radar data observations effectively, together with other sources of information.
-Although there are challenges, radar data assimilation could be
-very promising for short-range numerical weather prediction.
-To assimilate Doppler radial velocities, the WRF 3D-Var has been included
-vertical velocity ($w$) increments \citep{xiao05}. This is important
-when radar data are included in the analysis and for small-scale
-convective weather systems. Mixing ratios of cloud water ($q_c$) and
-rainwater ($q_r$) are included in the background fields. When 3D-Var
-system is run in cycling mode, passing $q_c$ and $q_r$ to the next cycle can
-alleviate the spin-up problems for the subsequent forecast.
-For radar reflectivity assimilation, the inclusion of the analyses
-(increments) of rainwater and cloud water mixing ratios in the
-3D-Var system is vital \citep{xiao07}. In the continuous
-cycling mode, 3D-Var assimilation of radar reflectivity data can
-produce relatively rational analyses of the hydrometeor fields.
-A case study for Typhoon Rusa (2002) in East Asia showed very
-positive impact of the Doppler radar data assimilation.
-Although 3D-Var without radar data could improve the typhoon forecast
-\citep{gu05,xiao06}, inclusion of Doppler radar data further improved
-the forecast of the typhoon track and intensity \citep{xiao07}.
+Although there are challenges, radar data assimilation could be very promising for short-range numerical weather prediction. To assimilate Doppler radial velocities, the WRF 3D-Var has been included vertical velocity ($w$) increments \citep{xiao05}. This is important when radar data are included in the analysis and for small-scale convective weather systems. Mixing ratios of cloud water ($q_c$) and rainwater ($q_r$) are included in the background fields. When 3D-Var system is run in cycling mode, passing $q_c$ and $q_r$ to the next cycle can alleviate the spin-up problems for the subsequent forecast. For radar reflectivity assimilation, the inclusion of the analyses (increments) of rainwater and cloud water mixing ratios in the 3D-Var system is vital \citep{xiao07}. In the continuous cycling mode, 3D-Var assimilation of radar reflectivity data can produce relatively rational analyses of the hydrometeor fields. A case study for Typhoon Rusa (2002) in East Asia showed very pos
itive impact of the Doppler radar data assimilation. Although 3D-Var without radar data could improve the typhoon forecast \citep{gu05,xiao06}, inclusion of Doppler radar data further improved the forecast of the typhoon track and intensity \citep{xiao07}.
-A significant advantage of 3D-Var is its greater computational
-efficiency than other assimilation techniques (e.g. 4D-Var or
-ensemble Kalman filter). This makes 3D-Var more feasible in real-time
-or operational forecasting. In this chapter, we will
-briefly introduce the radar data preprocessing
-procedure, including data quality control, data thinning, and a
-simple observation error statistics in Section \ref{radar-prep}.
-The description of the preprocessing is in conceptual
-level, and the users should have their
-own preprocessing of the radar data before assimilation. However, we
-will present details of the techniques for Doppler radar data
-assimilation. The assimilation of Doppler radial vedlocity will be
-described in Section \ref{radar_rv}, and that of reflectivity will
-be in Section \ref{radar_rf}.
+A significant advantage of 3D-Var is its greater computational efficiency than other assimilation techniques (e.g. 4D-Var or ensemble Kalman filter). This makes 3D-Var more feasible in real-time or operational forecasting. In this chapter, we will briefly introduce the radar data preprocessing procedure, including data quality control, data thinning, and a simple observation error statistics in Section \ref{radar-prep}. The description of the preprocessing is in conceptual level, and the users should have their own preprocessing of the radar data before assimilation. However, we will present details of the techniques for Doppler radar data assimilation. The assimilation of Doppler radial velocity will be described in Section \ref{radar_rv}, and that of reflectivity will be in Section \ref{radar_rf}.
\section{Preprocessing of Doppler Radar Data}
\label{radar-prep}
-The raw Doppler radar data require to be processed before they
-can be assimilated in WRF-Var analysis. The main steps include data
-quality control, data thinning, and estimating radar
-observation errors.
+The raw Doppler radar data require to be processed before they can be assimilated in WRF-Var analysis. The main steps include data quality control, data thinning, and estimating radar observation errors.
\subsection{Quality control of Doppler radar data}
-There are several commonly seen non-meteorological returns in
-the raw radar data, including ground clutter, anomalously-propagated
-ground clutter, second trip echo, sea clutter and other noise.
-We should conduct quality control using manual editting or automatic
-software. For example, the radar data can be interactively edited
-using NCAR SOLO software \citep{oye95} to conduct the data
-quality control. Each scan was carefully examined in order to
-identify unwanted radar echoes. These unwanted echoes were either
-recovered (e.g., velocity folding) or removed
-(all other unwanted returns).
+There are several commonly seen non-meteorological returns in the raw radar data, including ground clutter, anomalously-propagated ground clutter, second trip echo, sea clutter and other noise. We should conduct quality control using manual editing or automatic software. For example, the radar data can be interactively edited using NCAR SOLO software \citep{oye95} to conduct the data quality control. Each scan was carefully examined in order to identify unwanted radar echoes. These unwanted echoes were either recovered (e.g., velocity folding) or removed (all other unwanted returns).
-Data quality control is an important step in data assimilation.
-Too many bad-quality data could ruin the 3D-Var analyses.
-Without removal of the unwanted radar data, the minimization of
-the 3D-Var system does not converge well, or the analysis is wired
-even it converges. Information from the bad-quality data entered
-the 3D-Var minimization, which could make it fail to converge
-or produce large analysis departure from other good observations.
-In the operational environment, an objective approach for
-Doppler radar data quality control is necessary.
+Data quality control is an important step in data assimilation. Too many bad-quality data could ruin the 3D-Var analyses. Without removal of the unwanted radar data, the minimization of the 3D-Var system does not converge well, or the analysis is wired even it converges. Information from the bad-quality data entered the 3D-Var minimization, which could make it fail to converge or produce large analysis departure from other good observations. In the operational environment, an objective approach for Doppler radar data quality control is necessary.
\subsection{Data thinning or super-observations}
-Radar data are sampled on radar spherical coordinates (range,
-azimuth, and elevation) with a resolution much higher than
-the numerical model. A strategy for data thinning or super-observations
-should be developed to process the data to a
-regular grid at a resolution compatible with the analysis system.
-For example, the radar data can be mapped to the Cartesian grids
-with the same map projection as the model before being injected into
-the 3D-Var system. This reduces redundant data (especially near
-the radar site) and high frequency features that cannot be resolved by
-the numerical model.
+Radar data are sampled on radar spherical coordinates (range, azimuth, and elevation) with a resolution much higher than the numerical model. A strategy for data thinning or super-observations should be developed to process the data to a regular grid at a resolution compatible with the analysis system. For example, the radar data can be mapped to the Cartesian grids with the same map projection as the model before being injected into the 3D-Var system. This reduces redundant data (especially near the radar site) and high frequency features that cannot be resolved by the numerical model.
-The thinning of radar data can be performed using NCARs software
-SPRINT (Sorted Position Radar INTerpolation) and CEDRIC (Custom
-Editing and Display of Reduced Information in Cartesian space)
-developed by \citet{mohr79} and \citet{mohr81}. Data for each
-Cartesian grid are interpolated using the surrounding eight points
-from the four beams (two on either side, above and below). Each
-volume data are put at the same time. To get rid of grid data that
-might be affected by noise during the interpolation, a local standard
-deviation of the eight points used in the interpolation is
-calculated and the radial velocity data with standard deviation
-greater than 14 m/s are removed (The threshold of 14 m/s is chosen
-because the radial velocity histogram dips at 14 m/s). Spatial
-data filtering (with the influence radius of 2km) is performed
-for the grid radar data to remove small-sale features that cannot
-be represented in the model analyses.
+The thinning of radar data can be performed using NCAR's software SPRINT (Sorted Position Radar INTerpolation) and CEDRIC (Custom Editing and Display of Reduced Information in Cartesian space) developed by \citet{mohr79} and \citet{mohr81}. Data for each Cartesian grid are interpolated using the surrounding eight points from the four beams (two on either side, above and below). Each volume data are put at the same time. To get rid of grid data that might be affected by noise during the interpolation, a local standard deviation of the eight points used in the interpolation is calculated and the radial velocity data with standard deviation greater than 14 m/s are removed (The threshold of 14 m/s is chosen because the radial velocity histogram dips at 14 m/s). Spatial data filtering (with the influence radius of 2km) is performed for the grid radar data to remove small-sale features that cannot be represented in the model analyses.
\subsection{Estimate of the radar observation errors}
-If the NCAR software SPRINT is used, the standard deviation calculated
-in SPRINT during the interpolation can be used as the observation errors.
-Since the four adjacent data points each representing a pulse volume
-are used to perform the interpolation, the standard deviation
-computed in SPRINT represents the radial velocity errors in m/s.
-The horizontal distribution of the standard deviation represents
-the error structure. However, larger values are sometimes found due
-to some voids of the raw radar data. Empirical rescaling of the
-calculated errors is usually necessary before the error statistics
-are used in 3D-Var. The Gaussian distribution of the errors is
-assumed at each level during rescaling. We believe data
-thinning is necessary, which can results in more benefit even
-the spatial error correlations are neglected. After the thinned
-observations and related errors are calculated, they are converted
-to 3D-Var input format.
+If the NCAR software SPRINT is used, the standard deviation calculated in SPRINT during the interpolation can be used as the observation errors. Since the four adjacent data points each representing a pulse volume are used to perform the interpolation, the standard deviation computed in SPRINT represents the radial velocity errors in m/s. The horizontal distribution of the standard deviation represents the error structure. However, larger values are sometimes found due to some voids of the raw radar data. Empirical rescaling of the calculated errors is usually necessary before the error statistics are used in 3D-Var. The Gaussian distribution of the errors is assumed at each level during rescaling. We believe data thinning is necessary, which can results in more benefit even the spatial error correlations are neglected. After the thinned observations and related errors are calculated, they are converted to 3D-Var input format.
\section{Assimilation of Doppler Radial Velocities}
\label{radar_rv}
-The configuration of the WRF 3D-Var system is based on a multivariate
-incremental formulation \citep{courtier94}. The preconditioned
-control variables are described in Chapter 2. For radail velocity
-assimilation, we added a new balance equation, the Richardson's
-equation, for generating the vertical velocity increments \citep{xiao05}.
-
+The configuration of the WRF 3D-Var system is based on a multivariate incremental formulation \citep{courtier94}. The preconditioned control variables are described in Chapter 2. For radail velocity assimilation, we added a new balance equation, the Richardson's equation, for generating the vertical velocity increments \citep{xiao05}.
+
\subsection{Vertical velocity increments}
-In order to include a capability to assimilate the vertical component of
-Doppler radial velocity data, the WRF 3D-Var includes vertical velocity
-increments. Based on \citet{richardson22} and \citet{white00}, a balance
-equation that combines the continuity equation, adiabatic
-thermodynamic equation, and hydrostatic relation is derived. Details of
-the derivation can be found in \citet{xiao05}.
+In order to include a capability to assimilate the vertical component of Doppler radial velocity data, the WRF 3D-Var includes vertical velocity increments. Based on \citet{richardson22} and \citet{white00}, a balance equation that combines the continuity equation, adiabatic thermodynamic equation, and hydrostatic relation is derived. Details of the derivation can be found in \citet{xiao05}.
\begin{equation}
-{\gamma p} {\partial w \over \partial z} =
+{\gamma p} {\partial w \over \partial z} =
-\gamma p {\bf </font>
<font color="black">abla \cdot V_h} - {V_h \cdot </font>
<font color="black">abla} p +
g \int _z ^\infty {\bf </font>
<font color="red">abla \cdot (\rho {\bf v_h})dz}
\label{richdson_b}
\end{equation}
-</font>
<font color="red">oindent where $w$ is vertical velocity, $\bf V_h$ is the vector of horizontal
-velocity (components $u$ and $v$), $\gamma$ the ratio of specific
-heat capacities of air at constant pressure/volume, $p$ pressure,
-$\rho$ density, $T$ temperature, $c_p$ specific heat capacity of air
-at constant pressure, $z$ height, and $g$ the acceleration due to
-gravity. For simplicity, hereafter Eq. (\ref{richdson_b}) will be referred to as
-Richardsons equation. Linearizing Eq. (\ref{richdson_b}) by writing each variable
-in terms of a basic state (overbar) plus a small increment (prime)
-gives
+</font>
<font color="gray">oindent where $w$ is vertical velocity, $\bf V_h$ is the vector of horizontal velocity (components $u$ and $v$), $\gamma$ the ratio of specific heat capacities of air at constant pressure/volume, $p$ pressure, $\rho$ density, $T$ temperature, $c_p$ specific heat capacity of air at constant pressure, $z$ height, and $g$ the acceleration due to gravity. For simplicity, hereafter Eq. (\ref{richdson_b}) will be referred to as Richardson's equation. Linearizing Eq. (\ref{richdson_b}) by writing each variable in terms of a basic state (overbar) plus a small increment (prime) gives
\begin{eqnarray}
&{\gamma \overline p} {\partial w' \over \partial z} =
@@ -209,58 +70,21 @@
\label{r_l}
\end{eqnarray}
-The basic state (overbar) variables satisfy Eq. (\ref{richdson_b}). They also
-satisfy the continuity equation, adiabatic equation and hydrostatic
-equation. The linear Richardson's equation (\ref{r_l})
-is discretized, and its adjoint code
-is developed according to the code of the linearized equation. The
-correctness of the adjoint check following the method proposed by
-\citet{navon92} is verified.
+The basic state (overbar) variables satisfy Eq. (\ref{richdson_b}). They also satisfy the continuity equation, adiabatic equation and hydrostatic equation. The linear Richardson's equation (\ref{r_l}) is discretized, and its adjoint code is developed according to the code of the linearized equation. The correctness of the adjoint check following the method proposed by \citet{navon92} is verified.
-The Richardsons equation is chosen due to the following reasons:
-a). It is a higher order approximation of the continuity equation
-than incompressible continuity equation or anelastic continuity
-equation, and the computation is affordable; b). It can build
-efficient linkage between dynamic and thermodynamic fields because
-the thermodynamic equation is directly involved in the derivation.
-The analysis fields should be more balanced than using simple
-incompressible continuity equation or anelastic continuity equation.
-c). In the Richardsons equation, the local derivative of air density
-is dropped from continuity equation by assuming hydrostatic and
-adiabatic atmosphere. It therefore avoids the difficulties in
-implementation of the continuity equation in the 3D-Var system, which
-is not designed to take local time derivates into account. Although
-4D-Var can handle the time derivates with integrations, it is much
-more expensive and complicate than 3D-Var. It must be noted that
-Richardsons equation (with adiabatic assumption) can still induce
-errors for heavy rain event where latent heat release and evaporation
-are important. However, in the 3D-Var cycling procedure, the influence
-of latent heat release, evaporation and other microphysics process
-is reflected in the model forecast. The 3D-Var cycling uses the model
-forecast as the first guess for the next cycle. This can alleviate
-the problem. In the future, it is necessary to further assess the
-impact of the adiabatic assumption on the 3D-Var analyses by
-comparing the adiabatic and diabatic Richardsons equations
-in the 3D-Var system.
+The Richardson's equation is chosen due to the following reasons:
+\begin{itemize}
+\item It is a higher order approximation of the continuity equation than incompressible continuity equation or anelastic continuity equation, and the computation is affordable;
+\item It can build efficient linkage between dynamic and thermodynamic fields because the thermodynamic equation is directly involved in the derivation. The analysis fields should be more balanced than using simple incompressible continuity equation or anelastic continuity equation.
+\item In the Richardson's equation, the local derivative of air density is dropped from continuity equation by assuming hydrostatic and adiabatic atmosphere. It therefore avoids the difficulties in implementation of the continuity equation in the 3D-Var system, which is not designed to take local time derivatives into account.
+\end{itemize}
+
+Although 4D-Var can handle the time derivatives with integrations, it is much more expensive and complicate than 3D-Var. It must be noted that Richardson's equation (with adiabatic assumption) can still induce errors for heavy rain event where latent heat release and evaporation are important. However, in the 3D-Var cycling procedure, the influence of latent heat release, evaporation and other microphysics process is reflected in the model forecast. The 3D-Var cycling uses the model forecast as the first guess for the next cycle. This can alleviate the problem. In the future, it is necessary to further assess the impact of the adiabatic assumption on the 3D-Var analyses by comparing the adiabatic and diabatic Richardson's equations in the 3D-Var system.
+
\subsection{Inclusion of background $q_c$ and $q_r$ in the 3D-Var system}
-In WRF-Var, the background fields can be WRF input (analysis),
-or WRF forecasts. Usually the input (analysis) does not contain
-cloud water and rainwater fields. However, if
-WRF 3D-Var is set up for a continuous update cycle, inclusion of
-cloud water and rainwater mixing ratios $q_c$ and $q_r$ in analysis
-is possible. With cloud water and rainwater produced by the previous
-cycles, inclusion of background $q_c$ and $q_r$ in the 3D-Var
-system enables the information of these variables to be passed on
-to the next cycle. This can reduce the time required for cloud water
-and rainwater spin-up when the model is integrated from the analysis
-as part of the cycling procedure. Moreover, observation operators
-for Doppler velocity and reflectivity require inclusion of cloud
-water and rainwater information. In the Doppler radial velocity
-operator, rainwater terminal velocity is included, and terminal
-velocity is calculated based on the rainwater mixing
-ratio \citep{sun98}.
+In WRF-Var, the background fields can be WRF input (analysis), or WRF forecasts. Usually the input (analysis) does not contain cloud water and rainwater fields. However, if WRF 3D-Var is set up for a continuous update cycle, inclusion of cloud water and rainwater mixing ratios $q_c$ and $q_r$ in analysis is possible. With cloud water and rainwater produced by the previous cycles, inclusion of background $q_c$ and $q_r$ in the 3D-Var system enables the information of these variables to be passed on to the next cycle. This can reduce the time required for cloud water and rainwater spin-up when the model is integrated from the analysis as part of the cycling procedure. Moreover, observation operators for Doppler velocity and reflectivity require inclusion of cloud water and rainwater information. In the Doppler radial velocity operator, rainwater terminal velocity is included, and terminal velocity is calculated based on the rainwater mixing ratio \citep{sun98}.
\subsection{Observation operator for Doppler radial velocity}
@@ -272,62 +96,35 @@
\label{rv_operator}
\end{equation}
-</font>
<font color="red">oindent where ($u,v,w$) are the wind components, ($x,y,z$) are the radar
-location, ($x_i,y_i,z_i$) are the location of the radar observation,
-$r_i$ is the distance between the radar and the observation,
-and $v_T$ is terminal velocity. For radar scans at nonzero
-elevation angles, the fall speed of precipitation particles has
-to be taken into account. There are different ways to calculate
-terminal velocity. Here, we use the algorithm of \citet{sun98}
-to calculate terminal velocity $v_T$ (m/s),
+</font>
<font color="red">oindent where ($u,v,w$) are the wind components, ($x,y,z$) are the radar location, ($x_i,y_i,z_i$) are the location of the radar observation, $r_i$ is the distance between the radar and the observation, and $v_T$ is terminal velocity. For radar scans at nonzero elevation angles, the fall speed of precipitation particles has to be taken into account. There are different ways to calculate terminal velocity. Here, we use the algorithm of \citet{sun98} to calculate terminal velocity $v_T$ (m/s),
\begin{equation}
v_T = 5.40 a \cdot q_r^{0.125} ,
\label{v_T}
\end{equation}
-</font>
<font color="red">oindent where $q_r$ is rainwater mixing ratio ($g/kg$). The quantity $a$ is
-a correction factor defined by
+</font>
<font color="red">oindent where $q_r$ is rainwater mixing ratio ($g/kg$). The quantity $a$ is a correction factor defined by
\begin{equation}
a = (p_0/\overline p ) ^{0.4} ,
\label{v_T_a}
\end{equation}
-</font>
<font color="red">oindent where $\overline p$ is the base-state pressure and $p_0$
-is the pressure at the ground.
+</font>
<font color="gray">oindent where $\overline p$ is the base-state pressure and $p_0$ is the pressure at the ground.
\section{Radar Reflectivity Assimilation}
\label{radar_rf}
-Radar reflectivity measures the radar signal reflected by
-precipitation hydrometeors. To assimilate radar reflectivity directly,
-the WRF 3D-Var system should be able to produce the increments of
-the hydrometeors (at least the rainwater mixing ratio). However,
-it is not appropriate to perform the background error
-statistics for the rainwater mixing ratio, because it will result in
-zero errors in most of the domain grid points. Instead, we chose
-total water mixing ratio $q_t$ as a control variable and
-conducted background error statistics for the WRF 3D-Var when
-radar reflectivity is to be assimilated \citep{xiao07}.
+Radar reflectivity measures the radar signal reflected by precipitation hydrometeors. To assimilate radar reflectivity directly, the WRF 3D-Var system should be able to produce the increments of the hydrometeors (at least the rainwater mixing ratio). However, it is not appropriate to perform the background error statistics for the rainwater mixing ratio, because it will result in zero errors in most of the domain grid points. Instead, we chose total water mixing ratio $q_t$ as a control variable and conducted background error statistics for the WRF 3D-Var when radar reflectivity is to be assimilated \citep{xiao07}.
\subsection{Partitioning of moisture and hydrometeor increments}
-Because total water mixing ratio $q_t$ is used as a control variable,
-partitioning of the moisture and hydrometeor increments is necessary
-in the 3D-Var system. We introduced the warm rain process of
-\citet{dudhia89}, which includes condensation of water vapor into
-cloud ($P_{CON}$), accretion of cloud by rain ($P_{RA}$), automatic
-conversion of cloud to rain ($P_{RC}$), and evaporation of rain to
-water vapor ($P_{RE}$). These are the major processes of hydrometeor
-cycle in the summer season. For the winter season, the partitioning
-scheme should include ice-phase microphuysics. This will be developed
-in the future release.
+Because total water mixing ratio $q_t$ is used as a control variable, partitioning of the moisture and hydrometeor increments is necessary in the 3D-Var system. We introduced the warm rain process of \citet{dudhia89}, which includes condensation of water vapor into cloud ($P_{CON}$), accretion of cloud by rain ($P_{RA}$), automatic conversion of cloud to rain ($P_{RC}$), and evaporation of rain to water vapor ($P_{RE}$). These are the major processes of hydrometeor cycle in the summer season. For the winter season, the partitioning scheme should include ice-phase microphuysics. This will be developed in the future release.
The autoconversion term, $P_{RC}$, is represented by
\begin{equation}
-P_{RC} =
+P_{RC} =
\begin{cases}
k_1 (q_c - q_{crit}), &if\ q_c \ge q_{crit}; \\
0. &if\ q_c < q_{crit},
@@ -335,9 +132,7 @@
\label{P_rc}
\end{equation}
-</font>
<font color="red">oindent where $q_c$ is the cloud water mixing ratio. According to
-\citet{kessler69}, $k_1=10^{-3}\ s^{-1}$, $q_{crit}=0.5 g\cdot kg^{-1}$.
-The accretion of cloud water by rain is parameterized by
+</font>
<font color="gray">oindent where $q_c$ is the cloud water mixing ratio. According to \citet{kessler69}, $k_1=10^{-3}\ s^{-1}$, $q_{crit}=0.5 g\cdot kg^{-1}$. The accretion of cloud water by rain is parameterized by
\begin{equation}
P_{RA} = \frac{1}{4}\pi \rho a q_c EN_0(\frac{p_0}{p})^{0.4}
@@ -345,9 +140,7 @@
\label{P_ra}
\end{equation}
-</font>
<font color="red">oindent where $\Gamma$ is the gamma-function; $E$ is the collection efficiency;
-$p$ is pressure; $p_0$=1000 $hPa$, $N_0$=8X106 $m^{-4}$, $a$=841.99667 and
-$b$=0.8. The evaporation of rain can be determined from the equation:
+</font>
<font color="gray">oindent where $\Gamma$ is the gamma-function; $E$ is the collection efficiency; $p$ is pressure; $p_0$=1000 $hPa$, $N_0$=8X106 $m^{-4}$, $a$=841.99667 and $b$=0.8. The evaporation of rain can be determined from the equation:
\begin{equation}
P_{RE} = \frac{2 \pi N_0 (S-1)}{A+B} \Biggl \lbrack \frac{f_1}{\lambda^2}+
@@ -356,78 +149,30 @@
\label{P_re}
\end{equation}
-</font>
<font color="red">oindent where f1=0.78, f2=0.32. The condensation $P_{CON}$ is determined
-according to Asai (1965) by
+</font>
<font color="red">oindent where f1=0.78, f2=0.32. The condensation $P_{CON}$ is determined according to Asai (1965) by
\begin{equation}
P_{CON} = \frac{q_v - q_{vs}} {1 + \frac{L_v^2 q_{vs}} {R_v C_{pm} T^2}}
\label{P_con}
\end{equation}
-</font>
<font color="red">oindent where $q_{vs}$ is saturated water vapor mixing ratio,
-$L_v$, $R_v$, and $C_{pm}$ are latent heat of condensation, gas constant
-for water vapor, and specific heat at constant pressure for moist air,
-respectively.
+</font>
<font color="red">oindent where $q_{vs}$ is saturated water vapor mixing ratio, $L_v$, $R_v$, and $C_{pm}$ are latent heat of condensation, gas constant for water vapor, and specific heat at constant pressure for moist air, respectively.
-The tangent linear and its adjoint of the warm rain scheme
-(\ref{P_rc}) - (\ref{P_con}) were developed and
-incorporated into the WRF 3D-Var system. Although the control variable
-is $q_t$, the $q_v$, $q_c$ and $q_r$ increments are produced through the
-partitioning procedure during the 3D-Var minimization. The warm rain
-parameterization builds a constraint: the relation among rainwater,
-cloud water, moisture, and temperature. When rainwater information
-(from reflectivity) enters the minimization iteration procedure, the
-forward warm rain process and its backward adjoint distribute this
-information to the increments of other variables (under the constraint
-of the warm rain scheme).
+The tangent linear and its adjoint of the warm rain scheme (\ref{P_rc}) - (\ref{P_con}) were developed and incorporated into the WRF 3D-Var system. Although the control variable is $q_t$, the $q_v$, $q_c$ and $q_r$ increments are produced through the partitioning procedure during the 3D-Var minimization. The warm rain parameterization builds a constraint: the relation among rainwater, cloud water, moisture, and temperature. When rainwater information (from reflectivity) enters the minimization iteration procedure, the forward warm rain process and its backward adjoint distribute this information to the increments of other variables (under the constraint of the warm rain scheme).
\subsection{Observation operator for radar reflectivity}
-Once the 3D-Var system can produce $q_c$ and $q_r$ increments, the setup
-of the observation operator for assimilation of reflectivity is
-straightforward. Simply, we adopted the observation operator from
-\citet{sun97}:
+Once the 3D-Var system can produce $q_c$ and $q_r$ increments, the setup of the observation operator for assimilation of reflectivity is straightforward. Simply, we adopted the observation operator from \citet{sun97}:
\begin{equation}
Z = 43.1+17.5log(\rho q_r),
\label{Z_operator}
\end{equation}
-</font>
<font color="red">oindent where $Z$ is reflectivity in the unit of $dBZ$ and $q_r$ is
-the rainwater mixing ratio. The relation (\ref{Z_operator})
-is derived analytically
-by assuming the Marshal-Palmer distribution of raindrop size.
+</font>
<font color="gray">oindent where $Z$ is reflectivity in the unit of $dBZ$ and $q_r$ is the rainwater mixing ratio. The relation (\ref{Z_operator}) is derived analytically by assuming the Marshal-Palmer distribution of raindrop size.
\subsection{Summary of the implementation procedure}
-Great efforts were made to incorporate the reflectivity assimilation into
-the WRF 3D-Var system. The flow chart of computations in the WRF 3D-Var
-minimization procedure can be found in \citet{xiao07}. For clarity of
-the procedure, we summarized some implementation details in the following.
+Great efforts were made to incorporate the reflectivity assimilation into the WRF 3D-Var system. The flow chart of computations in the WRF 3D-Var minimization procedure can be found in \citet{xiao07}. For clarity of the procedure, we summarized some implementation details in the following.
-First of all, the control variable transform was built to bridge
-the control variables $V$ and the analyzed variable increments $X$.
-The partitioning of the moisture and hydrometeor increments is added
-to the transform. Since we use $q_t$ as a control variable, development
-of the linear warm rain process is important to partition the $q_v$,
-$q_c$ and $q_r$ increments. At the first iteration of the WRF 3D-Var
-minimization, the $q_c$ and $q_r$ increments are zero, and the $q_v$
-increment is equal to the $q_t$ increment. We treated the warm rain
-process as a column model. If any column is detected updraft and
-super-saturation, an average 30 minutes of updraft time is taken
-to produce the cloud water and rainwater using the one-dimensional
-column model. During the process, moisture and temperature should
-also be changed due to the condensation and evaporation involved
-in the process. When reflectivity observation is assimilated,
-the adjoint of the reflectivity operator will produce the cost function
-gradient with respect to the $q_r$ by the adjoint of the reflectivity
-operator. The adjoint of moisture and hydrometeor partitioning scheme will
-distribute the information to the gradients with respect to $q_c$, $q_v$
-and temperature $T$, and produce the gradient with respect to $q_t$.
-Afterwards, the adjoint of the control variable transform will
-propagate the information to other variables and produce the cost
-function gradient of other control variables. The process is iterated
-back and forth in the WRF 3D-Var minimization procedure. When it
-converges, the increments of $q_c$, $q_r$, $q_v$ and $T$ are
-produced by the reflectivity assimilation. The radar reflectivity
-observations is therefore assimilated into the 3D-Var analusis.
+First of all, the control variable transform was built to bridge the control variables $V$ and the analyzed variable increments $X$. The partitioning of the moisture and hydrometeor increments is added to the transform. Since we use $q_t$ as a control variable, development of the linear warm rain process is important to partition the $q_v$, $q_c$ and $q_r$ increments. At the first iteration of the WRF 3D-Var minimization, the $q_c$ and $q_r$ increments are zero, and the $q_v$ increment is equal to the $q_t$ increment. We treated the warm rain process as a column model. If any column is detected updraft and super-saturation, an average 30 minutes of updraft time is taken to produce the cloud water and rainwater using the one-dimensional column model. During the process, moisture and temperature should also be changed due to the condensation and evaporation involved in the process. When reflectivity observation is assimilated, the adjoint of the reflectivity operator will prod
uce the cost function gradient with respect to the $q_r$ by the adjoint of the reflectivity operator. The adjoint of moisture and hydrometeor partitioning scheme will distribute the information to the gradients with respect to $q_c$, $q_v$ and temperature $T$, and produce the gradient with respect to $q_t$. Afterwards, the adjoint of the control variable transform will propagate the information to other variables and produce the cost function gradient of other control variables. The process is iterated back and forth in the WRF 3D-Var minimization procedure. When it converges, the increments of $q_c$, $q_r$, $q_v$ and $T$ are produced by the reflectivity assimilation. The radar reflectivity observations is therefore assimilated into the 3D-Var analysis.
Added: trunk/wrfvar/3DVAR_technote/tutorial.tex
===================================================================
--- trunk/wrfvar/3DVAR_technote/tutorial.tex (rev 0)
+++ trunk/wrfvar/3DVAR_technote/tutorial.tex 2013-05-16 19:09:45 UTC (rev 432)
@@ -0,0 +1,4 @@
+\chapter{Tutorial Case}
+\label{tutorial-case}
+
+For our users' convenience, a package containing a tutorial case, including all the input files needed to run WRFDA\textendash 3DVAR, is provided at our website, (\url{http://www.mmm.ucar.edu/wrf/users/wrfda/download/testdata.html}).
\ No newline at end of file
</font>
</pre>