[1080] | 1 | %$Id: ncl.tex 1515 2015-01-02 11:35:51Z hoffmann $ |
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| 2 | \input{header_tmp.tex} |
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| 3 | %\input{../header_lectures.tex} |
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| 4 | |
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| 5 | \usepackage[utf8]{inputenc} |
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| 6 | \usepackage{ngerman} |
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| 7 | \usepackage{pgf} |
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| 8 | \usetheme{Dresden} |
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| 9 | \usepackage{subfigure} |
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| 10 | \usepackage{units} |
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| 11 | \usepackage{multimedia} |
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| 12 | \usepackage{hyperref} |
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| 13 | \newcommand{\event}[1]{\newcommand{\eventname}{#1}} |
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| 14 | \usepackage{xmpmulti} |
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| 15 | \usepackage{tikz} |
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| 16 | \usetikzlibrary{shapes,arrows,positioning} |
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| 17 | \usetikzlibrary{calc} %neues paket |
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| 18 | \usetikzlibrary{decorations.markings} %neues paket |
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| 19 | \usetikzlibrary{decorations.pathreplacing} %neues paket |
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| 20 | \def\Tiny{\fontsize{4pt}{4pt}\selectfont} |
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| 21 | \usepackage{amsmath} |
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| 22 | \usepackage{amssymb} |
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| 23 | \usepackage{multicol} |
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| 24 | \usepackage{pdfcomment} |
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| 25 | \usepackage{graphicx} |
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| 26 | \usepackage{listings} |
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| 27 | \lstset{showspaces=false,language=fortran,basicstyle= |
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| 28 | \ttfamily,showstringspaces=false,captionpos=b} |
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| 29 | |
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| 30 | \institute{Institut fÌr Meteorologie und Klimatologie, Leibniz UniversitÀt Hannover} |
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| 31 | \date{last update: \today} |
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| 32 | \event{PALM Seminar} |
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| 33 | \setbeamertemplate{navigation symbols}{} |
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| 34 | |
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| 35 | \setbeamertemplate{footline} |
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| 36 | { |
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| 37 | \begin{beamercolorbox}[rightskip=-0.1cm]& |
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| 38 | {\includegraphics[height=0.65cm]{imuk_logo.pdf}\hfill \includegraphics[height=0.65cm]{luh_logo.pdf}} |
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| 39 | \end{beamercolorbox} |
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| 40 | \begin{beamercolorbox}[ht=2.5ex,dp=1.125ex, |
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| 41 | leftskip=.3cm,rightskip=0.3cm plus1fil]{title in head/foot} |
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| 42 | {\leavevmode{\usebeamerfont{author in head/foot}\insertshortauthor} \hfill \eventname \hfill \insertframenumber \; / \inserttotalframenumber} |
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| 43 | \end{beamercolorbox} |
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| 44 | \begin{beamercolorbox}[colsep=1.5pt]{lower separation line foot} |
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| 45 | \end{beamercolorbox} |
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| 46 | } |
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| 47 | %\logo{\includegraphics[width=0.3\textwidth]{luhimuk_logo.pdf}} |
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| 48 | |
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| 49 | \title[Introduction to NCL]{Introduction to NCL} |
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| 50 | \author{Siegfried Raasch} |
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| 51 | |
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| 52 | \begin{document} |
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| 53 | |
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| 54 | % Folie 1 |
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| 55 | \begin{frame} |
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| 56 | \titlepage |
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| 57 | \end{frame} |
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| 58 | |
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| 59 | \section{Introduction to NCL} |
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| 60 | \subsection{Introduction to NCL} |
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| 61 | |
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| 62 | % Folie 2 |
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| 63 | \begin{frame} |
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| 64 | \frametitle{Visualization of PALM Output Data} |
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| 65 | \small |
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| 66 | \begin{itemize} |
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| 67 | \item<1-> There are several ways how you can visualize netCDF data |
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| 68 | \item<1-> If you are lacking experience in the visualization of netCDF data or if you have not yet found your favourite way how to visualize netCDF data, here is one recommendation: |
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| 69 | \item<2-> NCL â The \textbf{N}CAR \textbf{C}ommand \textbf{L}anguage |
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| 70 | \item<2-> Developed by the Computational \& Information Systems Laboratory at the NCAR (continuously updated) |
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| 71 | \item<2-> Detailed information is available under http://www.ncl.ucar.edu |
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| 72 | \item<3-> With the information revealed in this talk you will be able to visualize the output of this week's simulations |
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| 73 | \end{itemize} |
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| 74 | \end{frame} |
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| 75 | |
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| 76 | % Folie 3 |
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| 77 | \begin{frame} |
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| 78 | \frametitle{What is NCL and Which are its Advantages? (I)} |
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| 79 | \small |
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| 80 | \begin{itemize} |
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[1515] | 81 | \item<1-> Interpreted language designed specifically for scientific |
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| 82 | data processing and visualization, freely available |
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| 83 | \item<2-> Portable: it is running on many different operating systems |
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| 84 | including AIX, Linux, MacOSX, Cygwin/Windows |
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| 85 | \item<3-> It's a powerful tool for file input and output, visualization |
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| 86 | and data analysis (but please \textbf{avoid the excessive usage |
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| 87 | of loops}, as NCL is an interpreted language) $\rightarrow$ |
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| 88 | integrated processing environment |
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[1080] | 89 | \end{itemize} |
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| 90 | \centering |
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| 91 | \onslide<3-> \includegraphics[scale=0.28]{ncl_figures/ncl.png} |
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| 92 | |
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| 93 | \end{frame} |
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| 94 | |
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| 95 | % Folie 4 |
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| 96 | \begin{frame} |
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| 97 | \frametitle{What is NCL and Which are its Advantages? (II)} |
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| 98 | \small |
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| 99 | \begin{itemize} |
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| 100 | \item<1-> Supports calling C and FORTRAN extended routines |
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[1515] | 101 | \item<1-> Over 600 functions and procedures for visualization and |
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| 102 | data analysis are provided with NCL |
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[1080] | 103 | \item<2-> Interactive mode: \texttt{\$ ncl}\\ |
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| 104 | \texttt{ncl 0>} |
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| 105 | \item<3-> each line is interpreted as it is entered |
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[1515] | 106 | \item<4-> Batch mode: \texttt{\$ ncl ncl\underline{ }script.ncl}\\ |
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[1080] | 107 | interpreter of complete scripts, variables within the NCL script can\\ |
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| 108 | be steered by providing additional parameters with the ncl call\\ |
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| 109 | \texttt{\$ ncl ncl\underline{ }script.ncl parameter1=value} |
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| 110 | \texttt{'parameter2=\dq string\dq ' ...} |
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| 111 | \end{itemize} |
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| 112 | |
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| 113 | \end{frame} |
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| 114 | |
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| 115 | % Folie 5 |
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| 116 | \begin{frame} |
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| 117 | \frametitle{What is NCL and Which are its Advantages? (III)} |
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| 118 | |
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| 119 | \begin{itemize} |
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| 120 | \item<1-> Complete Programming Language |
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| 121 | \begin{itemize} |
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| 122 | \footnotesize |
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| 123 | \item<1-> data types |
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| 124 | \item<1-> variables |
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| 125 | \item<1-> operators |
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| 126 | \item<1-> expressions |
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| 127 | \item<1-> loops |
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| 128 | \item<1-> functions/procedures/graphics |
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| 129 | \end{itemize} |
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| 130 | \item<2-> Features |
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| 131 | \begin{itemize} |
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| 132 | \footnotesize |
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| 133 | \item<2-> query / manipulate meta data |
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| 134 | \item<2-> import data in a variety of formats |
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| 135 | \item<2-> array syntax / operations |
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| 136 | \item<2-> can use user FORTRAN/C codes and commercial libraries |
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| 137 | \item<2-> most functions/procedures ignore missing data |
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| 138 | \end{itemize} |
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| 139 | \end{itemize} |
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| 140 | |
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| 141 | \end{frame} |
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| 142 | |
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| 143 | % Folie 6 |
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| 144 | \begin{frame} |
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| 145 | \frametitle{How to Install NCL (Under Linux) (I)?} |
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| 146 | \small |
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| 147 | \begin{itemize} |
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[1515] | 148 | \item<1-> Detailed information is available under\\ |
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| 149 | \underline{http://www.ncl.ucar.edu/Download/index.shtml} |
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| 150 | \item<1-> Request an Earth System Grid account |
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| 151 | \underline{http://www.earthsystemgrid.org/} |
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| 152 | \item<2-> Download the appropriate binaries e.g. \texttt{A.tar.gz} |
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| 153 | for your system e.g. to \texttt{\$HOME} |
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[1080] | 154 | \item<2-> \texttt{\% gunzip \$HOME/A.tar.gz} |
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| 155 | \item<2-> \texttt{\% mkdir -p /usr/local}\\ |
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| 156 | \quad \texttt{\% cd /usr/local}\\ |
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| 157 | \quad \texttt{\% tar -xvf \$HOME/A.tar} |
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| 158 | \end{itemize} |
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| 159 | |
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| 160 | \end{frame} |
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| 161 | |
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| 162 | % Folie 7 |
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| 163 | \begin{frame} |
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| 164 | \frametitle{How to Install NCL (Under Linux) (II)?} |
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| 165 | \footnotesize |
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| 166 | \begin{itemize} |
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[1515] | 167 | \item<1-> Set the \texttt{NCARG\underline{ }ROOT} environment variable and |
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| 168 | your search path to where NCL/NCARG resides\\ |
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| 169 | csh: \texttt{setenv NCARG\underline{ }ROOT /usr/local/}\\ |
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| 170 | \hspace{1.6em} \texttt{setenv PATH /usr/local/bin:\$PATH}\\ |
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| 171 | bash/ksh: \texttt{export NCARG\underline{ }ROOT=/usr/local/}\\ |
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| 172 | \hspace{4.1em} \texttt{export PATH=/usr/local/bin:\$PATH}\\ |
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[1080] | 173 | \vspace{3mm} |
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[1515] | 174 | \item<2-> Set the DISPLAY environment variable to indicate where to |
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| 175 | display graphics as for any X11 Windows application that you |
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| 176 | run\\ |
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| 177 | e.g. ksh: \texttt{export DISPLAY=localhost:13.0}, or use |
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| 178 | \texttt{ssh -X} to tunnel X-communication.\\ |
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| 179 | \vspace{3mm} |
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[1080] | 180 | \item<3-> Test your NCL installation\\ |
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[1515] | 181 | \quad \texttt{\% ng4ex gsun01}\\ |
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| 182 | NCL script gsun01n.ncl is copied to your working directory and |
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| 183 | run through NCL. An X11 window should pop up. |
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[1080] | 184 | \end{itemize} |
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| 185 | |
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| 186 | \end{frame} |
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| 187 | |
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| 188 | % Folie 8 |
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| 189 | \begin{frame} |
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| 190 | \frametitle{NCL Scripts Delivered with PALM (I)} |
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| 191 | \footnotesize |
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| 192 | \begin{itemize} |
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[1515] | 193 | \item<1-> Together with the PALM installation you have also received four NCL scripts, a configuration file and a manual; they can be found in the directory\\ |
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| 194 | \texttt{\$HOME/palm/current\underline{ }version/trunk/SCRIPTS/NCL/} |
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| 195 | \item<2-> All standard netCDF data output of PALM can be visualized by one |
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| 196 | of the scripts: |
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| 197 | \begin{itemize} |
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| 198 | \scriptsize |
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| 199 | \item[-]<2-> \texttt{cross\underline{ }sections.ncl} |
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| 200 | (2D/3D data, e.g. contour or vector plots) |
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| 201 | \item[-]<2-> \texttt{profiles.ncl} (profile data) |
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| 202 | \item[-]<2-> \texttt{timeseries.ncl} (time series data) |
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| 203 | \item[-]<2-> \texttt{spectra.ncl} (spectra data) |
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| 204 | \end{itemize} |
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| 205 | \item<3-> To run these NCL scripts you can use the shell script |
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| 206 | \texttt{palmplot} which can be found in the directory\\ |
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| 207 | \texttt{\$HOME/palm/current\underline{ }version/trunk/SCRIPTS} |
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| 208 | \item<4-> The output of the plots can be changed with several parameters; |
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| 209 | these parameters can be either written in the prompt |
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| 210 | (when calling the shell script \texttt{palmplot}) or set |
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| 211 | within the configuration file \texttt{.ncl.config} |
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[1080] | 212 | \end{itemize} |
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| 213 | |
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| 214 | \end{frame} |
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| 215 | |
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| 216 | % Folie 9 |
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| 217 | \begin{frame} |
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| 218 | \frametitle{NCL Scripts Delivered with PALM (II)} |
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| 219 | |
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| 220 | Using \texttt{.ncl.config} |
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| 221 | \small |
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| 222 | \begin{itemize} |
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[1515] | 223 | \item[-]<1-> Please create a personal configuration file by copying |
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| 224 | the default configuration file |
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| 225 | \texttt{.ncl.config.default} to the PALM working |
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| 226 | directory \texttt{\$HOME/palm/current\underline{ }version} |
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| 227 | and naming it \texttt{.ncl.config} |
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| 228 | \item[-]<2-> \texttt{.ncl.config} is used by NCL directly, thus the |
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| 229 | parameters have to be written according to the rules of the |
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| 230 | scripting language NCL |
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| 231 | \item[-]<3-> The configuration file contains all steering parameters with |
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| 232 | a short description and can be adjusted to personal needs |
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[1080] | 233 | \end{itemize} |
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| 234 | |
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| 235 | \end{frame} |
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| 236 | |
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| 237 | % Folie 10 |
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| 238 | \begin{frame} |
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| 239 | \frametitle{NCL Scripts Delivered with PALM (III)} |
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| 240 | |
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| 241 | Using \texttt{palmplot} (I) |
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| 242 | \footnotesize |
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| 243 | \begin{itemize} |
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[1515] | 244 | \item[-]<1-> The shell script is used as follows:\\ |
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| 245 | \texttt{palmplot <plot\underline{ }identifier>} |
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| 246 | \item[-]<1-> \texttt{<plot\underline{ }identifier>} has to be \texttt{xy}, |
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| 247 | \texttt{xz}, \texttt{yz}, \texttt{pr}, \texttt{sp} or |
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| 248 | \texttt{ts} depending on the data to be plotted |
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[1080] | 249 | \end{itemize} |
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| 250 | \vspace{3mm} |
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[1515] | 251 | \onslide<2-> |
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| 252 | \begin{tabular}{ccc} |
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| 253 | \textbf{plot\underline{ }identifier} & \textbf{data used} & \textbf{ncl script}\\ |
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| 254 | xy & instantaneous or time-averaged xy or 3D data & cross\underline{ }sections.ncl\\ |
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| 255 | xz & instantaneous or time-averaged xz or 3D data & cross\underline{ }sections.ncl\\ |
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| 256 | yz & instantaneous or time-averaged yz or 3D data & cross\underline{ }sections.ncl\\ |
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| 257 | pr & profile or 3D data & profiles.ncl\\ |
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| 258 | sp & spectra data & spectra.ncl\\ |
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| 259 | ts & time series data & timeseries.ncl\\ |
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[1080] | 260 | \end{tabular} |
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| 261 | |
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| 262 | \end{frame} |
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| 263 | |
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| 264 | % Folie 11 |
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| 265 | \begin{frame} |
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| 266 | \frametitle{NCL Scripts Delivered with PALM (IV)} |
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| 267 | |
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| 268 | Using \texttt{palmplot} (II) |
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| 269 | \footnotesize |
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| 270 | \begin{itemize} |
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[1515] | 271 | \item[-]<1-> To change the output of the plot you can also use:\\ |
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| 272 | \scriptsize |
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| 273 | \texttt{palmplot \textbf{plot\underline{ }identifier} |
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| 274 | parameter=value parameter=string ...} |
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[1080] | 275 | \footnotesize \\ |
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| 276 | \vspace{2mm} |
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[1515] | 277 | \item[-]<2-> A list of all available parameters can be found in the |
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| 278 | configuration file \texttt{.ncl.config} or in the |
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| 279 | documentation:\\ |
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| 280 | \uncover<3->{\texttt{http://palm.muk.uni-hannover.de/wiki/doc/app/nclparlist}}\\ |
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[1080] | 281 | \vspace{2mm} |
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[1515] | 282 | \item[-]<4-> Parameters specified in the prompt override parameters given |
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| 283 | in the configuration file\\ |
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[1080] | 284 | \vspace{2mm} |
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[1515] | 285 | \item[-]<5-> String parameters which can contain lists (\texttt{var}, |
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| 286 | \texttt{c\underline{ }var}, \texttt{vec1}, \texttt{vec2}, |
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| 287 | \texttt{plotvec}) have to be set in single quotes and the |
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| 288 | list itself has to be separated by blanks, e.g. |
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| 289 | \texttt{var='pt u w'}\\ |
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[1080] | 290 | \vspace{2mm} |
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[1515] | 291 | \item[-]<6-> A short introduction for using the shell script is given by |
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| 292 | typing\\ |
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| 293 | \texttt{palmplot ?} |
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[1080] | 294 | \end{itemize} |
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| 295 | |
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| 296 | \end{frame} |
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| 297 | |
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| 298 | % Folie 12 |
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| 299 | \begin{frame} |
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[1515] | 300 | \frametitle{Application Example: Visualization of the Output of the Example |
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| 301 | Run (example\underline{ }cbl) (I)} |
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[1080] | 302 | \small |
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| 303 | \begin{itemize} |
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[1515] | 304 | \item<1-> Starting the example run with the command\\ |
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| 305 | \vspace{2mm} |
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| 306 | \texttt{mrun -d example\underline{ }cbl ... -r |
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| 307 | 'd3\# pr\# ts\# xy\# xz\#'}\\ |
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| 308 | \vspace{2mm} |
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| 309 | results in the following output files in\\ |
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| 310 | \vspace{2mm} |
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| 311 | \texttt{\$HOME/palm/current\underline{ }version/JOBS/example\underline{ }cbl/OUTPUT/}:\\ |
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| 312 | \texttt{example\underline{ }cbl\underline{ }pr.nc}, \texttt{example\underline{ }cbl\underline{ }xy.nc}, \texttt{example\underline{ }cbl\underline{ }xz.nc},\\ |
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| 313 | \texttt{example\underline{ }cbl\underline{ }ts.nc} |
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[1080] | 314 | \item<2-> Example: Visualization of the time series data\\ |
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[1515] | 315 | \vspace{2mm} |
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| 316 | Goal: Output as eps-file \texttt{timeseries.eps} (by default the |
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| 317 | plot would be output to an X11 window) |
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[1080] | 318 | \end{itemize} |
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| 319 | |
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| 320 | \end{frame} |
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| 321 | |
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| 322 | % Folie 13 |
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| 323 | \begin{frame} |
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[1515] | 324 | \frametitle{Application Example: Visualization of the Output of the Example |
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| 325 | Run (example\underline{ }cbl) (II)} |
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[1080] | 326 | \small |
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| 327 | \begin{itemize} |
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[1515] | 328 | \item<1-> In order to reach the goal you can either ... |
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[1080] | 329 | \item<1-> ... Change to the directory\\ |
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[1515] | 330 | \texttt{\$HOME/palm/current\underline{ }version/JOBS/example\underline{ }cbl/OUTPUT/}\\ |
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| 331 | and use the shell script with the command\\ |
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| 332 | \vspace{2mm} |
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| 333 | \texttt{palmplot ts file\underline{ }1=example\underline{ }cbl\underline{ }ts.nc format\underline{ }out=eps file\underline{ }out=timeseries}\\ |
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| 334 | \vspace{2mm} |
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| 335 | Thus, the script \texttt{timeseries.ncl} is called and some of the parameters in the configuration file \texttt{.ncl.config} are directly set by specifying the related parameters in the command line,\\ |
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| 336 | \vspace{2mm} |
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| 337 | \onslide<2-> e.g. \texttt{file\underline{ }1 = <netCDF file>} |
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| 338 | \textbf{(Note: the input file has always to be specified!)}, \texttt{file\underline{ }out = <output file>} |
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[1080] | 339 | \end{itemize} |
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| 340 | |
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| 341 | \end{frame} |
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| 342 | |
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| 343 | % Folie 14 |
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| 344 | \begin{frame} |
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[1515] | 345 | \frametitle{Application Example: Visualization of the Output of the Example |
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| 346 | Run (example\underline{ }cbl) (III)} |
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[1080] | 347 | \footnotesize |
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| 348 | ... or you can modify the configuration file \texttt{.ncl.config}, e.g.\\ |
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| 349 | \vspace{2mm} |
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| 350 | \texttt{if(.not. isvar(\dq file\underline{ }1\dq))then}\\ |
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| 351 | \quad \quad \texttt{file\underline{ }1 = \dq File in\dq}\\ |
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| 352 | \texttt{end if}\\ |
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| 353 | \vspace{2mm} |
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| 354 | \onslide<2-> has to be changed to\\ |
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| 355 | \vspace{2mm} |
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| 356 | \texttt{if(.not. isvar(\dq file\underline{ }1\dq))then}\\ |
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| 357 | \quad \quad \texttt{file\underline{ }1 = \dq \$HOME/palm/current\underline{ }version/JOBS/example\underline{ }cbl/OUTPUT/example\underline{ }cbl\underline{ }ts.nc\dq}\\ |
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| 358 | \texttt{end if} |
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| 359 | |
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| 360 | \end{frame} |
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| 361 | |
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| 362 | % Folie 15 |
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| 363 | \begin{frame} |
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[1515] | 364 | \frametitle{Application Example: Visualization of the Output of the Example |
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| 365 | Run (example\underline{ }cbl) (IV)} |
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[1080] | 366 | \footnotesize |
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| 367 | \begin{itemize} |
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[1515] | 368 | \item<1-> Both ways will create a new file called \texttt{timeseries.eps} |
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| 369 | in the directory\\ |
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| 370 | \texttt{\$HOME/palm/current\underline{ }version/JOBS/example\underline{ }cbl/OUTPUT/} |
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[1080] | 371 | \end{itemize} |
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| 372 | \centering |
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[1515] | 373 | \onslide<2->\includegraphics[scale=0.25]{ncl_figures/vis1.png} |
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[1080] | 374 | |
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| 375 | \end{frame} |
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| 376 | |
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| 377 | % Folie 16 |
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| 378 | \begin{frame} |
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[1515] | 379 | \frametitle{Application Example: Visualization of the Output of the Example |
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| 380 | Run (example\underline{ }cbl) (V)} |
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[1080] | 381 | \footnotesize |
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| 382 | \begin{itemize} |
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| 383 | \item<1-> If you only want to get the plot of the time series of one variable, e.g. the maximum of the velocity component u, you can add the command line parameter \texttt{var='umax'} or modify the configuration file respectively, e.g.\\ |
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| 384 | \vspace{2mm} |
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| 385 | \texttt{if(.not. isvar(\dq var\dq ))then}\\ |
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| 386 | \quad \quad \texttt{var = \dq ,umax,\dq }\\ |
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| 387 | \texttt{end if} |
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| 388 | \end{itemize} |
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| 389 | \centering |
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[1515] | 390 | \onslide<2->\includegraphics[scale=0.3]{ncl_figures/vis2.png} |
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[1080] | 391 | |
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| 392 | \end{frame} |
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| 393 | |
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| 394 | % Folie 17 |
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| 395 | \begin{frame}[t] |
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| 396 | \tikzstyle{plain} = [rectangle, text width=0.27\textwidth, font=\small] |
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[1515] | 397 | \frametitle{Application Example: Visualization of the Output of the Example |
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| 398 | Run (example\underline{ }cbl) (VI)} |
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[1080] | 399 | \footnotesize |
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| 400 | Plot profiles with the command\\ |
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| 401 | \quad \texttt{palmplot pr file\underline{ }1=example\underline{ }cbl\underline{ }pr.nc}\\ |
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| 402 | \vspace{3mm} |
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| 403 | Profiles of same dimension are plotted\\ |
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| 404 | together, e.g. total, resolved and\\ |
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| 405 | subgridscale temperature flux (default)\\ |
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| 406 | \vspace{3mm} |
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| 407 | (This composition is written to the\\ |
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| 408 | NetCDF header by the \texttt{d3par}\\ |
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| 409 | parameter \texttt{cross\underline{ }profiles})\\ |
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| 410 | \vspace{3mm} |
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| 411 | If you add the parameter var=all to\\ |
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| 412 | the command, all profiles will be plotted\\ |
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| 413 | separately |
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| 414 | \begin{tikzpicture}[remember picture, overlay] |
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| 415 | \node at (current page.north west){% |
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| 416 | \begin{tikzpicture}[overlay] |
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[1515] | 417 | \node[plain,anchor=west] at (72mm,-51.5mm) |
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| 418 | {\includegraphics[scale=0.32]{ncl_figures/vis3.png}}; |
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[1080] | 419 | \end{tikzpicture} |
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| 420 | }; |
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| 421 | \end{tikzpicture} |
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| 422 | |
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| 423 | \end{frame} |
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| 424 | |
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| 425 | % Folie 18 |
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| 426 | \begin{frame} |
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| 427 | \frametitle{More Comments} |
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| 428 | \small |
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| 429 | \begin{itemize} |
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[1515] | 430 | \item<1-> The other NCL scripts delivered with PALM can be used in |
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| 431 | a similar way, however the parameters that can be specified |
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| 432 | differ from script to script |
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| 433 | \item<2-> There are plenty of parameters for each script. Please have a |
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| 434 | look to the NCL documentation |
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| 435 | (\texttt{http://palm.muk.uni-hannover.de/wiki/doc/app/nclparlist}) |
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| 436 | for detailed information |
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| 437 | \item<3-> If one of the program aborts and there is no comment, |
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| 438 | check the configuration file - the scripts should not abort with |
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| 439 | the default values. Be sure to use the right data type |
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| 440 | (e.g.: integer = 2; float = 2.0; double = 2.0d; |
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| 441 | string = \dq name\dq ) |
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[1080] | 442 | \end{itemize} |
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| 443 | \end{frame} |
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| 444 | |
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| 445 | |
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| 446 | |
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| 447 | |
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| 448 | |
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| 449 | |
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| 450 | |
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| 451 | |
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| 452 | \end{document} |
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