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\documentclass[a4j,12pt]{jarticle}
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\usepackage{Dennou6}                      % dennou-sty-6 $B$r;HMQ(B

\Dtitle[$B5eLL@u?eJ}Dx<0%b%G%k(B : $B12EYH/;67?(B]        % $B%X%C%@It%?%$%H%k(B, $B%b%G%kL>$HF1$8(B
{ {\large SPMODEL $B%5%s%W%k%W%m%0%i%`(B} \\  % $B$3$3$OJQ99$7$J$$(B 
   $B5eLL@u?eJ}Dx<0%b%G%k(B : $B12EYH/;67?(B \\   % $B%b%G%kL>(B
  {\large shallow\_zd.f90}                % $B%W%m%0%i%`L>(B
}
%
\Dauthor[$B>.9b(B $B@5;L(B]{$B>.9b(B $B@5;L(B}            % $BCx<T(B
\Ddate{2004 $BG/(B 6 $B7n(B 16 $BF|(B}                % $BF|IU(B
\Dnoparindent                             % $BCJMn$N;z2<$2$r$7$J$$(B
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%   1. $B$O$8$a$K(B 
%   2. $B;YG[J}Dx<07O(B
%   3. $BN%;62=(B
%   4. $BMxMQ%b%8%e!<%k$H$=$NB>$N@_Dj(B
%   5. $B?tCM<B83(B
%   6. $B;29MJ88%(B
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% $BI,MW$K1~$8$F9=@.$rJQ99$9$k$3$H(B.
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\begin{document}

\maketitle                                % $B%?%$%H%k$N:n@.(B
\tableofcontents                          % $BL\<!$N:n@.(B
\pagebreak                                

%----------------------------------------------------------------------
\Dparskip
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage                                  % $B2~%Z!<%8(B
\section{$B35MW(B}

SPMODEL $B%5%s%W%k%W%m%0%i%`!X(Bshallow\_zd.f90$B!Y(B, $B!X(Bshallow\_zd\_ab.f90$B!Y(B, 
$B!X(Bshallow\_zd\_rk.f90$B!Y$KMQ$$$i$l$F$$$k4pACJ}Dx<0$H6-3&>r7o(B, $B$*$h$S(B, $B$3(B
$B$N%W%m%0%i%`$rMQ$$$??tCM<B83$NJ}K!$K$D$$$F2r@b$9$k(B. $B4pACJ}Dx<0$O(B, $B12EY$H(B
$BH/;6$rMQ$$$FI=8=$7$?5eLL>e$N@u?eJ}Dx<0$G$"$k(B.  $B7W;;$O%9%Z%/%H%kK!$rMQ$$(B
$B$F9T$$(B, $BE83+4X?t$O5eLLD4OB4X?t$G$"$k(B. $BGH?t@ZCG$O;03Q@ZCG$G$"$k(B. $B%9%Z%/%H(B
$B%kJQ49$H5UJQ49$*$h$SHyJ,1i;;$K$O(B, SPMODEL $B%i%$%V%i%j(B(spml)$B$rMQ$$$F$$$k(B. 
$B;~4V@QJ,$O(B leapfrog $BK!$HBf7A8x<0$rAH$_9g$o$;$?(B semi-imlicit $BK!$rMQ$$$F9T(B
$B$$(B, $B7W;;%b!<%I$NA}I}$rM^@)$9$k$?$a(B Asselin (1972) $B$N;~4V%U%#%k%?!<$r(B 1 
$B%9%F%C%WKh$KE,MQ$9$k(B. $B?tCM<B83$H$7$F(B Williamson {\it et al}. (1992) $B$K$h$C(B
$B$FDs0F$5$l$?(B, $B5eLL@u?eJ}Dx<0%b%G%k$NI8=`;n83(B Case5 $B$N<B83$r9T$&(B.

{\bf $B%W%m%0%i%`L>(B} \\                  % $B%W%m%0%i%`L>(B
{\footnotesize
shallow\_zd.f90                   
}

{\bf $B%W%m%0%i%`<hF@85(B}\\               % $B%W%m%0%i%`<hF@@h(B
{\footnotesize
http:\slash \slash www.gfd-dennou.org\slash arch\slash spmodel\slash 2d-sphere-w\slash shallow-zd\slash SIGEN.htm
}

{\bf SPMODEL $B%5%s%W%k%W%m%0%i%`L\<!(B}\\ % $B%5%s%W%k%W%m%0%i%`L\<!(B($BJQ99$7$J$$(B)
{\footnotesize
 http:\slash \slash www.gfd-dennou.org\slash arch\slash spmodel\slash sample.htm 
}

{\bf SPMODEL $B$N;H$$J}(B}\\               % SPMODEL $B$N;H$$J}(B($BJQ99$7$J$$(B)
{\footnotesize
http:\slash \slash www.gfd-dennou.org\slash arch\slash spmodel\/
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage                                  % $B2~%Z!<%8(B
\section{$B;YG[J}Dx<07O(B}
$B$3$3$G$O;YG[J}Dx<07O$H6-3&>r7o$r5-$9(B. 

\subsection{$B;YG[J}Dx<07O(B}
$B;YG[J}Dx<07O$O12EYH/;67?$N5eLL@u?eJ}Dx<07O$G$"$k(B. 
\begin{eqnarray}
  \DP{\zeta }{t} &=& -\frac{1}{a(1-\mu ^{2})}
                      \DP{(f+\zeta)U}{\lambda}
                    - \frac{1}{a}\DP{(f+\zeta)V}{\mu} \nonumber \\
                  & & -K_{m}\left[(-1)^{N_{d}/2}\nabla ^{N_{d}} 
                        - \left(\frac{2}{a^{2}}\right)^{N_{d}}\right]\zeta, 
                    \Deqlab{$B12EYJ}Dx<0(B} \\
  \DP{D}{t} &=& \frac{1}{a(1-\mu ^{2})}
                \DP{(f+\zeta)V}{\lambda}
                - \frac{1}{a}\DP{(f+\zeta)U}{\mu} 
                - \Dlapla \left[g (h+h_{s}) + E\right] \nonumber \\
            & & -K_{m}\left[(-1)^{N_{d}/2}\nabla ^{N_{d}} 
                       - \left(\frac{2}{a^{2}}\right)^{N_{d}/2}\right]D,
                \Deqlab{$BH/;6J}Dx<0(B} \\
  \DP{h}{t} &=& - \frac{1}{a(1-\mu ^{2})}\DP{(hU)}{\lambda}
                - \frac{1}{a}\DP{(hV)}{\mu}  
                - (-1)^{N_{d}/2}K_{h}\nabla ^{N_{d}}h. 
                \Deqlab{$B<ANLJ]B8$N<0(B} 
\end{eqnarray}
$B3F5-9f$NDj5A$O(B\Dtabref{$BJQ?t(B, $BJ*M}Dj?t$NDj5A(B}$B$K<($7$?(B.
$B12EY(B $\zeta $ $B$HH/;6(B $D$ , $BC10L<ANL$"$?$j$N1?F0%(%M%k%.!<(B $E$, 
$B1i;;;R(B $\nabla ^{2}$ $B$O0J2<$N$h$&$KDj5A$5$l$k(B.
\begin{eqnarray}
  \zeta &=& \frac{1}{a(1-\mu ^{2})}\DP{V}{\lambda} - \frac{1}{a}\DP{U}{\mu}, \\
  D     &=& \frac{1}{a(1-\mu ^{2})}\DP{U}{\lambda} + \frac{1}{a}\DP{V}{\mu}, \\
  E     &=& \frac{U^{2}+V^{2}}{2(1-\mu ^{2})}, \\ 
  \nabla^{2} A &=& \frac{1}{a^{2}(1-\mu ^{2})}\DP[2]{A}{\lambda}
              + \frac{1}{a^{2}}\DP{}{\mu}\left[(1-\mu^{2})\DP{A}{\mu}\right].
\end{eqnarray}
$B$3$3$G(B $A$ $B$OG$0U$N%9%+%i!<$G$"$k(B. $BN.@~4X?t(B $\psi $ $B$HB.EY%]%F%s%7%cN0(B 
$\chi$ $B$rF3F~$9$k$H(B,
\begin{eqnarray}
  U &=& -\frac{1-\mu^ {2}}{a}\DP{\psi}{\mu}
        +\frac{1}{a}\DP{\chi}{\lambda}, \\
  V &=& \frac{1}{a}\DP{\psi}{\lambda}
        + \frac{1-\mu^{2}}{a}\DP{\chi}{\mu}, \\
  \zeta &=& \nabla ^{2} \psi, \\
  D     &=& \nabla ^{2} \chi
\end{eqnarray}
$B$HI=$5$l$k(B. 
\begin{table}[h]
 \begin{center}
  \begin{tabular}{c l l  } \hline
   $B5-9f(B    &\qquad\qquad&  $BJQ?t(B/$BJ*M}Dj?t(B   \\ \hline 
   $\lambda$&& $B7PEY(B            \\
   $\phi$   && $B0^EY(B            \\
   $\mu $   && $\sin$ $B0^EY(B ($\equiv \sin \phi$) \\
   $t$      && $B;~4V(B            \\ 
   $u$      && $B7PEYJ}8~N.B.(B    \\ 
   $v$      && $B0^EYJ}8~N.B.(B    \\ 
   $U$      && $u\cos \phi $  \\ 
   $V$      && $v\cos \phi $  \\ 
   $h$      && $BN.BN$NA48|$5(B    \\ 
   $\zeta$  && $B12EY(B            \\ 
   $D$      && $BH/;6(B            \\
   $E$      && $B1?F0%(%M%k%.!<(B \\
   $\psi$   && $BN.@~4X?t(B        \\
   $\chi$   && $BB.EY%]%F%s%7%c%k(B \\
   $f$      && $2\Omega \sin \phi$ \\
   $\Omega$ && $B<+E>3QB.EY(B      \\
   $g$      && $B=ENO2CB.EY(B     \\
   $a$      && $BOG@1H>7B(B       \\
   $K_{m}$  && $B?eJ?3H;678?t(B   \\
   $K_{h}$  && $B?eJ?3H;678?t(B   \\
   $N_{d}$      && $BD6G4@-$N<!?t(B \\ \hline
  \end{tabular} 
 \end{center}
 \caption{$BJQ?t(B, $BJ*M}Dj?t$NDj5A(B}
 \Dtablab{$BJQ?t(B, $BJ*M}Dj?t$NDj5A(B}
\end{table}

\subsection{$B6-3&>r7o(B}

$B6-3&>r7o$O0^EY(B, $B7PEYJ}8~$H$b$K<~4|6-3&>r7o$G$"$k(B. 
\begin{eqnarray}
  \zeta (\lambda + 2\pi, \phi)  &=& \zeta (\lambda, \phi), \\
  \zeta (\lambda , \phi + 2\pi) &=& \zeta (\lambda, \phi).
\end{eqnarray}
$B$J$I$II=$5$l$k(B.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage                                  % $B2~%Z!<%8(B
\section{$BN%;62=(B}
$B$3$N@a$G$OJ}Dx<07O$N6u4VN%;62=$*$h$S;HMQ$7$?;~4V@QJ,K!$K$D$$$F@bL@(B, 
$B%W%m%0%i%`Fb$G<B:]$KMQ$$$i$l$F$$$kJ}Dx<0$r5-=R$9$k(B.

\subsection{$B?eJ?N%;62=(B}
$B;YG[J}Dx<0(B\Deqref{$B12EYJ}Dx<0(B},\Deqref{$BH/;6J}Dx<0(B},\Deqref{$B<ANLJ]B8$N<0(B},
$B$NN%;6I=8=$O0J2<$N$h$&$K$J$k(B. 
\begin{eqnarray}
  \DP{\zeta _{i,j}}{t} 
             &=& -\frac{1}{a(1-\mu_{j} ^{2})}
                 \DP{(f_{j}+\zeta_{i,j})U_{i,j}}{\lambda}
                 - \frac{1}{a}\DP{(f_{j}+\zeta_{i,j})V_{i,j}}{\mu} \nonumber \\
             & & -K_{m}\left[(-1)^{N_{d}/2}\nabla ^{N_{d}} 
                      - \left(\frac{2}{a^{2}}\right)^{N_{d}/2}
                  \right]\zeta_{i,j}, 
                  \Deqlab{$BN%;62=$5$l$?12EYJ}Dx<0(B} \\
  \DP{D_{i,j}}{t} 
             &=& \frac{1}{a(1-\mu _{j}^{2})}
                 \DP{(f_{j}+\zeta_{i,j})V_{i,j}}{\lambda}
                 - \frac{1}{a}\DP{(f_{j}+\zeta_{i,j})U_{i,j}}{\mu} \nonumber \\
             & &- \Dlapla \left[g (h_{i,j}+h_{s_{i,j}}) + E_{i,j}\right]
                -K_{m}\left[(-1)^{N_{d}/2}\nabla ^{N_{d}} 
                       - \left(\frac{2}{a^{2}}\right)^{N_{d}/2}\right]D_{i,j},
                \Deqlab{$BN%;62=$5$l$?H/;6J}Dx<0(B} \\
  \DP{h_{i,j}}{t} 
             &=& - \frac{1}{a(1-\mu _{j}^{2})}
                   \DP{(h_{i,j}U_{i,j})}{\lambda}
                 - \frac{1}{a}\DP{(h_{i,j}V_{i,j})}{\mu} 
                 - (-1)^{N_{d}/2}K_{h}\nabla ^{N_{d}}h_{i,j}. 
                \Deqlab{$BN%;62=$5$l$?<ANLJ]B8$N<0(B} 
\end{eqnarray}
$BE:;z(B $i,j$ $B$O3J;RE@(B $(\lambda _{i}, \mu _{j})$ $B>e$NCM$G$"$k$3$H$r<($9(B.
$B3J;RE@$O7PEYJ}8~$K$OEy4V3V(B, $B0^EYJ}8~$K$O%,%&%90^EY>e$KCV$/(B. 

\subsection{$B?eJ?J}8~$N%9%Z%/%H%kI=8=(B}
$B6u4VN%;62=$7$?;YG[J}Dx<0(B\Deqref{$BN%;62=$5$l$?12EYJ}Dx<0(B}, \Deqref{$BN%;62=(B
$B$5$l$?H/;6J}Dx<0(B}, \Deqref{$BN%;62=$5$l$?<ANLJ]B8$N<0(B} $B$r%9%Z%/%H%kK!$rMQ(B
$B$$$FI=8=$9$k(B.  $B%9%Z%/%H%k(B $BE83+$O5eLLD4OB4X?t$rMQ$$$F9T$&(B. $BGH?t@ZCG$O;03Q(B
$B@ZCG$G$"$k(B.$B%k%8%c%s%I%k@5JQ49$N@QJ,$O%,%&%9(B--$B%k%8%c%s%I%k$N@QJ,8x<0$rMQ(B
$B$$$F9T$&(B. $BHs@~7A9`$r07$&>l9g$O(B, $B@h$K3J;RE@>e$G$NHs@~7A9`$NCM$r7W;;$7(B, $B$=(B
$B$NCM$N%9%Z%/%H%k$r5a$a$kJ}K!(B($BJQ49K!(B)$B$rMQ$$$k(B. $B0J2<$G$O(B $m,n$ $B$r$=$l$>$l(B
$B7PEYJ}8~GH?t$HA4GH?t(B, $M,N$ $B$r@ZCGGH?t(B, $I,J$ $B$r3J;RE@?t$H$9$k(B.

$\zeta_{i,j}, D_{i,j}, h_{i,j}, U_{i,j}, V_{i,j}$ $B$O%9%Z%/%H%k5UJQ49$K$h$C(B
$B$F0J2<$N$h$&$KE83+$5$l$k(B.
\begin{eqnarray}
 \zeta_{i,j} &=& \sum _{n=0}^{M}\sum _{m=-n}^{n}
                 P_{n}^{m}(\mu)e ^{im\lambda} \hat \zeta_{m,n}, \\
 D_{i,j} &=& \sum _{n=0}^{M}\sum _{m=-n}^{n}
                 P_{n}^{m}(\mu)e ^{im\lambda} \hat D_{m,n}, \\
 h_{i,j} &=& \sum _{n=0}^{M}\sum _{m=-n}^{n}
                 P_{n}^{m}(\mu)e ^{im\lambda} \hat h_{m,n}, \\
 U_{i,j} &=& \sum _{n=0}^{M}\sum _{m=-n}^{n}
                 P_{n}^{m}(\mu)e ^{im\lambda} \hat U_{m,n}, \\
 V_{i,j} &=& \sum _{n=0}^{M}\sum _{m=-n}^{n}
                 P_{n}^{m}(\mu)e ^{im\lambda} \hat V_{m,n}.
\end{eqnarray}
$B$3$3$G(B $P_{n}^{m}$ $B$O(B 2 $B$K5,3J2=$5$l$?%k%8%c%s%I%kGf4X?t$G$"$k(B.  $B%9%Z%/(B
$B%H%k78?t(B $\hat \zeta_{i,j}, \hat D_{i,j}, \hat h_{i,j}$ $B$O%9%Z%/%H%kJQ49(B
$B$K$h$C$F0J2<$N$h$&$KM?$($i$l$k(B.
\begin{eqnarray}
 \hat \zeta_{m,n} &=& \frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
                  \zeta _{i,j}e^{-i m \lambda _{i}}P_{n}^{m}(\mu_{j})w_{j},\\
 \hat D_{m,n} &=& \frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
                  D _{i,j}e^{-i m \lambda _{i}}P_{n}^{m}(\mu_{j})w_{j},\\
 \hat h_{m,n} &=& \frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
                  h _{i,j}e^{-i m \lambda _{i}}P_{n}^{m}(\mu _{j})w_{j}.
\end{eqnarray}
$B$3$3$G(B $w_{j}$ $B$O%,%&%9=E$_$G$"$k(B. $\hat U_{m,m}, \hat V_{n,m}$ $B$ON.@~4X(B
$B?t$HB.EY%]%F%s%7%c%k$N%9%Z%/%H%k78?t(B
\begin{eqnarray}
 \hat \psi_{n,m} &=& -\frac{\zeta_{m,n}}{n(n+1)/a^{2}},  \\
 \hat \chi_{n,m} &=& -\frac{D_{m,n}}{n(n+1)/a^{2}}  
\end{eqnarray}
$B$rF3F~$7(B, $B0J2<$N$h$&$KI=$5$l$k(B\footnote{
$B%k%8%c%s%I%kGf4X?t$N4X78<0(B
\[
  (1-\mu^{2})\DD{P_{n}^{m}}{\mu} = 
  (n+1)\sqrt{\frac{n^{2}-m^{2}}{4n^{2}-1}}\hat P_{n-1}^{m} -   
  n\sqrt{\frac{(n+1)^{2}-m^{2}}{4(n+1)^{2}-1}}\hat P_{n+1}^{m} 
\]
$B$rMQ$$$k(B.}. 
\begin{eqnarray}
 \hat U _{m,n} &=& \frac{1}{a}
          \left[
            (n-1)\sqrt{\frac{n^{2}-m^{2}}{4n^{2}-1}}\hat \psi_{m,n-1} - 
            (n+2)\sqrt{\frac{(n+1)^{2}-m^{2}}{4(n+1)^{2}-1}}\hat \psi_{m,n+1}
          \right] \nonumber \\
           & & +\frac{im}{a\sqrt{1-\mu ^{2}}}\DP{\hat \chi _{m,n}}{\lambda}, \\
 \hat V _{m,n} &=& - \frac{1}{a}
          \left[
            (n-1)\sqrt{\frac{n^{2}-m^{2}}{4n^{2}-1}}\hat \chi_{m,n-1} - 
            (n+2)\sqrt{\frac{(n+1)^{2}-m^{2}}{4(n+1)^{2}-1}}\hat \chi_{m,n+1}
          \right] \nonumber \\
           & &+\frac{im}{a\sqrt{1-\mu ^{2}}}\DP{\hat \psi _{m,n}}{\lambda}.
\end{eqnarray}

$B0J>e$rMQ$$$k$H;YG[J}Dx<0(B\Deqref{$BN%;62=$5$l$?12EYJ}Dx<0(B}, \Deqref{$BN%;62=(B
$B$5$l$?H/;6J}Dx<0(B}, \Deqref{$BN%;62=$5$l$?<ANLJ]B8$N<0(B}$B$N%9%Z%/%H%kI=8=$O0J(B
$B2<$N$h$&$K$J$k(B.
\begin{eqnarray}
  \DP{\hat \zeta _{m,n}}{t} &=& 
                  \frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
                  \frac{im}{a(1-\mu_{j} ^{2})}[(f_{j}+\zeta_{i,j})U_{i,j}]
                  e^{-im\lambda_{i}}P_{n}^{m}(\mu_{j})w_{j}\nonumber \\
             & & -\frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
                  \frac{1}{a}\left[(f_{j}+\zeta_{i,j})V_{i,j}\right]
                  e^{-im\lambda_{i}}
                  \left.\DP{P_{n}^{m}}{\mu}\right|_{j}w_{j} \nonumber \\
             & & -K_{m}\left[\left\{\frac{n(n+1)}{a^{2}}\right\}^{N_{d}/2}
                        - \left(\frac{2}{a^{2}}\right)^{N_{d}/2}
                  \right]\zeta_{m,n}, 
                  \Deqlab{$B12EYJ}Dx<0$N%9%Z%/%H%kI=8=(B} \\
  \DP{\hat D_{m,n}}{t} &=& 
                 - \frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
                   \frac{im}{a(1-\mu_{j} ^{2})}[(f_{j}+\zeta_{i,j})V_{i,j}]
                   e^{-im\lambda_{i}}P_{n}^{m}(\mu_{j})w_{j}\nonumber \\
             & &   -\frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
                    \frac{1}{a}\left[(f_{j}+\zeta_{i,j})U_{i,j}\right]
                   e^{-im\lambda_{i}}
                   \left.\DP{P_{n}^{m}}{\mu}\right|_{j}w_{j} \nonumber \\
             & & + \frac{n(n+1)}{a^{2}}
                   \left[g (\hat h_{m,n} + \hat h_{s_{m,n}}) 
                               + \hat E_{n,m}\right] \nonumber \\
             & & -K_{m}\left[\left\{\frac{n(n+1)}{a^{2}}\right\}^{N_{d}/2}
                   - \left(\frac{2}{a^{2}}\right)^{N_{d}/2}
                  \right]\hat D_{m,n}, 
                  \Deqlab{$BH/;6J}Dx<0$N%9%Z%/%H%kI=8=(B} \\
  \DP{\hat h_{m,n}}{t} &=& 
                  \frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
                  \frac{im}{a(1-\mu _{j}^{2})}
                  (h_{i,j}U_{i,j})
                  e^{-im\lambda_{i}}P_{n}^{m}(\mu_{j})w_{j}\nonumber \\
             & & - \frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
                 \frac{1}{a}(h_{i,j}V_{i,j})
                  e^{-im\lambda_{i}}
                 \left.\DP{P_{n}^{m}}{\mu}\right|_{j}w_{j},\nonumber \\
    & & - K_{h}\left\{\frac{n(n+1)}{a^{2}}\right\}^{N_{d}/2}\hat h_{m,n}. 
                 \Deqlab{$B<ANLJ]B8$N<0$N%9%Z%/%H%kI=8=(B} 
\end{eqnarray}
$B$3$3$G(B,
\begin{eqnarray}
  \hat E_{m,n} &=& \frac{\hat U_{m,n}^{2} + \hat V_{m,n}^{2}}{1-\mu^{2}}, \\
  \hat h_{s_{m,n}} &=& \frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
                  h _{s_{i,j}}e^{-i m \lambda _{i}}P_{n}^{m}(\mu_{j})w_{j}
\end{eqnarray}
$B$G$"$k(B.

\subsection{$B;~4V@QJ,(B}
$B$3$3$G$O;~4V@QJ,K!$K$D$$$F5-=R$7(B, $B%W%m%0%i%`Fb$G<B:]$KMQ$$$i$l$F$$$kJ}Dx(B
$B<0$r5-=R$9$k(B. $B0J2<$G$O(B $\Delta t$ $B$r;~4V3J;R4V3V(B, $B;~9o(B $\tau \Delta t$ 
$B$K$*$1$k(B $\hat \zeta_{m,n}$ $B$NCM$r(B $\hat \zeta_{m,n}^{\tau}$ $BEy$HI=$9(B. 
$B;~4V@QJ,$O(B semi-implicit $BK!$rMQ$$$F9T$&(B. $B=ENOGH$K4X78$9$k@~7A9`$O1"E*$K(B
$B2r$-(B, $B$=$NB>$N9`$OM[E*$K2r$/(B.

\Deqref{$B12EYJ}Dx<0$N%9%Z%/%H%kI=8=(B}$B$N;~4V@QJ,$OM[E*2rK!$rMQ$$$F9T$&(B. $BK`(B
$B;$9`$KBP$7$F$O(B Euler $BK!(B, $B$=$NB>$N9`$KBP$7$F$O(B Leapfrog $BK!$rE,MQ$9$k(B.
\begin{eqnarray}
  \hat \zeta _{m,n}^{\tau +1} &=& \hat \zeta _{m,n}^{\tau -1} + 
         2\Delta t \left(
         \frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
         \frac{im}{a(1-\mu_{j} ^{2})}[(f_{j}+\zeta_{i,j}^{\tau})U_{i,j}^{\tau}]
         e^{-im\lambda_{i}}P_{n}^{m}(\mu_{j})w_{j}\right.\nonumber \\
         & & -\frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
              \frac{1}{a}\left[(f_{j}+\zeta_{i,j}^{\tau})V_{i,j}^{\tau}\right]
              e^{-im\lambda_{i}}
               \left.\DP{P_{n}^{m}}{\mu}\right|_{j}w_{j} \nonumber \\
         & & \left.
         -K_{m}\left[\left\{\frac{n(n+1)}{a^{2}}\right\}^{N_{d}/2}
         - \left(\frac{2}{a^{2}}\right)^{N_{d}/2}
           \right]\zeta_{m,n}^{\tau-1}\right). 
                \Deqlab{$B12EYJ}Dx<0$N;~4V@QJ,(B} 
\end{eqnarray}

\Deqref{$BH/;6J}Dx<0$N%9%Z%/%H%kI=8=(B}, \Deqref{$B<ANLJ]B8$N<0$N%9%Z%/%H%kI=(B
$B8=(B}$B$O;~4VJ}8~$KN%;62=$9$kA0$K=ENOGH@.J,$NJ,N%$r9T$&(B. $h$ $B$NJ?6Q@.J,$r(B 
$\overline{h}$ $B$H$7(B, $h=\overline{h}+h'$ $B$HI=$9(B. $B$3$N$H$-(B\Deqref{$BH/;6J}(B
$BDx<0$N%9%Z%/%H%kI=8=(B}, \Deqref{$B<ANLJ]B8$N<0$N%9%Z%/%H%kI=8=(B}$B$O0J2<$N$h$&(B
$B$KI=$5$l$k(B.
\begin{eqnarray}
  \DP{\hat D_{m,n}}{t} &=& F_{1}(\zeta, D, U, V)  
                          + n(n+1) g \hat h'_{m,n} 
                          - K_{m_{n,N_{d}}}\hat D_{m,n}
                  \Deqlab{$B=ENOGH$rJ,N%$7$?H/;6J}Dx<0$N%9%Z%/%H%kI=8=(B} \\
  \DP{\hat h'_{m,n}}{t} &=& F_{2}(\zeta, D, U, V)
                       - \overline{h}\hat D_{m,n} 
                       - K_{h_{n,N_{d}}}\hat h'_{i,j} 
                  \Deqlab{$B=ENOGH$rJ,N%$7$?<ANLJ]B8$N<0$N%9%Z%/%H%kI=8=(B} 
\end{eqnarray}
\Deqref{$B=ENOGH$rJ,N%$7$?H/;6J}Dx<0$N%9%Z%/%H%kI=8=(B}, \Deqref{$B=ENOGH$rJ,(B
$BN%$7$?<ANLJ]B8$N<0$N%9%Z%/%H%kI=8=(B}$B$N$=$l$>$l1&JUBh(B 2 $B9`$,=ENOGH$K4X78$9(B
$B$k@~7A9`$G$"$k(B. $B$3$3$G(B, 
\begin{eqnarray}
  F_{1}(\zeta, D, U, V) &=&
                 - \frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
                   \frac{im}{a(1-\mu_{j} ^{2})}[(f_{j}+\zeta_{i,j})V_{i,j}]
                   e^{-im\lambda_{i}}P_{n}^{m}(\mu_{j})w_{j}\nonumber \\
             & &   -\frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
                    \frac{1}{a}\left[(f_{j}+\zeta_{i,j})U_{i,j}\right]
                   e^{-im\lambda_{i}}
                   \left.\DP{P_{n}^{m}}{\mu}\right|_{j}w_{j} \nonumber \\
             & & + \frac{n(n+1)}{a^{2}} \left[g \hat h_{s_{m,n}} 
                               + \hat E_{n,m}\right] \\
  F_{2}(\zeta, D, U, V) &=&
                  \frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
                  \frac{im}{a(1-\mu _{j}^{2})}
                  (h'_{i,j}U_{i,j})
                  e^{-im\lambda_{i}}P_{n}^{m}(\mu_{j})w_{j}\nonumber \\
             & & - \frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
                 \frac{1}{a}(h'_{i,j}V_{i,j})
                  e^{-im\lambda_{i}}
                 \left.\DP{P_{n}^{m}}{\mu}\right|_{j}w_{j}, \\
  K_{m_{n,N_{d}}} &=& K_{m}\left[\left\{\frac{n(n+1)}{a^{2}}\right\}^{N_{d}/2}
                  - \left(\frac{2}{a^{2}}\right)^{N_{d}/2}\right], \\
  K_{h_{n,N_{d}}} &=& K_{h}\left\{\frac{n(n+1)}{a^{2}}\right\}^{N_{d}/2}
\end{eqnarray}
$B$H$7$?(B. 

\Deqref{$B=ENOGH$rJ,N%$7$?H/;6J}Dx<0$N%9%Z%/%H%kI=8=(B}, \Deqref{$B=ENOGH$rJ,(B
$BN%$7$?<ANLJ]B8$N<0$N%9%Z%/%H%kI=8=(B}$B$r;~4VJ}8~$KN%;62=$9$k(B. $B$=$l$>$l$N<0(B
$B$N1&JUBh(B 2 $B9`$KBP$7$F$OBf7A7?$N1"2rK!(B, $BK`;$9`$KBP$7$F$O(B Euler $BK!(B, $B$=$NB>(B
$B$N9`$KBP$7$F$O(B Leapfrog $BK!$rE,MQ$9$k(B. 
\begin{eqnarray}
  \frac{\hat D_{m,n}^{\tau +1} - \hat D_{m,n}^{\tau -1}}{2\Delta t}
    &=& F_{1}(\zeta, D, U, V)^{\tau}
     + n(n+1) g \frac{\hat h_{m,n}^{' \tau +1} + \hat h_{m,n}^{' \tau - 1}}{2}
     - K_{m_{n,N_{d}}}\hat D_{m,n}^{\tau-1}, \\
  \frac{\hat h_{m,n}^{' \tau +1} - \hat h_{m,n}^{' \tau -1}}{2\Delta t}
    &=& F_{2}(\zeta, D, U, V)^{\tau}
    - \overline{h}\frac{\hat D_{m,n}^{\tau +1} + \hat D_{m,n}^{\tau -1}}{2}
    - K_{h_{n,N_{d}}}\hat h_{i,j}^{' \tau -1}.
\end{eqnarray}
$B$3$l$i$r(B $\hat D_{m,n}^{\tau +1}, \hat h_{m,n}^{' \tau +1}$ $B$K$D$$$F2r$/(B
$B$H0J2<$N<0$,F@$i$l$k(B (Krishnamurti {\it et al.}, 1998; Satoh, 2004).
\begin{eqnarray}
\left(1 + \Delta t^{2}g\overline{h}\frac{n(n+1)}{a^{2}}\right)
  \hat D_{m,n}^{\tau +1}  &=&
  \left(1 - \Delta t^{2}g\overline{h}\frac{n(n+1)}{a^{2}}  
          - 2\Delta t K_{m_{n,N_{d}}}\right)\hat D_{m,n}^{\tau -1} \nonumber \\ 
  && + 2\Delta t G_{1}(\zeta, D, U, V),\Deqlab{$BH/;6J}Dx<0$N;~4V@QJ,(B} \\
\left(1 + \Delta t^{2}g\overline{h}\frac{n(n+1)}{a^{2}}\right)
  \hat h_{m,n}^{' \tau +1}  &=&
  \left(1 - \Delta t^{2}g\overline{h}\frac{n(n+1)}{a^{2}}
          - 2\Delta t K_{h_{n,N_{d}}}\right)
  \hat h_{m,n}^{' \tau -1} \nonumber \\
  && + 2\Delta t G_{2}(\zeta, D, U, V) \Deqlab{$B<ANLJ]B8$N<0$N;~4V@QJ,(B} 
\end{eqnarray}
\begin{eqnarray}
  G_{1}(\zeta, D, U, V) &=&  F_{1}(\zeta, D, U, V)^{\tau} 
                 + \frac{n(n+1)}{a^{2}} g 
                   (1-\Delta t K_{h_{n,p}})\hat h_{m,n}^{' \tau-1} \nonumber \\
                & & - gF_{2}(\zeta, D, U, V)^{\tau}\Delta t, \\
  G_{2}(\zeta, D, U, V) &=& F_{2}(\zeta, D, U, V)^{\tau}
                 - \overline{h}(1- \Delta tK_{m_{n,p}}) \hat D_{m,n}^{\tau-1}
                    \nonumber \\
                & & - \overline{h}F_{1}(\zeta, D, U, V)^{\tau}\Delta t
\end{eqnarray}

\subsection{$B;~4V%U%#%k%?!<(B}

$B7W;;%b!<%I$NA}I}$rM^@)$9$k$?$a(B Asselin (1972) $B$N;~4V%U%#%k%?!<$r(B 1 $B%9%F%C(B
$B%WKh$KE,MQ$9$k(B. $BNc$($P(B\Deqref{$B12EYJ}Dx<0$N;~4V@QJ,(B}$B$rMQ$$$F(B $\hat \zeta
_{m,n}^{\tau +1}$ $B$r7W;;$9$k>l9g$O0J2<$N$h$&$K9T$&(B. 
\begin{eqnarray}
  \hat \zeta _{m,n}^{*} &=& \hat \zeta _{m,n}^{\tau -1} + 
         2\Delta t \left(
         \frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
         \frac{im}{a(1-\mu_{j} ^{2})}[(f_{j}+\zeta_{i,j}^{\tau})U_{i,j}^{\tau}]
         e^{-im\lambda_{i}}P_{n}^{m}(\mu_{j})w_{j}\right.\nonumber \\
         & & \left.-\frac{1}{2I} \sum _{j=1}^{J} \sum _{i=1}^{I}
              \frac{1}{a}\left[(f_{j}+\zeta_{i,j}^{\tau})V_{i,j}^{\tau}\right]
              e^{-im\lambda_{i}}
               \DP{P_{n}^{m}}{\mu}\right|_{j}w_{j} 
         \left.-K_{m_{n,N_{d}}}\zeta_{m,n}^{\tau-1}\right),        \\ 
  \hat \zeta _{m,n}^{\tau +1 } &=& (1-2\gamma)\hat \zeta _{m,n}^{\tau}
                                   + \gamma (\hat \zeta _{m,n}^{*} +  
                                             \hat \zeta _{m,n}^{\tau-1}).
\end{eqnarray}
$B$3$3$G(B $\gamma $ $B$O%U%#%k%?!<$N78?t$G$"$k(B. 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage                                  % $B2~%Z!<%8(B
\section{$B;HMQ%b%8%e!<%k$H$=$NB>$N@_Dj(B}

$B%9%Z%/%H%kJQ49$H5UJQ49(B, $BHyJ,1i;;$O(B SPMODEL $B%i%$%V%i%j(B (spml) $B$N(B
wt\_module $B$K4^$^$l$k4X?t$rMQ$$$F9T$&(B. $B%9%Z%/%H%kJQ49$H5UJQ49$N:]$N?tCM(B
$B@QJ,$OBf7A8x<0$rMQ$$$F9T$&(B. spml $B$,2<0L$G;HMQ$9$k(B ISPACK $B$N;EMM$+$i(B, $B3J(B
$B;RE@?t(B $I$ $B$O6v?t$G(B, $B$+$D(B $I/2 =2^{a}3^{b}5^{c}$ ($a, b, c$ $B$O(B 0 $B$^$?$O(B
$B@0?t(B) $B$G$J$1$l$P$J$i$J$$(B. $BHs@~7A9`$N7W;;$K$h$C$F@8$8$k%(%j%"%8%s%0$rKI$0(B
$B$?$a(B, $B3J;RE@?t(B $I,J$ $B$O@ZCGGH?t(B $M$ $B$KBP$7(B $I>3M+1,J>3M/2$ $B$rK~$?$9$h$&(B
$B$KM?$($k(B.





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage                                  % $B2~%Z!<%8(B
\section{$B?tCM<B83(B}

\subsection{$B<B83@_Dj(B}

$B?tCM<B83$H$7$F(B Williamson {\it et al}. (1992) $B$K$h$C$FDs0F$5$l$?(B, $B5eLL@u(B
$B?eJ}Dx<0%b%G%k$NI8=`;n83(B Case 5 $B$r9T$&(B. $B$3$l$OCf0^EY$K8IN)$7$?;3$rCV$-(B, 
$B$=$l$K$h$kN.BN$N1~Ez$rD4$Y$k<B83$G$"$k(B. $BDlLL$NCO7AJ,I[(B $h_{s}$ $B$O0J2<$N(B
$B$h$&$KM?$($k(B.
\begin{equation}
  h_{s} = h_{s0} \left(1 - \frac{1}{R}\sqrt{\mbox{min}[R^{2}, (\lambda -\lambda _{c})^{2}+(\theta - \theta _{c})^{2}]}\right)
\end{equation}
$B=i4|$NN.$l>l$H$7$F9dBN2sE>$NN.$l$rM?$($k(B. $BN.@~4X?t$HB.EY%]%F%s%7%c%k$N=i4|CM$O(B
\begin{eqnarray}
  \psi &=&  -U_{0}a\sin \theta, \\
  \chi &=& 0
\end{eqnarray}
$B$G$"$k(B. $B$3$l$h$j(B
\begin{eqnarray}
  \zeta &=& \frac{2U_{0}}{a}\sin \theta, \\
  D &=& 0
\end{eqnarray}
$B$G$"$k(B.
$B=i4|$NN.BN$NA48|$5(B $h$ $B$O>e5-$N9dBN2sE>$NN.$l$KCO9UN.%P%i%s%9$7$?J,I[$r(B
$BM?$($k(B.
\begin{equation}
  h = \overline{h} - (a\Omega U_{0} + U_{0}^{2}/2)\frac{\sin ^{2}\theta }{g}
\end{equation}

$B;HMQ$7$?%Q%i%a!<%?$NCM$O(B\Dtabref{$B;HMQ$7$?%Q%i%a!<%?$NCM(B}$B$K$^$H$a$?(B. $B3J;R(B
$BE@?t(B $I, J$ $B$H@ZCGGH?t(B $M$ $B$O$=$l$>$l(B $I=64, J=32, M=21$ $B$H$9$k(B.  $B;~4V3J(B
$B;R4V3V(B $\Delta t$ $B$O(B $1800$ sec, $B7W;;$O(B 15 $B%b%G%kF|4V9T$&(B. 

\begin{table}[htb]
 \begin{center}
  \begin{tabular}{cll} \hline
   $B%Q%i%a!<%?(B    &\qquad\qquad&  $B?tCM(B   \\ \hline 
   $\Omega$      && 7.292$\times 10^{-5}$ sec${}^{-1}$\\
   $g$           && 9.8 m sec${}^{-2}$\\
   $a$           && 6.37$\times 10^{6}$ m\\
   $K_{m}$       && 0.0 \\
   $K_{h}$       && 0.0 \\
   $p$           && 0.0 \\
   $\gamma $     && 0.05 \\
   $h_{s}$       && 2.0 $\time 10^{3}$ m\\ 
   $\lambda _{c}$ && 0.5 $\pi$ \\
   $\theta  _{c}$ && $\pi/6$ \\
   $R$           && $\pi/9$ \\
   $U_{0}$      && 20 m sec${}^{-1}$ \\
   $\overline{h}$&& 5.96$\times 10^{3}$ m \\ \hline
 \end{tabular} 
\caption{$B;HMQ$7$?%Q%i%a!<%?$NCM(B}
\Dtablab{$B;HMQ$7$?%Q%i%a!<%?$NCM(B}
\end{center}
\end{table}

\subsection{$B<B9TJ}K!(B}

$B7W;;$N<B9T$O0J2<$N<j=g$G9T$&(B. $B$?$@$7I,MW$J%i%$%V%i%j$N%$%s%9%H!<%k$,(B
$B;vA0$K:Q$s$G$$$k$3$H$rA0Ds$H$9$k(B. 
\begin{enumerate}
\item $B%W%m%0%i%`<hF@85$h$j(B
      {\tt shallow\_zd.f90}, {\tt shallow\_zd\_init.f90}, 
      {\tt shallow\_zd.sh}, 
      {\tt Makefile}, {\tt shallow\_zd\_init.nml},
      {\tt shallow\_zd.nml} $B$r:n6HNN0h$K%@%&%s%m!<%I$9$k(B.

\item NAMELIST $B%U%!%$%k(B {\tt shallo\_zd\_init.nml} , {\tt shallo\_zd.nml} 
$B$rE,59JT=8$9$k(B. NAMELIST $BJQ?t$K$D$$$F$O(B
\Dtabref{$B=i4|CM:n@.%W%m%0%i%`MQ(B NAMELIST $BJQ?t(B}, 
\Dtabref{$B<B9T%W%m%0%i%`MQ(B NAMELIST $BJQ?t(B}$B$r;2>H$5$l$?$$(B. 

\item $B%3%s%Q%$%k(B
\begin{verbatim}
$ make
\end{verbatim}

\item $B=i4|CM$N@8@.(B

$B=i4|CM:n@.%W%m%0%i%`(B {\tt shallow\_zd\_init.f90} $B$N%3%s%Q%$%k$H<B9T(B
$B$r9T$$(B, $B=i4|CM%U%!%$%k$r:n@.$9$k(B.

\begin{verbatim}
$ make init
\end{verbatim}

\item $B7W;;$r<B9T(B
\begin{verbatim}
$  ./shallow_zd.sh
\end{verbatim}
\end{enumerate}

\begin{table}[p]
 \begin{center}
\begin{tabular}{||c|c|c|l||} \hline\hline
         $BL>(B   & $BJQ?t(B  &  $B7?(B & $B@bL@(B         \\  \hline \hline
  {\tt expset}
              &                &        & $B<B83$N%i%Y%k(B \\ \hline
              & {\tt ExpTitle} & $BJ8;z7?(B & $B<B83$NL>A0(B   \\
              & {\tt ExpInst}  & $BJ8;z7?(B & $B<B9T<TL>(B     \\  
              & {\tt ExpSrc}   & $BJ8;z7?(B & $B%=!<%9%W%m%0%i%`L>(B \\  
              & {\tt ExpModel} & $BJ8;z7?(B & $B%b%G%kL>(B, 'shallow' $B$+(B 'baro' $B$rA*Br(B \\  
              & {\tt ExpCase}  & $BJ8;z7?(B & $B<B83@_DjL>(B, 'case1' $B$+$i(B 'case6' $B$^$G(B \\ \hline \hline

  {\tt dateset}
              &                 &        & $BNq$N4IM}(B         \\ \hline
              & {\tt UnitYear}  & $B@0?t7?(B & 1 $BG/$ND9$5(B($BF|(B)   \\
              & {\tt UnitDay}   & $B@0?t7?(B & 1 $BF|$ND9$5(B($B;~4V(B) \\  
              & {\tt UnitHour}  & $B@0?t7?(B & 1 $B;~4V$ND9$5(B($BJ,(B) \\  
              & {\tt UnitMinit} & $B@0?t7?(B & 1 $BJ,$ND9$5(B($BIC(B)   \\  \hline\hline

  {\tt timeset}
              &                   &        & $B;~4V@QJ,@_Dj(B     \\ \hline
	      & {\tt TimeIntYear} & $B<B?t7?(B & $B@QJ,;~4V(B($BG/(B) \\
	      & {\tt TimeIntDay}  & $B<B?t7?(B & $B@QJ,;~4V(B($BF|(B) \\
	      & {\tt TimeIntHour} & $B<B?t7?(B & $B@QJ,;~4V(B($B;~(B) \\
              & {\tt TimeIntMinit}& $B<B?t7?(B & $B@QJ,;~4V(B($BJ,(B) \\
              & {\tt TimeIntSec}  & $B<B?t7?(B & $B@QJ,;~4V(B($BIC(B) \\
              & {\tt OutputYear}  & $B<B?t7?(B & $B=PNO4V3V(B($BG/(B) \\
	      & {\tt OutputDay}   & $B<B?t7?(B & $B=PNO4V3V(B($BF|(B) \\
	      & {\tt OutputHour}  & $B<B?t7?(B & $B=PNO4V3V(B($B;~(B) \\
	      & {\tt OutputMinit} & $B<B?t7?(B & $B=PNO4V3V(B($BJ,(B) \\
	      & {\tt OutputSec}   & $B<B?t7?(B & $B=PNO4V3V(B($BIC(B) \\
              & {\tt DelTime}     & $B<B?t7?(B & $B;~4V3J;R4V3V(B($BIC(B) \\
	      & {\tt IntScheme}   & $BJ8;z7?(B & $B;~4V@QJ,K!(B, 'implicit' $B$+(B 'explicit' \\  \hline \hline
  {\tt fileset}
              &                     &        & $B%U%!%$%k@)8f(B          \\\hline
              & {\tt InputRstFile}  & $BJ8;z7?(B & $BF~NO%j%9%?!<%H%U%!%$%kL>(B \\
              & {\tt OutputRstFile} & $BJ8;z7?(B & $B=PNO%j%9%?!<%H%U%!%$%kL>(B \\
              & {\tt OutputFile}    & $BJ8;z7?(B & $B=PNO%U%!%$%kL>(B \\  \hline\hline
  {\tt gridset}
              &            & &$BJ,2rG=$N@_Dj(B                    \\ \hline
              & {\tt nm}   & $B@0?t7?(B & $B@ZCGGH?t(B  \\ 
              & {\tt im}   & $B@0?t7?(B & $B7PEYJ}8~3J;RE@?t(B ($> 3{\tt nm}+1$) \\ 
              & {\tt jm}   & $B@0?t7?(B & $B0^EYJ}8~3J;RE@?t(B ($> 3{\tt nm}/2$) \\ \hline\hline
  {\tt paramset}
              &               & & $BJ*M}Dj?t(B    \\ \hline
              & {\tt Rplanet} & $B<B?t7?(B & $BOG@1H>7B(B    \\
              & {\tt Grav}    & $B<B?t7?(B & $B=ENO2CB.EY(B  \\
              & {\tt Omega}   & $B<B?t7?(B & $B<+E>3QB.EY(B  \\
              & {\tt TfilCoef} & $B<B?t7?(B & $B;~4V%U%#%k%?!<78?t(B \\
              & {\tt VisOrder} & $B<B?t7?(B & $BD6G4@-$N<!?t(B \\
              & {\tt VisCoef} & $B<B?t7?(B & $BD6G4@-78?t(B \\
  {\tt debugset}
              &               & & $B%G%P%C%0@)8f(B    \\ \hline
              & {\tt DebugOn} & $BO@M}7?(B & $B%G%P%C%0=PNO%9%$%C%A(B  \\ \hline \hline
\end{tabular}
\caption{$B<B9T%W%m%0%i%`MQ(B NAMELIST $BJQ?t(B} 
\Dtablab{$B<B9T%W%m%0%i%`MQ(B NAMELIST $BJQ?t(B} 
\end{center}
\end{table}

\begin{table}[p]
 \begin{center}
\begin{tabular}{||c|c|c|l||} \hline\hline
         $BL>(B   & $BJQ?t(B  &  $B7?(B & $B@bL@(B         \\  \hline \hline
  {\tt expset}
              &                &        & $B<B83$N%i%Y%k(B \\ \hline
              & {\tt ExpTitle} & $BJ8;z7?(B & $B<B83$NL>A0(B   \\
              & {\tt ExpInst}  & $BJ8;z7?(B & $B<B9T<TL>(B     \\  
              & {\tt ExpSrc}   & $BJ8;z7?(B & $B%=!<%9%W%m%0%i%`L>(B \\  
              & {\tt ExpModel} & $BJ8;z7?(B & $B%b%G%kL>(B, 'shallow' $B$+(B 'baro' $B$rA*Br(B \\  
              & {\tt ExpCase}  & $BJ8;z7?(B & $B<B83@_DjL>(B, 'case1' $B$+$i(B 'case6' $B$^$G(B \\ \hline \hline
  {\tt fileset}
              &            & & $B%U%!%$%k@)8f(B               \\\hline
              & {\tt OutputRstFile} & $BJ8;z7?(B & $B=PNO%j%9%?!<%H%U%!%$%kL>(B  \\ \hline\hline
  {\tt gridset}
              &            & & $BJ,2rG=$N@_Dj(B                    \\ \hline
              & {\tt nm}   & $B@0?t7?(B & $B@ZCGGH?t(B  \\ 
              & {\tt im}   & $B@0?t7?(B & $B7PEYJ}8~3J;RE@?t(B ($> 3{\tt nm}+1$) \\ 
              & {\tt jm}   & $B@0?t7?(B & $B0^EYJ}8~3J;RE@?t(B ($> 3{\tt nm}/2$) \\ \hline\hline

  {\tt paramset}                 
              &               & & $BJ*M}Dj?t(B    \\ \hline
              & {\tt Rplanet} & $B<B?t7?(B & $BOG@1H>7B(B    \\
              & {\tt Grav}    & $B<B?t7?(B &$B=ENO2CB.EY(B  \\
              & {\tt Omega}   & $B<B?t7?(B &$B<+E>3QB.EY(B  \\
              & {\tt HsfcAvr} & $B<B?t7?(B &$BJ?6Q8|$5(B    \\ \hline \hline
  {\tt debugset}
              &               & & $B%G%P%C%0@)8f(B    \\ \hline
              & {\tt DebugOn} & $BO@M}7?(B & $B%G%P%C%0=PNO%9%$%C%A(B  \\ \hline \hline
\end{tabular}
\caption{$B=i4|CM:n@.%W%m%0%i%`MQ(B NAMELIST $BJQ?t(B} 
\Dtablab{$B=i4|CM:n@.%W%m%0%i%`MQ(B NAMELIST $BJQ?t(B} 
\end{center}
\end{table}


\subsection{$B7W;;7k2L(B}

$B12EY(B $\zeta$ $B$HA48|$5(B $h$ $B$N=i4|J,I[$H(B, $B7W;;3+;O8e(B 5 $BF|Kh$NJ,I[$r(B
\Dfigref{Case5 $B$N7W;;7k2L(B}$B$K<($9(B. $B8IN)$7$?;3$K$h$jNe5/$5$l$?GH$,5eLL>e$r(B
$BEAGE$9$kMM;R$,$o$+$k(B. 

\begin{figure}[p]
\begin{center}
\Depsf[15cm][]{./figs/shallow-zd_case5.ps}
\vspace*{-1.0cm}
\caption{Williamson {\it et al}. (1992) $B$N%F%9%H(B Case 5 $B$N7k2L(B. 
      ($B:8(B) $B12EY(B. ($B1&(B) $BN.BN$NA48|$5(B. $B>e$+$i=g$K=i4|J,I[(B, 5, 10, 15 $BF|8e$NJ,I[(B.}
\Dfiglab{Case5 $B$N7W;;7k2L(B}
\end{center}
\end{figure}



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\newpage                                  % $B2~%Z!<%8(B

\section{$B;29MJ88%(B}
\begin{description}
 \item Asselin, R. A., 1972: 
       Frequency filter for time integrations.
       {\it Mon. Wea. Rev.}, {\bf 100}, 487--490.

 \item $B@P2,7=0l(B, 200X:
       $B%9%Z%/%H%kK!$K$h$k?tCM7W;;F~Lg(B, $BEl5~Bg3X=PHG2q(B

 \item Krishnamurti, T. N., H. S. Bedi, and V. M. Hardiker, 1998:
       An introduction to global spectral modeling. 
       Ocford Univ. Press, 253 pp.

 \item Satoh, M., 2004: Atmospheric circulation dynamics and circulation 
       models.
       Springer-Verlag, 643 pp.

 \item $BC]9-??0l(B, $B@P2,7=0l(B, $BK-ED1Q;J(B, $B@PEO@5<y(B, $BNS>M2p(B, SPMODEL $B3+H/%0%k!<%W(B, 
       2002: 
       $B3,AXE*CO5eN.BNNO3X%9%Z%/%H%k%b%G%k=8(B (SPMODEL),
       http:\slash \slash www.gfd-dennou.org\slash arch\slash spmodel\slash ,
       $BCO5eN.BNEEG>6f3ZIt(B. 

 \item Williamson, D. L., J. B. Drake, J. J. Hack, R. Jakob, and P. N. Swarztrauber, 1992:
      A Standard Test Set for Numerical Approximations to the Shallow
      Water Equation in Spherical Geometry.
      {\it J. Comput. Phys.}, {\bf 102},  211--224.
\end{description}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage                                  % $B2~%Z!<%8(B
\section*{$B<U<-(B}                           % $B<U<-(B. $B$3$N$^$^MxMQ$9$k(B.
\markright{$B<U<-(B}                          % $B%X%C%@$KI=<((B

$BK\;q8;$O(B, $BCO5eN.BNEEG>6f3ZIt$N%$%s%?!<%M%C%H>e$G$N3X=QCN<1$N=8@Q$H3hMQ(B
$B$N<B83$N0l4D$H$7$F(B
\begin{center}
 http:\slash \slash www.gfd-dennou.org\slash arch\slash spmodel\slash 
\end{center}
$B$K$*$$$F8x3+$5$l$F$$$k$b$N$G$"$k(B 
(\copyright $BCO5eN.BNEEG>6f3ZIt%9%Z%/%H%k%b%G%k%W%m%8%'%/%H(B 
spmodel@gfd-dennou.org 2002. ). 
$BK\;q8;$O(B, $BCx:n<T$N=t8"Mx$KDq?($7$J$$(B($BLBOG$r$+$1$J$$(B)$B8B$j$K$*$$$F<+M3$K(B
$BMxMQ$7$F$$$?$@$$$F9=$o$J$$(B. $B$J$*(B, $BMxMQ$9$k:]$K$O:#0lEY<+$iFbMF$r3N$+$a(B
$B$k$3$H$r$*4j$$$9$k(B($BL5J]>ZL5@UG$86B'(B).

$BK\;q8;$K4^$^$l$k85;q8;Ds6!<T(B($B?^Ey$NHG85Ey$r4^$`(B)$B$+$i$O(B,  $BD>@\E*$J7A$G(B
$B$N(B WEB $B>e$G$NCx:n8"$^$?$O;HMQ5vBz$rF@$F$$$J$$>l9g$,$"$k$,(B,  $B>!<j$J$,$i(B, 
$B!VL$Mh$N650i!W$N$?$a$N<B83$H$$$&3X=QL\E*$G$"$k$3$H$r$4M}2r$$$?$@$1$k$b(B
$B$N$H?.$8(B,  $B3X=QI8=`$N0zMQ<j=g$r<i$k$3$H$G=t<jB3$-$rN,$5$;$F$$$?$@$$$F(B
$B$$$k(B.  $BK\;q8;$NMxMQ<T$K$O(B, $B$3$NE@$rM}2r$N>e(B,  $BCm0U$7$F07$C$F$$$?$@$1$k(B
$B$h$&$*4j$$$9$k(B.  $BK|0l(B, $BITET9g$N$"$k>l9g$K$O(B
\begin{center}
 spmodel@gfd-dennou.org
\end{center}
$B$^$GO"Mm$7$F$$$?$@$1$l$P9,$$$G$"$k(B. 


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\end{document}

