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\section{Getting started} |
%\section{Getting started} |
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In this part, we describe how to use the model. In the first section, we |
In this section, we describe how to use the model. In the first |
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provide enough information to help you get started with the model. We |
section, we provide enough information to help you get started with |
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believe the best way to familiarize yourself with the model is to run the |
the model. We believe the best way to familiarize yourself with the |
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case study examples provided with the base version. Information on how to |
model is to run the case study examples provided with the base |
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obtain, compile, and run the code is found there as well as a brief |
version. Information on how to obtain, compile, and run the code is |
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description of the model structure directory and the case study examples. |
found there as well as a brief description of the model structure |
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The latter and the code structure are described more fully in sections 2 and |
directory and the case study examples. The latter and the code |
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3, respectively. In section 4, we provide information on how to customize |
structure are described more fully in chapters |
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the code when you are ready to try implementing the configuration you have |
\ref{chap:discretization} and \ref{chap:sarch}, respectively. Here, in |
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in mind. |
this section, we provide information on how to customize the code when |
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you are ready to try implementing the configuration you have in mind. |
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\section{Where to find information} |
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\label{sect:whereToFindInfo} |
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\begin{rawhtml} |
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<!-- CMIREDIR:whereToFindInfo: --> |
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\end{rawhtml} |
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A web site is maintained for release 2 (``Pelican'') of MITgcm: |
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\begin{rawhtml} <A href=http://mitgcm.org/pelican/ target="idontexist"> \end{rawhtml} |
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\begin{verbatim} |
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http://mitgcm.org/pelican |
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\end{verbatim} |
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\begin{rawhtml} </A> \end{rawhtml} |
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Here you will find an on-line version of this document, a |
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``browsable'' copy of the code and a searchable database of the model |
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and site, as well as links for downloading the model and |
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documentation, to data-sources, and other related sites. |
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There is also a web-archived support mailing list for the model that |
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you can email at \texttt{MITgcm-support@mitgcm.org} or browse at: |
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\begin{rawhtml} <A href=http://mitgcm.org/mailman/listinfo/mitgcm-support/ target="idontexist"> \end{rawhtml} |
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http://mitgcm.org/mailman/listinfo/mitgcm-support/ |
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http://mitgcm.org/pipermail/mitgcm-support/ |
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\end{verbatim} |
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\begin{rawhtml} </A> \end{rawhtml} |
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Essentially all of the MITgcm web pages can be searched using a |
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popular web crawler such as Google or through our own search facility: |
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\begin{rawhtml} <A href=http://mitgcm.org/mailman/htdig/ target="idontexist"> \end{rawhtml} |
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http://mitgcm.org/htdig/ |
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\end{verbatim} |
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\begin{rawhtml} </A> \end{rawhtml} |
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%%% http://www.google.com/search?q=hydrostatic+site%3Amitgcm.org |
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\section{Obtaining the code} |
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\label{sect:obtainingCode} |
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<!-- CMIREDIR:obtainingCode: --> |
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\end{rawhtml} |
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MITgcm can be downloaded from our system by following |
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the instructions below. As a courtesy we ask that you send e-mail to us at |
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\begin{rawhtml} <A href=mailto:MITgcm-support@mitgcm.org> \end{rawhtml} |
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MITgcm-support@mitgcm.org |
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\begin{rawhtml} </A> \end{rawhtml} |
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to enable us to keep track of who's using the model and in what application. |
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You can download the model two ways: |
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\begin{enumerate} |
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\item Using CVS software. CVS is a freely available source code management |
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tool. To use CVS you need to have the software installed. Many systems |
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come with CVS pre-installed, otherwise good places to look for |
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the software for a particular platform are |
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\begin{rawhtml} <A href=http://www.cvshome.org/ target="idontexist"> \end{rawhtml} |
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cvshome.org |
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\begin{rawhtml} </A> \end{rawhtml} |
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and |
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\begin{rawhtml} <A href=http://www.wincvs.org/ target="idontexist"> \end{rawhtml} |
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wincvs.org |
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\begin{rawhtml} </A> \end{rawhtml} |
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. |
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\item Using a tar file. This method is simple and does not |
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require any special software. However, this method does not |
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provide easy support for maintenance updates. |
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\subsection{Obtaining the code} |
\end{enumerate} |
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The reference web site for the model is: |
\subsection{Method 1 - Checkout from CVS} |
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\begin{verbatim} |
\label{sect:cvs_checkout} |
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http://mitgcm.org |
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\end{verbatim} |
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On this site, you can download the model as well as find useful information, |
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some of which might overlap with what is written here. There is also a |
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support news group for the model located at (send your message to \texttt{% |
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support@mitgcm.org}): |
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\begin{verbatim} |
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news://mitgcm.org/mitgcm.support |
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\end{verbatim} |
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If CVS is available on your system, we strongly encourage you to use it. CVS |
If CVS is available on your system, we strongly encourage you to use it. CVS |
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provides an efficient and elegant way of organizing your code and keeping |
provides an efficient and elegant way of organizing your code and keeping |
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track of your changes. If CVS is not available on your machine, you can also |
track of your changes. If CVS is not available on your machine, you can also |
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download a tar file. |
download a tar file. |
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\subsubsection{Using CVS} |
Before you can use CVS, the following environment variable(s) should |
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be set within your shell. For a csh or tcsh shell, put the following |
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Before you can use CVS, the following environment variable has to be set in |
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your .cshrc or .tcshrc: |
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\begin{verbatim} |
\begin{verbatim} |
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% setenv CVSROOT :pserver:cvsanon@mitgcm.org:/u/u0/gcmpack |
% setenv CVSROOT :pserver:cvsanon@mitgcm.org:/u/gcmpack |
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% cvs login ( CVS password: cvsanon ) |
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\end{verbatim} |
\end{verbatim} |
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in your .cshrc or .tcshrc file. For bash or sh shells, put: |
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You only need to do ``cvs login'' once. To obtain the source for the release: |
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\begin{verbatim} |
\begin{verbatim} |
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% cvs co -d directory -P -r release1 MITgcmUV |
% export CVSROOT=':pserver:cvsanon@mitgcm.org:/u/gcmpack' |
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\end{verbatim} |
\end{verbatim} |
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in your \texttt{.profile} or \texttt{.bashrc} file. |
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This creates a directory called \textit{directory}. If \textit{directory} |
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exists this command updates your code based on the repository. Each |
To get MITgcm through CVS, first register with the MITgcm CVS server |
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directory in the source tree contains a directory \textit{CVS}. This |
using command: |
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information is required by CVS to keep track of your file versions with |
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respect to the repository. Don't edit the files in \textit{CVS}! To obtain a |
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different \textit{version} that is not the latest source: |
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\begin{verbatim} |
\begin{verbatim} |
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% cvs co -d directory -P -r version MITgcm |
% cvs login ( CVS password: cvsanon ) |
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\end{verbatim} |
\end{verbatim} |
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or the latest development version: |
You only need to do a ``cvs login'' once. |
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To obtain the latest sources type: |
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\begin{verbatim} |
\begin{verbatim} |
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% cvs co -d directory -P MITgcm |
% cvs co MITgcm |
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\end{verbatim} |
\end{verbatim} |
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or to get a specific release type: |
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\subsubsection{other methods} |
\begin{verbatim} |
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% cvs co -P -r checkpoint52i_post MITgcm |
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You can download the model as a tar file from the reference web site at: |
\end{verbatim} |
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The MITgcm web site contains further directions concerning the source |
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code and CVS. It also contains a web interface to our CVS archive so |
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that one may easily view the state of files, revisions, and other |
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development milestones: |
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\begin{rawhtml} <A href=''http://mitgcm.org/download'' target="idontexist"> \end{rawhtml} |
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\begin{verbatim} |
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http://mitgcm.org/source_code.html |
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\end{verbatim} |
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\begin{rawhtml} </A> \end{rawhtml} |
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As a convenience, the MITgcm CVS server contains aliases which are |
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named subsets of the codebase. These aliases can be especially |
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helpful when used over slow internet connections or on machines with |
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restricted storage space. Table \ref{tab:cvsModules} contains a list |
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of CVS aliases |
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\begin{table}[htb] |
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\centering |
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\begin{tabular}[htb]{|lp{3.25in}|}\hline |
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\textbf{Alias Name} & \textbf{Information (directories) Contained} \\\hline |
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\texttt{MITgcm\_code} & Only the source code -- none of the verification examples. \\ |
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\texttt{MITgcm\_verif\_basic} |
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& Source code plus a small set of the verification examples |
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(\texttt{global\_ocean.90x40x15}, \texttt{aim.5l\_cs}, \texttt{hs94.128x64x5}, |
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\texttt{front\_relax}, and \texttt{plume\_on\_slope}). \\ |
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\texttt{MITgcm\_verif\_atmos} & Source code plus all of the atmospheric examples. \\ |
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\texttt{MITgcm\_verif\_ocean} & Source code plus all of the oceanic examples. \\ |
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\texttt{MITgcm\_verif\_all} & Source code plus all of the |
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verification examples. \\\hline |
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\end{tabular} |
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\caption{MITgcm CVS Modules} |
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\label{tab:cvsModules} |
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\end{table} |
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The checkout process creates a directory called \textit{MITgcm}. If |
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the directory \textit{MITgcm} exists this command updates your code |
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based on the repository. Each directory in the source tree contains a |
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directory \textit{CVS}. This information is required by CVS to keep |
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track of your file versions with respect to the repository. Don't edit |
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the files in \textit{CVS}! You can also use CVS to download code |
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updates. More extensive information on using CVS for maintaining |
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MITgcm code can be found |
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\begin{rawhtml} <A href=''http://mitgcm.org/usingcvstoget.html'' target="idontexist"> \end{rawhtml} |
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here |
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\begin{rawhtml} </A> \end{rawhtml} |
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. |
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It is important to note that the CVS aliases in Table |
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\ref{tab:cvsModules} cannot be used in conjunction with the CVS |
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\texttt{-d DIRNAME} option. However, the \texttt{MITgcm} directories |
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they create can be changed to a different name following the check-out: |
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\begin{verbatim} |
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% cvs co MITgcm_verif_basic |
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% mv MITgcm MITgcm_verif_basic |
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\end{verbatim} |
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\subsection{Method 2 - Tar file download} |
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\label{sect:conventionalDownload} |
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If you do not have CVS on your system, you can download the model as a |
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tar file from the web site at: |
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\begin{rawhtml} <A href=http://mitgcm.org/download target="idontexist"> \end{rawhtml} |
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\begin{verbatim} |
\begin{verbatim} |
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http://mitgcm.org/download/ |
http://mitgcm.org/download/ |
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\end{verbatim} |
\end{verbatim} |
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\begin{rawhtml} </A> \end{rawhtml} |
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\subsection{Model and directory structure} |
The tar file still contains CVS information which we urge you not to |
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delete; even if you do not use CVS yourself the information can help |
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The ``numerical'' model is contained within a execution environment support |
us if you should need to send us your copy of the code. If a recent |
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wrapper. This wrapper is designed to provide a general framework for |
tar file does not exist, then please contact the developers through |
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grid-point models. MITgcmUV is a specific numerical model that uses the |
the |
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framework. Under this structure the model is split into execution |
\begin{rawhtml} <A href=''mailto:MITgcm-support@mitgcm.org"> \end{rawhtml} |
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environment support code and conventional numerical model code. The |
MITgcm-support@mitgcm.org |
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execution environment support code is held under the \textit{eesupp} |
\begin{rawhtml} </A> \end{rawhtml} |
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directory. The grid point model code is held under the \textit{model} |
mailing list. |
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directory. Code execution actually starts in the \textit{eesupp} routines |
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and not in the \textit{model} routines. For this reason the top-level |
\subsubsection{Upgrading from an earlier version} |
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\textit{MAIN.F} is in the \textit{eesupp/src} directory. In general, |
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end-users should not need to worry about this level. The top-level routine |
If you already have an earlier version of the code you can ``upgrade'' |
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for the numerical part of the code is in \textit{model/src/THE\_MODEL\_MAIN.F% |
your copy instead of downloading the entire repository again. First, |
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}. Here is a brief description of the directory structure of the model under |
``cd'' (change directory) to the top of your working copy: |
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the root tree (a detailed description is given in section 3: Code structure). |
\begin{verbatim} |
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% cd MITgcm |
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\begin{itemize} |
\end{verbatim} |
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\item \textit{bin}: this directory is initially empty. It is the default |
and then issue the cvs update command such as: |
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directory in which to compile the code. |
\begin{verbatim} |
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% cvs -q update -r checkpoint52i_post -d -P |
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\end{verbatim} |
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This will update the ``tag'' to ``checkpoint52i\_post'', add any new |
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directories (-d) and remove any empty directories (-P). The -q option |
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means be quiet which will reduce the number of messages you'll see in |
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the terminal. If you have modified the code prior to upgrading, CVS |
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will try to merge your changes with the upgrades. If there is a |
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conflict between your modifications and the upgrade, it will report |
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that file with a ``C'' in front, e.g.: |
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\begin{verbatim} |
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C model/src/ini_parms.F |
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\end{verbatim} |
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If the list of conflicts scrolled off the screen, you can re-issue the |
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cvs update command and it will report the conflicts. Conflicts are |
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indicated in the code by the delimites ``$<<<<<<<$'', ``======='' and |
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``$>>>>>>>$''. For example, |
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{\small |
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\begin{verbatim} |
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<<<<<<< ini_parms.F |
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& bottomDragLinear,myOwnBottomDragCoefficient, |
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======= |
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& bottomDragLinear,bottomDragQuadratic, |
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>>>>>>> 1.18 |
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\end{verbatim} |
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} |
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means that you added ``myOwnBottomDragCoefficient'' to a namelist at |
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the same time and place that we added ``bottomDragQuadratic''. You |
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need to resolve this conflict and in this case the line should be |
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changed to: |
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{\small |
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\begin{verbatim} |
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& bottomDragLinear,bottomDragQuadratic,myOwnBottomDragCoefficient, |
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\end{verbatim} |
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} |
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and the lines with the delimiters ($<<<<<<$,======,$>>>>>>$) be deleted. |
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Unless you are making modifications which exactly parallel |
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developments we make, these types of conflicts should be rare. |
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\paragraph*{Upgrading to the current pre-release version} |
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We don't make a ``release'' for every little patch and bug fix in |
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order to keep the frequency of upgrades to a minimum. However, if you |
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have run into a problem for which ``we have already fixed in the |
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latest code'' and we haven't made a ``tag'' or ``release'' since that |
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patch then you'll need to get the latest code: |
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\begin{verbatim} |
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% cvs -q update -A -d -P |
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\end{verbatim} |
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Unlike, the ``check-out'' and ``update'' procedures above, there is no |
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``tag'' or release name. The -A tells CVS to upgrade to the |
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very latest version. As a rule, we don't recommend this since you |
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might upgrade while we are in the processes of checking in the code so |
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that you may only have part of a patch. Using this method of updating |
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also means we can't tell what version of the code you are working |
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with. So please be sure you understand what you're doing. |
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\section{Model and directory structure} |
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\begin{rawhtml} |
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<!-- CMIREDIR:directory_structure: --> |
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\end{rawhtml} |
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|
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The ``numerical'' model is contained within a execution environment |
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support wrapper. This wrapper is designed to provide a general |
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framework for grid-point models. MITgcmUV is a specific numerical |
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model that uses the framework. Under this structure the model is split |
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into execution environment support code and conventional numerical |
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model code. The execution environment support code is held under the |
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\textit{eesupp} directory. The grid point model code is held under the |
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\textit{model} directory. Code execution actually starts in the |
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\textit{eesupp} routines and not in the \textit{model} routines. For |
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this reason the top-level \textit{MAIN.F} is in the |
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\textit{eesupp/src} directory. In general, end-users should not need |
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to worry about this level. The top-level routine for the numerical |
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part of the code is in \textit{model/src/THE\_MODEL\_MAIN.F}. Here is |
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a brief description of the directory structure of the model under the |
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root tree (a detailed description is given in section 3: Code |
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structure). |
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\begin{itemize} |
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\item \textit{bin}: this directory is initially empty. It is the |
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default directory in which to compile the code. |
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\item \textit{diags}: contains the code relative to time-averaged |
\item \textit{diags}: contains the code relative to time-averaged |
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diagnostics. It is subdivided into two subdirectories \textit{inc} and |
diagnostics. It is subdivided into two subdirectories \textit{inc} |
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\textit{src} that contain include files (*.\textit{h} files) and fortran |
and \textit{src} that contain include files (*.\textit{h} files) and |
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subroutines (*.\textit{F} files), respectively. |
Fortran subroutines (*.\textit{F} files), respectively. |
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\item \textit{doc}: contains brief documentation notes. |
\item \textit{doc}: contains brief documentation notes. |
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\item \textit{eesupp}: contains the execution environment source code. Also |
\item \textit{eesupp}: contains the execution environment source code. |
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subdivided into two subdirectories \textit{inc} and \textit{src}. |
Also subdivided into two subdirectories \textit{inc} and |
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\textit{src}. |
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\item \textit{exe}: this directory is initially empty. It is the default |
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directory in which to execute the code. |
\item \textit{exe}: this directory is initially empty. It is the |
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default directory in which to execute the code. |
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\item \textit{model}: this directory contains the main source code. Also |
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subdivided into two subdirectories \textit{inc} and \textit{src}. |
\item \textit{model}: this directory contains the main source code. |
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Also subdivided into two subdirectories \textit{inc} and |
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\item \textit{pkg}: contains the source code for the packages. Each package |
\textit{src}. |
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corresponds to a subdirectory. For example, \textit{gmredi} contains the |
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code related to the Gent-McWilliams/Redi scheme, \textit{aim} the code |
\item \textit{pkg}: contains the source code for the packages. Each |
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relative to the atmospheric intermediate physics. The packages are described |
package corresponds to a subdirectory. For example, \textit{gmredi} |
| 312 |
in detail in section 3. |
contains the code related to the Gent-McWilliams/Redi scheme, |
| 313 |
|
\textit{aim} the code relative to the atmospheric intermediate |
| 314 |
\item \textit{tools}: this directory contains various useful tools. For |
physics. The packages are described in detail in section 3. |
| 315 |
example, \textit{genmake} is a script written in csh (C-shell) that should |
|
| 316 |
be used to generate your makefile. The directory \textit{adjoint} contains |
\item \textit{tools}: this directory contains various useful tools. |
| 317 |
the makefile specific to the Tangent linear and Adjoint Compiler (TAMC) that |
For example, \textit{genmake2} is a script written in csh (C-shell) |
| 318 |
generates the adjoint code. The latter is described in details in part V. |
that should be used to generate your makefile. The directory |
| 319 |
|
\textit{adjoint} contains the makefile specific to the Tangent |
| 320 |
|
linear and Adjoint Compiler (TAMC) that generates the adjoint code. |
| 321 |
|
The latter is described in details in part V. |
| 322 |
|
|
| 323 |
\item \textit{utils}: this directory contains various utilities. The |
\item \textit{utils}: this directory contains various utilities. The |
| 324 |
subdirectory \textit{knudsen2} contains code and a makefile that compute |
subdirectory \textit{knudsen2} contains code and a makefile that |
| 325 |
coefficients of the polynomial approximation to the knudsen formula for an |
compute coefficients of the polynomial approximation to the knudsen |
| 326 |
ocean nonlinear equation of state. The \textit{matlab} subdirectory contains |
formula for an ocean nonlinear equation of state. The |
| 327 |
matlab scripts for reading model output directly into matlab. \textit{scripts% |
\textit{matlab} subdirectory contains matlab scripts for reading |
| 328 |
} contains C-shell post-processing scripts for joining processor-based and |
model output directly into matlab. \textit{scripts} contains C-shell |
| 329 |
tiled-based model output. |
post-processing scripts for joining processor-based and tiled-based |
| 330 |
|
model output. |
| 331 |
|
|
| 332 |
|
\item \textit{verification}: this directory contains the model |
| 333 |
|
examples. See section \ref{sect:modelExamples}. |
| 334 |
|
|
|
\item \textit{verification}: this directory contains the model examples. See |
|
|
below. |
|
| 335 |
\end{itemize} |
\end{itemize} |
| 336 |
|
|
| 337 |
\subsection{Model examples} |
\section[MITgcm Example Experiments]{Example experiments} |
| 338 |
|
\label{sect:modelExamples} |
| 339 |
Now that you have successfully downloaded the model code we recommend that |
\begin{rawhtml} |
| 340 |
you first try to run the examples provided with the base version. You will |
<!-- CMIREDIR:modelExamples: --> |
| 341 |
probably want to run the example that is the closest to the configuration |
\end{rawhtml} |
| 342 |
you will use eventually. The examples are located in subdirectories under |
|
| 343 |
the directory \textit{verification} and are briefly described below (a full |
%% a set of twenty-four pre-configured numerical experiments |
| 344 |
description is given in section 2): |
|
| 345 |
|
The MITgcm distribution comes with more than a dozen pre-configured |
| 346 |
|
numerical experiments. Some of these example experiments are tests of |
| 347 |
|
individual parts of the model code, but many are fully fledged |
| 348 |
|
numerical simulations. A few of the examples are used for tutorial |
| 349 |
|
documentation in sections \ref{sect:eg-baro} - \ref{sect:eg-global}. |
| 350 |
|
The other examples follow the same general structure as the tutorial |
| 351 |
|
examples. However, they only include brief instructions in a text file |
| 352 |
|
called {\it README}. The examples are located in subdirectories under |
| 353 |
|
the directory \textit{verification}. Each example is briefly described |
| 354 |
|
below. |
| 355 |
|
|
| 356 |
\subsubsection{List of model examples} |
\subsection{Full list of model examples} |
| 357 |
|
|
| 358 |
\begin{itemize} |
\begin{enumerate} |
| 359 |
|
|
| 360 |
\item \textit{exp0} - single layer, ocean double gyre (barotropic with |
\item \textit{exp0} - single layer, ocean double gyre (barotropic with |
| 361 |
free-surface). |
free-surface). This experiment is described in detail in section |
| 362 |
|
\ref{sect:eg-baro}. |
|
\item \textit{exp1} - 4 layers, ocean double gyre. |
|
| 363 |
|
|
| 364 |
|
\item \textit{exp1} - Four layer, ocean double gyre. This experiment |
| 365 |
|
is described in detail in section \ref{sect:eg-baroc}. |
| 366 |
|
|
| 367 |
\item \textit{exp2} - 4x4 degree global ocean simulation with steady |
\item \textit{exp2} - 4x4 degree global ocean simulation with steady |
| 368 |
climatological forcing. |
climatological forcing. This experiment is described in detail in |
| 369 |
|
section \ref{sect:eg-global}. |
| 370 |
\item \textit{exp4} - flow over a Gaussian bump in open-water or channel |
|
| 371 |
with open boundaries. |
\item \textit{exp4} - Flow over a Gaussian bump in open-water or |
| 372 |
|
channel with open boundaries. |
| 373 |
\item \textit{exp5} - inhomogenously forced ocean convection in a doubly |
|
| 374 |
periodic box. |
\item \textit{exp5} - Inhomogenously forced ocean convection in a |
| 375 |
|
doubly periodic box. |
| 376 |
|
|
| 377 |
\item \textit{front\_relax} - relaxation of an ocean thermal front (test for |
\item \textit{front\_relax} - Relaxation of an ocean thermal front (test for |
| 378 |
Gent/McWilliams scheme). 2D (Y-Z). |
Gent/McWilliams scheme). 2D (Y-Z). |
| 379 |
|
|
| 380 |
\item \textit{internal wave} - ocean internal wave forced by open boundary |
\item \textit{internal wave} - Ocean internal wave forced by open |
| 381 |
conditions. |
boundary conditions. |
| 382 |
|
|
| 383 |
\item \textit{natl\_box} - eastern subtropical North Atlantic with KPP |
\item \textit{natl\_box} - Eastern subtropical North Atlantic with KPP |
| 384 |
scheme; 1 month integration |
scheme; 1 month integration |
| 385 |
|
|
| 386 |
\item \textit{hs94.1x64x5} - zonal averaged atmosphere using Held and Suarez |
\item \textit{hs94.1x64x5} - Zonal averaged atmosphere using Held and |
| 387 |
'94 forcing. |
Suarez '94 forcing. |
| 388 |
|
|
| 389 |
\item \textit{hs94.128x64x5} - 3D atmosphere dynamics using Held and Suarez |
\item \textit{hs94.128x64x5} - 3D atmosphere dynamics using Held and |
| 390 |
'94 forcing. |
Suarez '94 forcing. |
| 391 |
|
|
| 392 |
\item \textit{hs94.cs-32x32x5} - 3D atmosphere dynamics using Held and |
\item \textit{hs94.cs-32x32x5} - 3D atmosphere dynamics using Held and |
| 393 |
Suarez '94 forcing on the cubed sphere. |
Suarez '94 forcing on the cubed sphere. |
| 394 |
|
|
| 395 |
\item \textit{aim.5l\_zon-ave} - Intermediate Atmospheric physics, 5 layers |
\item \textit{aim.5l\_zon-ave} - Intermediate Atmospheric physics. |
| 396 |
Molteni physics package. Global Zonal Mean configuration, 1x64x5 resolution. |
Global Zonal Mean configuration, 1x64x5 resolution. |
| 397 |
|
|
| 398 |
\item \textit{aim.5l\_XZ\_Equatorial\_Slice} - Intermediate Atmospheric |
\item \textit{aim.5l\_XZ\_Equatorial\_Slice} - Intermediate |
| 399 |
physics, 5 layers Molteni physics package. Equatorial Slice configuration. |
Atmospheric physics, equatorial Slice configuration. 2D (X-Z). |
| 400 |
2D (X-Z). |
|
|
|
|
| 401 |
\item \textit{aim.5l\_Equatorial\_Channel} - Intermediate Atmospheric |
\item \textit{aim.5l\_Equatorial\_Channel} - Intermediate Atmospheric |
| 402 |
physics, 5 layers Molteni physics package. 3D Equatorial Channel |
physics. 3D Equatorial Channel configuration. |
| 403 |
configuration (not completely tested). |
|
| 404 |
|
\item \textit{aim.5l\_LatLon} - Intermediate Atmospheric physics. |
| 405 |
\item \textit{aim.5l\_LatLon} - Intermediate Atmospheric physics, 5 layers |
Global configuration, on latitude longitude grid with 128x64x5 grid |
| 406 |
Molteni physics package. Global configuration, 128x64x5 resolution. |
points ($2.8^\circ{\rm degree}$ resolution). |
| 407 |
|
|
| 408 |
|
\item \textit{adjustment.128x64x1} Barotropic adjustment problem on |
| 409 |
|
latitude longitude grid with 128x64 grid points ($2.8^\circ{\rm |
| 410 |
|
degree}$ resolution). |
| 411 |
|
|
| 412 |
|
\item \textit{adjustment.cs-32x32x1} Barotropic adjustment problem on |
| 413 |
|
cube sphere grid with 32x32 points per face ( roughly $2.8^\circ{\rm |
| 414 |
|
degree}$ resolution). |
| 415 |
|
|
| 416 |
|
\item \textit{advect\_cs} Two-dimensional passive advection test on |
| 417 |
|
cube sphere grid. |
| 418 |
|
|
| 419 |
|
\item \textit{advect\_xy} Two-dimensional (horizontal plane) passive |
| 420 |
|
advection test on Cartesian grid. |
| 421 |
|
|
| 422 |
|
\item \textit{advect\_yz} Two-dimensional (vertical plane) passive |
| 423 |
|
advection test on Cartesian grid. |
| 424 |
|
|
| 425 |
|
\item \textit{carbon} Simple passive tracer experiment. Includes |
| 426 |
|
derivative calculation. Described in detail in section |
| 427 |
|
\ref{sect:eg-carbon-ad}. |
| 428 |
|
|
| 429 |
|
\item \textit{flt\_example} Example of using float package. |
| 430 |
|
|
| 431 |
|
\item \textit{global\_ocean.90x40x15} Global circulation with GM, flux |
| 432 |
|
boundary conditions and poles. |
| 433 |
|
|
| 434 |
|
\item \textit{global\_ocean\_pressure} Global circulation in pressure |
| 435 |
|
coordinate (non-Boussinesq ocean model). Described in detail in |
| 436 |
|
section \ref{sect:eg-globalpressure}. |
| 437 |
|
|
| 438 |
|
\item \textit{solid-body.cs-32x32x1} Solid body rotation test for cube |
| 439 |
|
sphere grid. |
| 440 |
|
|
| 441 |
\item \textit{adjustment.128x64x1} |
\end{enumerate} |
| 442 |
|
|
| 443 |
\item \textit{adjustment.cs-32x32x1} |
\subsection{Directory structure of model examples} |
|
\end{itemize} |
|
|
|
|
|
\subsubsection{Directory structure of model examples} |
|
| 444 |
|
|
| 445 |
Each example directory has the following subdirectories: |
Each example directory has the following subdirectories: |
| 446 |
|
|
| 447 |
\begin{itemize} |
\begin{itemize} |
| 448 |
\item \textit{code}: contains the code particular to the example. At a |
\item \textit{code}: contains the code particular to the example. At a |
| 449 |
minimum, this directory includes the following files: |
minimum, this directory includes the following files: |
|
|
|
|
\begin{itemize} |
|
|
\item \textit{code/CPP\_EEOPTIONS.h}: declares CPP keys relative to the |
|
|
``execution environment'' part of the code. The default version is located |
|
|
in \textit{eesupp/inc}. |
|
|
|
|
|
\item \textit{code/CPP\_OPTIONS.h}: declares CPP keys relative to the |
|
|
``numerical model'' part of the code. The default version is located in |
|
|
\textit{model/inc}. |
|
|
|
|
|
\item \textit{code/SIZE.h}: declares size of underlying computational grid. |
|
|
The default version is located in \textit{model/inc}. |
|
|
\end{itemize} |
|
|
|
|
|
In addition, other include files and subroutines might be present in \textit{% |
|
|
code} depending on the particular experiment. See section 2 for more details. |
|
|
|
|
|
\item \textit{input}: contains the input data files required to run the |
|
|
example. At a mimimum, the \textit{input} directory contains the following |
|
|
files: |
|
|
|
|
|
\begin{itemize} |
|
|
\item \textit{input/data}: this file, written as a namelist, specifies the |
|
|
main parameters for the experiment. |
|
|
|
|
|
\item \textit{input/data.pkg}: contains parameters relative to the packages |
|
|
used in the experiment. |
|
|
|
|
|
\item \textit{input/eedata}: this file contains ``execution environment'' |
|
|
data. At present, this consists of a specification of the number of threads |
|
|
to use in $X$ and $Y$ under multithreaded execution. |
|
|
\end{itemize} |
|
|
|
|
|
In addition, you will also find in this directory the forcing and topography |
|
|
files as well as the files describing the initial state of the experiment. |
|
|
This varies from experiment to experiment. See section 2 for more details. |
|
|
|
|
|
\item \textit{results}: this directory contains the output file \textit{% |
|
|
output.txt} produced by the simulation example. This file is useful for |
|
|
comparison with your own output when you run the experiment. |
|
|
\end{itemize} |
|
|
|
|
|
Once you have chosen the example you want to run, you are ready to compile |
|
|
the code. |
|
| 450 |
|
|
| 451 |
\subsection{Compiling the code} |
\begin{itemize} |
| 452 |
|
\item \textit{code/CPP\_EEOPTIONS.h}: declares CPP keys relative to |
| 453 |
\subsubsection{The script \textit{genmake}} |
the ``execution environment'' part of the code. The default |
| 454 |
|
version is located in \textit{eesupp/inc}. |
| 455 |
To compile the code, use the script \textit{genmake} located in the \textit{% |
|
| 456 |
tools} directory. \textit{genmake} is a script that generates the makefile. |
\item \textit{code/CPP\_OPTIONS.h}: declares CPP keys relative to |
| 457 |
It has been written so that the code can be compiled on a wide diversity of |
the ``numerical model'' part of the code. The default version is |
| 458 |
machines and systems. However, if it doesn't work the first time on your |
located in \textit{model/inc}. |
| 459 |
platform, you might need to edit certain lines of \textit{genmake} in the |
|
| 460 |
section containing the setups for the different machines. The file is |
\item \textit{code/SIZE.h}: declares size of underlying |
| 461 |
structured like this: |
computational grid. The default version is located in |
| 462 |
\begin{verbatim} |
\textit{model/inc}. |
| 463 |
. |
\end{itemize} |
| 464 |
. |
|
| 465 |
. |
In addition, other include files and subroutines might be present in |
| 466 |
general instructions (machine independent) |
\textit{code} depending on the particular experiment. See Section 2 |
| 467 |
. |
for more details. |
| 468 |
. |
|
| 469 |
. |
\item \textit{input}: contains the input data files required to run |
| 470 |
- setup machine 1 |
the example. At a minimum, the \textit{input} directory contains the |
| 471 |
- setup machine 2 |
following files: |
| 472 |
- setup machine 3 |
|
| 473 |
- setup machine 4 |
\begin{itemize} |
| 474 |
etc |
\item \textit{input/data}: this file, written as a namelist, |
| 475 |
. |
specifies the main parameters for the experiment. |
| 476 |
. |
|
| 477 |
. |
\item \textit{input/data.pkg}: contains parameters relative to the |
| 478 |
\end{verbatim} |
packages used in the experiment. |
| 479 |
|
|
| 480 |
For example, the setup corresponding to a DEC alpha machine is reproduced |
\item \textit{input/eedata}: this file contains ``execution |
| 481 |
here: |
environment'' data. At present, this consists of a specification |
| 482 |
\begin{verbatim} |
of the number of threads to use in $X$ and $Y$ under multithreaded |
| 483 |
case OSF1+mpi: |
execution. |
| 484 |
echo "Configuring for DEC Alpha" |
\end{itemize} |
| 485 |
set CPP = ( '/usr/bin/cpp -P' ) |
|
| 486 |
set DEFINES = ( ${DEFINES} '-DTARGET_DEC -DWORDLENGTH=1' ) |
In addition, you will also find in this directory the forcing and |
| 487 |
set KPP = ( 'kapf' ) |
topography files as well as the files describing the initial state |
| 488 |
set KPPFILES = ( 'main.F' ) |
of the experiment. This varies from experiment to experiment. See |
| 489 |
set KFLAGS1 = ( '-scan=132 -noconc -cmp=' ) |
section 2 for more details. |
| 490 |
set FC = ( 'f77' ) |
|
| 491 |
set FFLAGS = ( '-convert big_endian -r8 -extend_source -automatic -call_shared -notransform_loops -align dcommons' ) |
\item \textit{results}: this directory contains the output file |
| 492 |
set FOPTIM = ( '-O5 -fast -tune host -inline all' ) |
\textit{output.txt} produced by the simulation example. This file is |
| 493 |
set NOOPTFLAGS = ( '-O0' ) |
useful for comparison with your own output when you run the |
| 494 |
set LIBS = ( '-lfmpi -lmpi -lkmp_osfp10 -pthread' ) |
experiment. |
| 495 |
set NOOPTFILES = ( 'barrier.F different_multiple.F external_fields_load.F') |
\end{itemize} |
| 496 |
set RMFILES = ( '*.p.out' ) |
|
| 497 |
breaksw |
Once you have chosen the example you want to run, you are ready to |
| 498 |
\end{verbatim} |
compile the code. |
| 499 |
|
|
| 500 |
Typically, these are the lines that you might need to edit to make \textit{% |
\section[Building MITgcm]{Building the code} |
| 501 |
genmake} work on your platform if it doesn't work the first time. \textit{% |
\label{sect:buildingCode} |
| 502 |
genmake} understands several options that are described here: |
\begin{rawhtml} |
| 503 |
|
<!-- CMIREDIR:buildingCode: --> |
| 504 |
\begin{itemize} |
\end{rawhtml} |
| 505 |
\item -rootdir=dir |
|
| 506 |
|
To compile the code, we use the {\em make} program. This uses a file |
| 507 |
indicates where the model root directory is relative to the directory where |
({\em Makefile}) that allows us to pre-process source files, specify |
| 508 |
you are compiling. This option is not needed if you compile in the \textit{% |
compiler and optimization options and also figures out any file |
| 509 |
bin} directory (which is the default compilation directory) or within the |
dependencies. We supply a script ({\em genmake2}), described in |
| 510 |
\textit{verification} tree. |
section \ref{sect:genmake}, that automatically creates the {\em |
| 511 |
|
Makefile} for you. You then need to build the dependencies and |
| 512 |
\item -mods=dir1,dir2,... |
compile the code. |
| 513 |
|
|
| 514 |
indicates the relative or absolute paths directories where the sources |
As an example, let's assume that you want to build and run experiment |
| 515 |
should take precedence over the default versions (located in \textit{model}, |
\textit{verification/exp2}. The are multiple ways and places to |
| 516 |
\textit{eesupp},...). Typically, this option is used when running the |
actually do this but here let's build the code in |
| 517 |
examples, see below. |
\textit{verification/exp2/input}: |
| 518 |
|
\begin{verbatim} |
| 519 |
\item -enable=pkg1,pkg2,... |
% cd verification/exp2/input |
| 520 |
|
\end{verbatim} |
| 521 |
enables packages source code \textit{pkg1}, \textit{pkg2},... when creating |
First, build the {\em Makefile}: |
| 522 |
the makefile. |
\begin{verbatim} |
| 523 |
|
% ../../../tools/genmake2 -mods=../code |
| 524 |
\item -disable=pkg1,pkg2,... |
\end{verbatim} |
| 525 |
|
The command line option tells {\em genmake} to override model source |
| 526 |
disables packages source code \textit{pkg1}, \textit{pkg2},... when creating |
code with any files in the directory {\em ../code/}. |
|
the makefile. |
|
|
|
|
|
\item -platform=machine |
|
|
|
|
|
specifies the platform for which you want the makefile. In general, you |
|
|
won't need this option. \textit{genmake} will select the right machine for |
|
|
you (the one you're working on!). However, this option is useful if you have |
|
|
a choice of several compilers on one machine and you want to use the one |
|
|
that is not the default (ex: \texttt{pgf77} instead of \texttt{f77} under |
|
|
Linux). |
|
|
|
|
|
\item -mpi |
|
|
|
|
|
this is used when you want to run the model in parallel processing mode |
|
|
under mpi (see section on parallel computation for more details). |
|
| 527 |
|
|
| 528 |
\item -jam |
On many systems, the {\em genmake2} program will be able to |
| 529 |
|
automatically recognize the hardware, find compilers and other tools |
| 530 |
|
within the user's path (``echo \$PATH''), and then choose an |
| 531 |
|
appropriate set of options from the files (``optfiles'') contained in |
| 532 |
|
the {\em tools/build\_options} directory. Under some circumstances, a |
| 533 |
|
user may have to create a new ``optfile'' in order to specify the |
| 534 |
|
exact combination of compiler, compiler flags, libraries, and other |
| 535 |
|
options necessary to build a particular configuration of MITgcm. In |
| 536 |
|
such cases, it is generally helpful to read the existing ``optfiles'' |
| 537 |
|
and mimic their syntax. |
| 538 |
|
|
| 539 |
|
Through the MITgcm-support list, the MITgcm developers are willing to |
| 540 |
|
provide help writing or modifing ``optfiles''. And we encourage users |
| 541 |
|
to post new ``optfiles'' (particularly ones for new machines or |
| 542 |
|
architectures) to the |
| 543 |
|
\begin{rawhtml} <A href=''mailto:MITgcm-support@mitgcm.org"> \end{rawhtml} |
| 544 |
|
MITgcm-support@mitgcm.org |
| 545 |
|
\begin{rawhtml} </A> \end{rawhtml} |
| 546 |
|
list. |
| 547 |
|
|
| 548 |
this is used when you want to run the model in parallel processing mode |
To specify an optfile to {\em genmake2}, the syntax is: |
| 549 |
under jam (see section on parallel computation for more details). |
\begin{verbatim} |
| 550 |
\end{itemize} |
% ../../../tools/genmake2 -mods=../code -of /path/to/optfile |
| 551 |
|
\end{verbatim} |
| 552 |
|
|
| 553 |
For some of the examples, there is a file called \textit{.genmakerc} in the |
Once a {\em Makefile} has been generated, we create the dependencies: |
|
\textit{input} directory that has the relevant \textit{genmake} options for |
|
|
that particular example. In this way you don't need to type the options when |
|
|
invoking \textit{genmake}. |
|
|
|
|
|
\subsubsection{Compiling} |
|
|
|
|
|
Let's assume that you want to run, say, example \textit{exp2} in the \textit{% |
|
|
input} directory. To compile the code, type the following commands from the |
|
|
model root tree: |
|
| 554 |
\begin{verbatim} |
\begin{verbatim} |
|
% cd verification/exp2/input |
|
|
% ../../../tools/genmake |
|
| 555 |
% make depend |
% make depend |
|
% make |
|
| 556 |
\end{verbatim} |
\end{verbatim} |
| 557 |
|
This modifies the {\em Makefile} by attaching a [long] list of files |
| 558 |
|
upon which other files depend. The purpose of this is to reduce |
| 559 |
|
re-compilation if and when you start to modify the code. The {\tt make |
| 560 |
|
depend} command also creates links from the model source to this |
| 561 |
|
directory. It is important to note that the {\tt make depend} stage |
| 562 |
|
will occasionally produce warnings or errors since the dependency |
| 563 |
|
parsing tool is unable to find all of the necessary header files |
| 564 |
|
(\textit{eg.} \texttt{netcdf.inc}). In these circumstances, it is |
| 565 |
|
usually OK to ignore the warnings/errors and proceed to the next step. |
| 566 |
|
|
| 567 |
If there is no \textit{.genmakerc} in the \textit{input} directory, you have |
Next compile the code: |
|
to use the following options when invoking \textit{genmake}: |
|
| 568 |
\begin{verbatim} |
\begin{verbatim} |
| 569 |
% ../../../tools/genmake -mods=../code |
% make |
| 570 |
\end{verbatim} |
\end{verbatim} |
| 571 |
|
The {\tt make} command creates an executable called \textit{mitgcmuv}. |
| 572 |
|
Additional make ``targets'' are defined within the makefile to aid in |
| 573 |
|
the production of adjoint and other versions of MITgcm. |
| 574 |
|
|
| 575 |
In addition, you will probably want to disable some of the packages. Taking |
Now you are ready to run the model. General instructions for doing so are |
| 576 |
again the case of \textit{exp2}, the full \textit{genmake} command will |
given in section \ref{sect:runModel}. Here, we can run the model with: |
|
probably look like this: |
|
| 577 |
\begin{verbatim} |
\begin{verbatim} |
| 578 |
% ../../../tools/genmake -mods=../code -disable=kpp,gmredi,aim,... |
./mitgcmuv > output.txt |
| 579 |
\end{verbatim} |
\end{verbatim} |
| 580 |
|
where we are re-directing the stream of text output to the file {\em |
| 581 |
|
output.txt}. |
| 582 |
|
|
| 583 |
|
|
| 584 |
The make command creates an executable called \textit{mitgcmuv}. |
\section[Running MITgcm]{Running the model in prognostic mode} |
| 585 |
|
\label{sect:runModel} |
| 586 |
|
\begin{rawhtml} |
| 587 |
|
<!-- CMIREDIR:runModel: --> |
| 588 |
|
\end{rawhtml} |
| 589 |
|
|
| 590 |
Note that you can compile and run the code in another directory than \textit{% |
If compilation finished succesfuully (section \ref{sect:buildingCode}) |
| 591 |
input}. You just need to make sure that you copy the input data files into |
then an executable called \texttt{mitgcmuv} will now exist in the |
| 592 |
the directory where you want to run the model. For example to compile from |
local directory. |
| 593 |
\textit{code}: |
|
| 594 |
|
To run the model as a single process (\textit{ie.} not in parallel) |
| 595 |
|
simply type: |
| 596 |
\begin{verbatim} |
\begin{verbatim} |
| 597 |
% cd verification/exp2/code |
% ./mitgcmuv |
| 598 |
% ../../../tools/genmake |
\end{verbatim} |
| 599 |
% make depend |
The ``./'' is a safe-guard to make sure you use the local executable |
| 600 |
% make |
in case you have others that exist in your path (surely odd if you |
| 601 |
|
do!). The above command will spew out many lines of text output to |
| 602 |
|
your screen. This output contains details such as parameter values as |
| 603 |
|
well as diagnostics such as mean Kinetic energy, largest CFL number, |
| 604 |
|
etc. It is worth keeping this text output with the binary output so we |
| 605 |
|
normally re-direct the {\em stdout} stream as follows: |
| 606 |
|
\begin{verbatim} |
| 607 |
|
% ./mitgcmuv > output.txt |
| 608 |
\end{verbatim} |
\end{verbatim} |
| 609 |
|
In the event that the model encounters an error and stops, it is very |
| 610 |
|
helpful to include the last few line of this \texttt{output.txt} file |
| 611 |
|
along with the (\texttt{stderr}) error message within any bug reports. |
| 612 |
|
|
| 613 |
|
For the example experiments in {\em verification}, an example of the |
| 614 |
|
output is kept in {\em results/output.txt} for comparison. You can |
| 615 |
|
compare your {\em output.txt} with the corresponding one for that |
| 616 |
|
experiment to check that the set-up works. |
| 617 |
|
|
| 618 |
|
|
| 619 |
|
|
| 620 |
|
\subsection{Output files} |
| 621 |
|
|
| 622 |
\subsection{Running the model} |
The model produces various output files. Depending upon the I/O |
| 623 |
|
package selected (either \texttt{mdsio} or \texttt{mnc} or both as |
| 624 |
|
determined by both the compile-time settings and the run-time flags in |
| 625 |
|
\texttt{data.pkg}), the following output may appear. |
| 626 |
|
|
|
The first thing to do is to run the code by typing \textit{mitgcmuv} and see |
|
|
what happens. You can compare what you get with what is in the \textit{% |
|
|
results} directory. Unless noted otherwise, most examples are set up to run |
|
|
for a few time steps only so that you can quickly figure out whether the |
|
|
model is working or not. |
|
| 627 |
|
|
| 628 |
\subsubsection{Output files} |
\subsubsection{MDSIO output files} |
| 629 |
|
|
| 630 |
The model produces various output files. At a minimum, the instantaneous |
The ``traditional'' output files are generated by the \texttt{mdsio} |
| 631 |
``state'' of the model is written out, which is made of the following files: |
package. At a minimum, the instantaneous ``state'' of the model is |
| 632 |
|
written out, which is made of the following files: |
| 633 |
|
|
| 634 |
\begin{itemize} |
\begin{itemize} |
| 635 |
\item \textit{U.00000nIter} - zonal component of velocity field (m/s and $> |
\item \textit{U.00000nIter} - zonal component of velocity field (m/s and $> |
| 677 |
used to restart the model but are overwritten every other time they are |
used to restart the model but are overwritten every other time they are |
| 678 |
output to save disk space during long integrations. |
output to save disk space during long integrations. |
| 679 |
|
|
|
\subsubsection{Looking at the output} |
|
|
|
|
|
All the model data are written according to a ``meta/data'' file format. |
|
|
Each variable is associated with two files with suffix names \textit{.data} |
|
|
and \textit{.meta}. The \textit{.data} file contains the data written in |
|
|
binary form (big\_endian by default). The \textit{.meta} file is a |
|
|
``header'' file that contains information about the size and the structure |
|
|
of the \textit{.data} file. This way of organizing the output is |
|
|
particularly useful when running multi-processors calculations. The base |
|
|
version of the model includes a few matlab utilities to read output files |
|
|
written in this format. The matlab scripts are located in the directory |
|
|
\textit{utils/matlab} under the root tree. The script \textit{rdmds.m} reads |
|
|
the data. Look at the comments inside the script to see how to use it. |
|
|
|
|
|
\section{Code structure} |
|
|
|
|
|
\section{Doing it yourself: customizing the code} |
|
|
|
|
|
\subsection{\protect\bigskip Configuration and setup} |
|
|
|
|
|
When you are ready to run the model in the configuration you want, the |
|
|
easiest thing is to use and adapt the setup of the case studies experiment |
|
|
(described previously) that is the closest to your configuration. Then, the |
|
|
amount of setup will be minimized. In this section, we focus on the setup |
|
|
relative to the ''numerical model'' part of the code (the setup relative to |
|
|
the ''execution environment'' part is covered in the parallel implementation |
|
|
section) and on the variables and parameters that you are likely to change. |
|
|
|
|
|
The CPP keys relative to the ''numerical model'' part of the code are all |
|
|
defined and set in the file \textit{CPP\_OPTIONS.h }in the directory \textit{% |
|
|
model/inc }or in one of the \textit{code }directories of the case study |
|
|
experiments under \textit{verification.} The model parameters are defined |
|
|
and declared in the file \textit{model/inc/PARAMS.h }and their default |
|
|
values are set in the routine \textit{model/src/set\_defaults.F. }The |
|
|
default values can be modified in the namelist file \textit{data }which |
|
|
needs to be located in the directory where you will run the model. The |
|
|
parameters are initialized in the routine \textit{model/src/ini\_parms.F}. |
|
|
Look at this routine to see in what part of the namelist the parameters are |
|
|
located. |
|
|
|
|
|
In what follows the parameters are grouped into categories related to the |
|
|
computational domain, the equations solved in the model, and the simulation |
|
|
controls. |
|
|
|
|
|
\subsubsection{Computational domain, geometry and time-discretization} |
|
|
|
|
|
\begin{itemize} |
|
|
\item dimensions |
|
|
\end{itemize} |
|
|
|
|
|
The number of points in the x, y,\textit{\ }and r\textit{\ }directions are |
|
|
represented by the variables \textbf{sNx}\textit{, }\textbf{sNy}\textit{, }% |
|
|
and \textbf{Nr}\textit{\ }respectively which are declared and set in the |
|
|
file \textit{model/inc/SIZE.h. }(Again, this assumes a mono-processor |
|
|
calculation. For multiprocessor calculations see section on parallel |
|
|
implementation.) |
|
|
|
|
|
\begin{itemize} |
|
|
\item grid |
|
|
\end{itemize} |
|
|
|
|
|
Three different grids are available: cartesian, spherical polar, and |
|
|
curvilinear (including the cubed sphere). The grid is set through the |
|
|
logical variables \textbf{usingCartesianGrid}\textit{, }\textbf{% |
|
|
usingSphericalPolarGrid}\textit{, }and \textit{\ }\textbf{% |
|
|
usingCurvilinearGrid}\textit{. }In the case of spherical and curvilinear |
|
|
grids, the southern boundary is defined through the variable \textbf{phiMin}% |
|
|
\textit{\ }which corresponds to the latitude of the southern most cell face |
|
|
(in degrees). The resolution along the x and y directions is controlled by |
|
|
the 1D arrays \textbf{delx}\textit{\ }and \textbf{dely}\textit{\ }(in meters |
|
|
in the case of a cartesian grid, in degrees otherwise). The vertical grid |
|
|
spacing is set through the 1D array \textbf{delz }for the ocean (in meters) |
|
|
or \textbf{delp}\textit{\ }for the atmosphere (in Pa). The variable \textbf{% |
|
|
Ro\_SeaLevel} represents the standard position of Sea-Level in ''R'' |
|
|
coordinate. This is typically set to 0m for the ocean (default value) and 10$% |
|
|
^{5}$Pa for the atmosphere. For the atmosphere, also set the logical |
|
|
variable \textbf{groundAtK1} to '.\texttt{TRUE}.'. which put the first level |
|
|
(k=1) at the lower boundary (ground). |
|
|
|
|
|
For the cartesian grid case, the Coriolis parameter $f$ is set through the |
|
|
variables \textbf{f0}\textit{\ }and \textbf{beta}\textit{\ }which correspond |
|
|
to the reference Coriolis parameter (in s$^{-1}$) and $\frac{\partial f}{% |
|
|
\partial y}$(in m$^{-1}$s$^{-1}$) respectively. If \textbf{beta }\textit{\ }% |
|
|
is set to a nonzero value, \textbf{f0}\textit{\ }is the value of $f$ at the |
|
|
southern edge of the domain. |
|
|
|
|
|
\begin{itemize} |
|
|
\item topography - full and partial cells |
|
|
\end{itemize} |
|
|
|
|
|
The domain bathymetry is read from a file that contains a 2D (x,y) map of |
|
|
depths (in m) for the ocean or pressures (in Pa) for the atmosphere. The |
|
|
file name is represented by the variable \textbf{bathyFile}\textit{. }The |
|
|
file is assumed to contain binary numbers giving the depth (pressure) of the |
|
|
model at each grid cell, ordered with the x coordinate varying fastest. The |
|
|
points are ordered from low coordinate to high coordinate for both axes. The |
|
|
model code applies without modification to enclosed, periodic, and double |
|
|
periodic domains. Periodicity is assumed by default and is suppressed by |
|
|
setting the depths to 0m for the cells at the limits of the computational |
|
|
domain (note: not sure this is the case for the atmosphere). The precision |
|
|
with which to read the binary data is controlled by the integer variable |
|
|
\textbf{readBinaryPrec }which can take the value \texttt{32} (single |
|
|
precision) or \texttt{64} (double precision). See the matlab program \textit{% |
|
|
gendata.m }in the \textit{input }directories under \textit{verification }to |
|
|
see how the bathymetry files are generated for the case study experiments. |
|
|
|
|
|
To use the partial cell capability, the variable \textbf{hFacMin}\textit{\ }% |
|
|
needs to be set to a value between 0 and 1 (it is set to 1 by default) |
|
|
corresponding to the minimum fractional size of the cell. For example if the |
|
|
bottom cell is 500m thick and \textbf{hFacMin}\textit{\ }is set to 0.1, the |
|
|
actual thickness of the cell (i.e. used in the code) can cover a range of |
|
|
discrete values 50m apart from 50m to 500m depending on the value of the |
|
|
bottom depth (in \textbf{bathyFile}) at this point. |
|
|
|
|
|
Note that the bottom depths (or pressures) need not coincide with the models |
|
|
levels as deduced from \textbf{delz}\textit{\ }or\textit{\ }\textbf{delp}% |
|
|
\textit{. }The model will interpolate the numbers in \textbf{bathyFile}% |
|
|
\textit{\ }so that they match the levels obtained from \textbf{delz}\textit{% |
|
|
\ }or\textit{\ }\textbf{delp}\textit{\ }and \textbf{hFacMin}\textit{. } |
|
|
|
|
|
(Note: the atmospheric case is a bit more complicated than what is written |
|
|
here I think. To come soon...) |
|
|
|
|
|
\begin{itemize} |
|
|
\item time-discretization |
|
|
\end{itemize} |
|
|
|
|
|
The time steps are set through the real variables \textbf{deltaTMom }and |
|
|
\textbf{deltaTtracer }(in s) which represent the time step for the momentum |
|
|
and tracer equations, respectively. For synchronous integrations, simply set |
|
|
the two variables to the same value (or you can prescribe one time step only |
|
|
through the variable \textbf{deltaT}). The Adams-Bashforth stabilizing |
|
|
parameter is set through the variable \textbf{abEps }(dimensionless). The |
|
|
stagger baroclinic time stepping can be activated by setting the logical |
|
|
variable \textbf{staggerTimeStep }to '.\texttt{TRUE}.'. |
|
|
|
|
|
\subsubsection{Equation of state} |
|
|
|
|
|
First, because the model equations are written in terms of perturbations, a |
|
|
reference thermodynamic state needs to be specified. This is done through |
|
|
the 1D arrays \textbf{tRef}\textit{\ }and \textbf{sRef}. \textbf{tRef }% |
|
|
specifies the reference potential temperature profile (in $^{o}$C for |
|
|
the ocean and $^{o}$K for the atmosphere) starting from the level |
|
|
k=1. Similarly, \textbf{sRef}\textit{\ }specifies the reference salinity |
|
|
profile (in ppt) for the ocean or the reference specific humidity profile |
|
|
(in g/kg) for the atmosphere. |
|
|
|
|
|
The form of the equation of state is controlled by the character variables |
|
|
\textbf{buoyancyRelation}\textit{\ }and \textbf{eosType}\textit{. }\textbf{% |
|
|
buoyancyRelation}\textit{\ }is set to '\texttt{OCEANIC}' by default and |
|
|
needs to be set to '\texttt{ATMOSPHERIC}' for atmosphere simulations. In |
|
|
this case, \textbf{eosType}\textit{\ }must be set to '\texttt{IDEALGAS}'. |
|
|
For the ocean, two forms of the equation of state are available: linear (set |
|
|
\textbf{eosType}\textit{\ }to '\texttt{LINEAR}') and a polynomial |
|
|
approximation to the full nonlinear equation ( set \textbf{eosType}\textit{\ |
|
|
}to '\texttt{POLYNOMIAL}'). In the linear case, you need to specify the |
|
|
thermal and haline expansion coefficients represented by the variables |
|
|
\textbf{tAlpha}\textit{\ }(in K$^{-1}$) and \textbf{sBeta}\textit{\ }(in ppt$% |
|
|
^{-1}$). For the nonlinear case, you need to generate a file of polynomial |
|
|
coefficients called \textit{POLY3.COEFFS. }To do this, use the program |
|
|
\textit{utils/knudsen2/knudsen2.f }under the model tree (a Makefile is |
|
|
available in the same directory and you will need to edit the number and the |
|
|
values of the vertical levels in \textit{knudsen2.f }so that they match |
|
|
those of your configuration). \textit{\ } |
|
|
|
|
|
\subsubsection{Momentum equations} |
|
|
|
|
|
In this section, we only focus for now on the parameters that you are likely |
|
|
to change, i.e. the ones relative to forcing and dissipation for example. |
|
|
The details relevant to the vector-invariant form of the equations and the |
|
|
various advection schemes are not covered for the moment. We assume that you |
|
|
use the standard form of the momentum equations (i.e. the flux-form) with |
|
|
the default advection scheme. Also, there are a few logical variables that |
|
|
allow you to turn on/off various terms in the momentum equation. These |
|
|
variables are called \textbf{momViscosity, momAdvection, momForcing, |
|
|
useCoriolis, momPressureForcing, momStepping}\textit{, }and \textit{\ }% |
|
|
\textbf{metricTerms }and are assumed to be set to '.\texttt{TRUE}.' here. |
|
|
Look at the file \textit{model/inc/PARAMS.h }for a precise definition of |
|
|
these variables. |
|
|
|
|
|
\begin{itemize} |
|
|
\item initialization |
|
|
\end{itemize} |
|
|
|
|
|
The velocity components are initialized to 0 unless the simulation is |
|
|
starting from a pickup file (see section on simulation control parameters). |
|
|
|
|
|
\begin{itemize} |
|
|
\item forcing |
|
|
\end{itemize} |
|
|
|
|
|
This section only applies to the ocean. You need to generate wind-stress |
|
|
data into two files \textbf{zonalWindFile}\textit{\ }and \textbf{% |
|
|
meridWindFile }corresponding to the zonal and meridional components of the |
|
|
wind stress, respectively (if you want the stress to be along the direction |
|
|
of only one of the model horizontal axes, you only need to generate one |
|
|
file). The format of the files is similar to the bathymetry file. The zonal |
|
|
(meridional) stress data are assumed to be in Pa and located at U-points |
|
|
(V-points). As for the bathymetry, the precision with which to read the |
|
|
binary data is controlled by the variable \textbf{readBinaryPrec}.\textbf{\ } |
|
|
See the matlab program \textit{gendata.m }in the \textit{input }directories |
|
|
under \textit{verification }to see how simple analytical wind forcing data |
|
|
are generated for the case study experiments. |
|
|
|
|
|
There is also the possibility of prescribing time-dependent periodic |
|
|
forcing. To do this, concatenate the successive time records into a single |
|
|
file (for each stress component) ordered in a (x, y, t) fashion and set the |
|
|
following variables: \textbf{periodicExternalForcing }to '.\texttt{TRUE}.', |
|
|
\textbf{externForcingPeriod }to the period (in s) of which the forcing |
|
|
varies (typically 1 month), and \textbf{externForcingCycle }to the repeat |
|
|
time (in s) of the forcing (typically 1 year -- note: \textbf{% |
|
|
externForcingCycle }must be a multiple of \textbf{externForcingPeriod}). |
|
|
With these variables set up, the model will interpolate the forcing linearly |
|
|
at each iteration. |
|
| 680 |
|
|
|
\begin{itemize} |
|
|
\item dissipation |
|
|
\end{itemize} |
|
|
|
|
|
The lateral eddy viscosity coefficient is specified through the variable |
|
|
\textbf{viscAh}\textit{\ }(in m$^{2}$s$^{-1}$). The vertical eddy viscosity |
|
|
coefficient is specified through the variable \textbf{viscAz }(in m$^{2}$s$% |
|
|
^{-1}$) for the ocean and \textbf{viscAp}\textit{\ }(in Pa$^{2}$s$^{-1}$) |
|
|
for the atmosphere. The vertical diffusive fluxes can be computed implicitly |
|
|
by setting the logical variable \textbf{implicitViscosity }to '.\texttt{TRUE}% |
|
|
.'. In addition, biharmonic mixing can be added as well through the variable |
|
|
\textbf{viscA4}\textit{\ }(in m$^{4}$s$^{-1}$). On a spherical polar grid, |
|
|
you might also need to set the variable \textbf{cosPower} which is set to 0 |
|
|
by default and which represents the power of cosine of latitude to multiply |
|
|
viscosity. Slip or no-slip conditions at lateral and bottom boundaries are |
|
|
specified through the logical variables \textbf{no\_slip\_sides}\textit{\ }% |
|
|
and \textbf{no\_slip\_bottom}. If set to '\texttt{.FALSE.}', free-slip |
|
|
boundary conditions are applied. If no-slip boundary conditions are applied |
|
|
at the bottom, a bottom drag can be applied as well. Two forms are |
|
|
available: linear (set the variable \textbf{bottomDragLinear}\textit{\ }in s$% |
|
|
^{-1}$) and quadratic (set the variable \textbf{bottomDragQuadratic}\textit{% |
|
|
\ }in m$^{-1}$). |
|
| 681 |
|
|
| 682 |
The Fourier and Shapiro filters are described elsewhere. |
\subsubsection{MNC output files} |
| 683 |
|
|
| 684 |
|
Unlike the \texttt{mdsio} output, the \texttt{mnc}--generated output |
| 685 |
|
is usually (though not necessarily) placed within a subdirectory with |
| 686 |
|
a name such as \texttt{mnc\_test\_\${DATE}\_\${SEQ}}. The files |
| 687 |
|
within this subdirectory are all in the ``self-describing'' netCDF |
| 688 |
|
format and can thus be browsed and/or plotted using tools such as: |
| 689 |
\begin{itemize} |
\begin{itemize} |
| 690 |
\item C-D scheme |
\item At a minimum, the \texttt{ncdump} utility is typically included |
| 691 |
\end{itemize} |
with every netCDF install: |
| 692 |
|
\begin{rawhtml} <A href="http://www.unidata.ucar.edu/packages/netcdf/"> \end{rawhtml} |
| 693 |
If you run at a sufficiently coarse resolution, you will need the C-D scheme |
\begin{verbatim} |
| 694 |
for the computation of the Coriolis terms. The variable\textbf{\ tauCD}, |
http://www.unidata.ucar.edu/packages/netcdf/ |
| 695 |
which represents the C-D scheme coupling timescale (in s) needs to be set. |
\end{verbatim} |
| 696 |
|
\begin{rawhtml} </A> \end{rawhtml} |
|
\begin{itemize} |
|
|
\item calculation of pressure/geopotential |
|
|
\end{itemize} |
|
|
|
|
|
First, to run a non-hydrostatic ocean simulation, set the logical variable |
|
|
\textbf{nonHydrostatic} to '.\texttt{TRUE}.'. The pressure field is then |
|
|
inverted through a 3D elliptic equation. (Note: this capability is not |
|
|
available for the atmosphere yet.) By default, a hydrostatic simulation is |
|
|
assumed and a 2D elliptic equation is used to invert the pressure field. The |
|
|
parameters controlling the behaviour of the elliptic solvers are the |
|
|
variables \textbf{cg2dMaxIters}\textit{\ }and \textbf{cg2dTargetResidual }% |
|
|
for the 2D case and \textbf{cg3dMaxIters}\textit{\ }and \textbf{% |
|
|
cg3dTargetResidual }for the 3D case. You probably won't need to alter the |
|
|
default values (are we sure of this?). |
|
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|
|
|
For the calculation of the surface pressure (for the ocean) or surface |
|
|
geopotential (for the atmosphere) you need to set the logical variables |
|
|
\textbf{rigidLid} and \textbf{implicitFreeSurface}\textit{\ }(set one to '.% |
|
|
\texttt{TRUE}.' and the other to '.\texttt{FALSE}.' depending on how you |
|
|
want to deal with the ocean upper or atmosphere lower boundary). |
|
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|
|
|
\subsubsection{Tracer equations} |
|
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|
|
|
This section covers the tracer equations i.e. the potential temperature |
|
|
equation and the salinity (for the ocean) or specific humidity (for the |
|
|
atmosphere) equation. As for the momentum equations, we only describe for |
|
|
now the parameters that you are likely to change. The logical variables |
|
|
\textbf{tempDiffusion}\textit{, }\textbf{tempAdvection}\textit{, }\textbf{% |
|
|
tempForcing}\textit{,} and \textbf{tempStepping} allow you to turn on/off |
|
|
terms in the temperature equation (same thing for salinity or specific |
|
|
humidity with variables \textbf{saltDiffusion}\textit{, }\textbf{% |
|
|
saltAdvection}\textit{\ }etc). These variables are all assumed here to be |
|
|
set to '.\texttt{TRUE}.'. Look at file \textit{model/inc/PARAMS.h }for a |
|
|
precise definition. |
|
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|
|
|
\begin{itemize} |
|
|
\item initialization |
|
|
\end{itemize} |
|
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|
|
|
The initial tracer data can be contained in the binary files \textbf{% |
|
|
hydrogThetaFile }and \textbf{hydrogSaltFile}. These files should contain 3D |
|
|
data ordered in an (x, y, r) fashion with k=1 as the first vertical level. |
|
|
If no file names are provided, the tracers are then initialized with the |
|
|
values of \textbf{tRef }and \textbf{sRef }mentioned above (in the equation |
|
|
of state section). In this case, the initial tracer data are uniform in x |
|
|
and y for each depth level. |
|
|
|
|
|
\begin{itemize} |
|
|
\item forcing |
|
|
\end{itemize} |
|
|
|
|
|
This part is more relevant for the ocean, the procedure for the atmosphere |
|
|
not being completely stabilized at the moment. |
|
| 697 |
|
|
| 698 |
A combination of fluxes data and relaxation terms can be used for driving |
\item The \texttt{ncview} utility is a very convenient and quick way |
| 699 |
the tracer equations. \ For potential temperature, heat flux data (in W/m$% |
to plot netCDF data and it runs on most OSes: |
| 700 |
^{2}$) can be stored in the 2D binary file \textbf{surfQfile}\textit{. }% |
\begin{rawhtml} <A href="http://meteora.ucsd.edu/~pierce/ncview_home_page.html"> \end{rawhtml} |
| 701 |
Alternatively or in addition, the forcing can be specified through a |
\begin{verbatim} |
| 702 |
relaxation term. The SST data to which the model surface temperatures are |
http://meteora.ucsd.edu/~pierce/ncview_home_page.html |
| 703 |
restored to are supposed to be stored in the 2D binary file \textbf{% |
\end{verbatim} |
| 704 |
thetaClimFile}\textit{. }The corresponding relaxation time scale coefficient |
\begin{rawhtml} </A> \end{rawhtml} |
| 705 |
is set through the variable \textbf{tauThetaClimRelax}\textit{\ }(in s). The |
|
| 706 |
same procedure applies for salinity with the variable names \textbf{EmPmRfile% |
\item MatLAB(c) and other common post-processing environments provide |
| 707 |
}\textit{, }\textbf{saltClimFile}\textit{, }and \textbf{tauSaltClimRelax}% |
various netCDF interfaces including: |
| 708 |
\textit{\ }for freshwater flux (in m/s) and surface salinity (in ppt) data |
\begin{rawhtml} <A href="http://woodshole.er.usgs.gov/staffpages/cdenham/public_html/MexCDF/nc4ml5.html"> \end{rawhtml} |
| 709 |
files and relaxation time scale coefficient (in s), respectively. Also for |
\begin{verbatim} |
| 710 |
salinity, if the CPP key \textbf{USE\_NATURAL\_BCS} is turned on, natural |
http://woodshole.er.usgs.gov/staffpages/cdenham/public_html/MexCDF/nc4ml5.html |
| 711 |
boundary conditions are applied i.e. when computing the surface salinity |
\end{verbatim} |
| 712 |
tendency, the freshwater flux is multiplied by the model surface salinity |
\begin{rawhtml} </A> \end{rawhtml} |
|
instead of a constant salinity value. |
|
|
|
|
|
As for the other input files, the precision with which to read the data is |
|
|
controlled by the variable \textbf{readBinaryPrec}. Time-dependent, periodic |
|
|
forcing can be applied as well following the same procedure used for the |
|
|
wind forcing data (see above). |
|
| 713 |
|
|
|
\begin{itemize} |
|
|
\item dissipation |
|
| 714 |
\end{itemize} |
\end{itemize} |
| 715 |
|
|
|
Lateral eddy diffusivities for temperature and salinity/specific humidity |
|
|
are specified through the variables \textbf{diffKhT }and \textbf{diffKhS }% |
|
|
(in m$^{2}$/s). Vertical eddy diffusivities are specified through the |
|
|
variables \textbf{diffKzT }and \textbf{diffKzS }(in m$^{2}$/s) for the ocean |
|
|
and \textbf{diffKpT }and \textbf{diffKpS }(in Pa$^{2}$/s) for the |
|
|
atmosphere. The vertical diffusive fluxes can be computed implicitly by |
|
|
setting the logical variable \textbf{implicitDiffusion }to '.\texttt{TRUE}% |
|
|
.'. In addition, biharmonic diffusivities can be specified as well through |
|
|
the coefficients \textbf{diffK4T }and \textbf{diffK4S }(in m$^{4}$/s). Note |
|
|
that the cosine power scaling (specified through \textbf{cosPower }- see the |
|
|
momentum equations section) is applied to the tracer diffusivities |
|
|
(Laplacian and biharmonic) as well. The Gent and McWilliams parameterization |
|
|
for oceanic tracers is described in the package section. Finally, note that |
|
|
tracers can be also subject to Fourier and Shapiro filtering (see the |
|
|
corresponding section on these filters). |
|
| 716 |
|
|
| 717 |
\begin{itemize} |
\subsection{Looking at the output} |
|
\item ocean convection |
|
|
\end{itemize} |
|
| 718 |
|
|
| 719 |
Two options are available to parameterize ocean convection: one is to use |
The ``traditional'' or mdsio model data are written according to a |
| 720 |
the convective adjustment scheme. In this case, you need to set the variable |
``meta/data'' file format. Each variable is associated with two files |
| 721 |
\textbf{cadjFreq}, which represents the frequency (in s) with which the |
with suffix names \textit{.data} and \textit{.meta}. The |
| 722 |
adjustment algorithm is called, to a non-zero value (if set to a negative |
\textit{.data} file contains the data written in binary form |
| 723 |
value by the user, the model will set it to the tracer time step). The other |
(big\_endian by default). The \textit{.meta} file is a ``header'' file |
| 724 |
option is to parameterize convection with implicit vertical diffusion. To do |
that contains information about the size and the structure of the |
| 725 |
this, set the logical variable \textbf{implicitDiffusion }to '.\texttt{TRUE}% |
\textit{.data} file. This way of organizing the output is particularly |
| 726 |
.' and the real variable \textbf{ivdc\_kappa }to a value (in m$^{2}$/s) you |
useful when running multi-processors calculations. The base version of |
| 727 |
wish the tracer vertical diffusivities to have when mixing tracers |
the model includes a few matlab utilities to read output files written |
| 728 |
vertically due to static instabilities. Note that \textbf{cadjFreq }and |
in this format. The matlab scripts are located in the directory |
| 729 |
\textbf{ivdc\_kappa }can not both have non-zero value. |
\textit{utils/matlab} under the root tree. The script \textit{rdmds.m} |
| 730 |
|
reads the data. Look at the comments inside the script to see how to |
| 731 |
\subsubsection{Simulation controls} |
use it. |
|
|
|
|
The model ''clock'' is defined by the variable \textbf{deltaTClock }(in s) |
|
|
which determines the IO frequencies and is used in tagging output. |
|
|
Typically, you will set it to the tracer time step for accelerated runs |
|
|
(otherwise it is simply set to the default time step \textbf{deltaT}). |
|
|
Frequency of checkpointing and dumping of the model state are referenced to |
|
|
this clock (see below). |
|
| 732 |
|
|
| 733 |
\begin{itemize} |
Some examples of reading and visualizing some output in {\em Matlab}: |
| 734 |
\item run duration |
\begin{verbatim} |
| 735 |
\end{itemize} |
% matlab |
| 736 |
|
>> H=rdmds('Depth'); |
| 737 |
|
>> contourf(H');colorbar; |
| 738 |
|
>> title('Depth of fluid as used by model'); |
| 739 |
|
|
| 740 |
The beginning of a simulation is set by specifying a start time (in s) |
>> eta=rdmds('Eta',10); |
| 741 |
through the real variable \textbf{startTime }or by specifying an initial |
>> imagesc(eta');axis ij;colorbar; |
| 742 |
iteration number through the integer variable \textbf{nIter0}. If these |
>> title('Surface height at iter=10'); |
|
variables are set to nonzero values, the model will look for a ''pickup'' |
|
|
file \textit{pickup.0000nIter0 }to restart the integration\textit{. }The end |
|
|
of a simulation is set through the real variable \textbf{endTime }(in s). |
|
|
Alternatively, you can specify instead the number of time steps to execute |
|
|
through the integer variable \textbf{nTimeSteps}. |
|
| 743 |
|
|
| 744 |
\begin{itemize} |
>> eta=rdmds('Eta',[0:10:100]); |
| 745 |
\item frequency of output |
>> for n=1:11; imagesc(eta(:,:,n)');axis ij;colorbar;pause(.5);end |
| 746 |
\end{itemize} |
\end{verbatim} |
| 747 |
|
|
| 748 |
Real variables defining frequencies (in s) with which output files are |
Similar scripts for netCDF output (\texttt{rdmnc.m}) are available. |
|
written on disk need to be set up. \textbf{dumpFreq }controls the frequency |
|
|
with which the instantaneous state of the model is saved. \textbf{chkPtFreq }% |
|
|
and \textbf{pchkPtFreq }control the output frequency of rolling and |
|
|
permanent checkpoint files, respectively. See section 1.5.1 Output files for the |
|
|
definition of model state and checkpoint files. In addition, time-averaged |
|
|
fields can be written out by setting the variable \textbf{taveFreq} (in s). |
|
|
The precision with which to write the binary data is controlled by the |
|
|
integer variable w\textbf{riteBinaryPrec }(set it to \texttt{32} or \texttt{% |
|
|
64}). |
|
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