%
% $BI=Bj(B   SPMODEL $B$N0l4D$H$7$F$N5eLL@u?e%b%G%k$rMQ$$$?(B
%        Williamson et al. (1992) $B$N%F%9%H(B
%
% $BMzNr(B   2005/05/11 $B>.9b(B $B@5;L(B  
%        2005/06/24 $B>.9b(B $B@5;L(B  
%
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\documentclass[a4j,12pt]{jarticle}
%
% $B%W%j%"%s%V%k(B
%
\usepackage{Dennou6}    % dennou-sty-6 $B$r;HMQ(B
\usepackage{html}	% latex2html $B%Q%C%1!<%8(B


\Dtitle[SPMODEL $B5eLL@u?e%b%G%k$N%F%9%H(B]
{SPMODEL $B$N0l4D$H$7$F$N5eLL@u?e%b%G%k$rMQ$$$?(B Williamson et al. (1992) $B$N%F%9%H(B}
%
\Dauthor[$B>.9b(B $B@5;L(B]{$B>.9b(B $B@5;L(B}            % $BCx<T(B
%\Ddate{2005 $BG/(B 5 $B7n(B 11 $BF|(B $B:n@.3+;O(B}       % $BF|IU(B
\Ddate{2005 $BG/(B 6 $B7n(B 24 $BF|(B}       % $BF|IU(B
\Dnoparindent                             % $BCJMn$N;z2<$2$r$7$J$$(B
%

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%
% $B@a(B, $B<0(B, $B?^(B, $BI=$NI=<(@_Dj(B
%\renewcommand{\thesection}{\arabic{section}}
%\renewcommand{\thesubsection}{\thesection.\arabic{subsection}}
%\renewcommand{\thesubsubsection}{\thesubsection.\arabic{subsubsection}}
%\renewcommand{\theequation}{\thesection.\arabic{equation}}
%\renewcommand{\thefigure}{\thesection.\arabic{figure}}
%\renewcommand{\thetable}{\arabic{table}}

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%
% $BK\J83+;O(B
%
% $B4pK\E*$J>O@a9=@.$O0J2<$NDL$j(B. 
%
%   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
%   -. $B<U<-(B
% 
% $BI,MW$K1~$8$F9=@.$rJQ99$9$k$3$H(B.
%
\begin{document}

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

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

SPMODEL $B$N0l4D$H$7$F$N3+H/$7$?5eLL@u?e%b%G%k$rMQ$$$F(B, Williamson {\it
et al.} (1992) $B$K$h$C$FDs0F$5$l$?5eLL@u?e%b%G%k$NI8=`<B83$r9T$C$?(B. $B2r(B
$BA|EY$O(B T21, T42, T63, T106, T213 $B$H$9$k(B.

\end{abstract}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage                                  % $B2~%Z!<%8(B
\section{$B$O$8$a$K(B}

$B?tCM%b%G%k$r3+H/$9$k:]$K$=$N?tCM%3!<%I$*$h$S7W;;7k2L$N@:EY$r3N$+$a$k$?(B
$B$a$K$O(B, $B4JC1$J=i4|>r7o$H6-3&>r7o$rM?$($??tCM<B83$r9T$$(B, $B7W;;7k2L$r2r@O(B
$B2r$^$?$OB>$N?tCM%b%G%k$K$h$C$FF@$i$l$?7W;;7k2L$HHf3S$9$k$3$H$,M-8z$G$"(B
$B$k(B. $B5eLL@u?eJ}Dx<07O$K4p$E$/?tCM%b%G%k$N$?$a$N$=$N$h$&$J?tCM<B83$H$7$F(B,
Williamson {\it et al.} (1992) $B$K$h$C$FDs0F$5$l$?(B 7 $B$D$NI8=`<B83(B ($B0J2<(B 
$B%F%9%H%1!<%9(B 1 $\sim$ 7 $B$H8F$V(B) $B$,$"$k(B. Williamson {\it et al.}
(1992) $B$N%F%9%H%1!<%9$O$=$b$=$bM-8B:9J,K!$K4p$E$/5eLL@u?e%b%G%k$N$?$a(B
$B$N?tCM<B83$H$7$F9M$($i$l$?(B. $B7W;;7k2L$N@:EY$r6cL#$9$k:]$K$O(B, $BF1DxEY$N6u(B
$B4VJ,2rG=$r;}$D%9%Z%/%H%kK!$K4p$E$/5eLL@u?e%b%G%k$N7k2L$HHf3S$9$k$3$H$,(B
$B;XDj$5$l$F$$$k(B. Jakob-Chien {\it et al.} (1995) $B$O;2>H@h$H$J$k%9%Z%/%H(B
$B%kK!$K4p$E$/5eLL@u?e%b%G%k$N7W;;@:EY$rD4$Y$k$?$a(B, NCAR $B$N%9%Z%/%H%k5e(B
$BLL@u?e%b%G%k(B STSWM (Jakob, 1992) $B$rMQ$$$F(B Williamson {\it et al.}
(1992) $B$N%F%9%H%1!<%9$r9T$C$F$$$k(B.

$BK\9F$G$O(B, SPMODEL $B$N0l4D$H$7$F3+H/$5$l$?5eLL@u?e%b%G%k$N?tCM%3!<%I$*$h(B
$B$S7W;;7k2L$N@:EY$r3N$+$a$k$?$a(B, $B$=$N%b%G%k$rMQ$$$F(B Williamson {\it et
al.} (1992) $B$N%F%9%H%1!<%9$r9T$&(B. $B3J;RE@?t$J$I$N?tCM7W;;@_Dj$O(B 
Jakob-Chien {\it et al.} (1995) $B$K=`$8$?$b$N$H$9$k(B.



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

$BMQ$$$??tCM%b%G%k$O(B SPMODEL $B$N0l4D$H$7$F3+H/$5$l$?5eLL@u?e%b%G%k(B
shallow-zd ($BC]9-(B $BB>(B, 2002)$B$G$"$k(B. $B%b%G%k$N;YG[J}Dx<07O$O12EYH/;67?$N5e(B
$BLL@u?eJ}Dx<07O$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 + F_{\zeta} 
                    \Deqlab{$B12EYJ}Dx<0(B} \\
  \DP{D}{t} &=& \frac{1}{a(1-\mu ^{2})}
                \DP{(f+\zeta)V}{\lambda}
                - \frac{1}{a}\DP{(f+\zeta)U}{\mu} 
                - \Dlapla \left[g (h+h_{s}) + E\right] \nonumber \\
            & & -K_{m}\left[(-1)^{N_{d}/2}\nabla ^{N_{d}} 
                     - \left(\frac{2}{a^{2}}\right)^{N_{d}/2}\right]D + F_{D} 
                \Deqlab{$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+F_{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}[p]
 \begin{center}
 \caption{$BJQ?t(B, $BJ*M}Dj?t$NDj5A(B}
 \Dtablab{$BJQ?t(B, $BJ*M}Dj?t$NDj5A(B}
  \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 \\ 
   $F_{\zeta, D, h}$  && $B6/@)9`(B \\ \hline
  \end{tabular} 
 \end{center}

%\begin{table}[h]
 \begin{center}
 \caption{$B%b%G%k$GMQ$$$?@ZCGGH?t$H3J;RE@?t(B, $B?eJ?3H;678?t(B, $B;~4V3J;R4V3V(B.}
 \Dtablab{$B@ZCGGH?t$H3J;RE@?t(B}
  \begin{tabular}{ccccc} \hline
   & \multicolumn{2}{c}{$B3J;RE@?t(B} & $K_{m}, K_{h}$ & $\Delta t$ \\ \cline{2-3}
   \multicolumn{1}{c}{\raisebox{1.5ex}[0pt]{$B@ZCGGH?t(B $M$}} &
   \multicolumn{1}{c}{$B7PEYJ}8~(B $I$} &
   \multicolumn{1}{c}{$B0^EYJ}8~(B $J$} &
   \multicolumn{1}{c}{(m${}^{4}$/sec)} &
   \multicolumn{1}{c}{(sec)} \\ \hline
   T42  & 128 & 64  & 0.50 $\times 10^{16}$ & 1200 \\
        &     &     &(5.00 $\times 10^{15}$) & (600) \\
   T63  & 192 & 96  & 1.00 $\times 10^{15}$ &  900 \\
        &     &     &                       & (450) \\
   T106 & 320 & 160 & 1.25 $\times 10^{14}$ &  600 \\
   T216 & 640 & 320 & 8.00 $\times 10^{12}$ &  360 \\ \hline
  \end{tabular} 
 \end{center}
\end{table}

$B6u4VN%;62=$O%9%Z%/%H%kK!$rMQ$$$F9T$&(B. $BE83+4X?t$O5eLLD4OB4X?t$rMQ$$$k(B. 
$BGH?t@ZCG$O;03Q@ZCG$G$"$k(B.$B%k%8%c%s%I%kJQ49$N:]$N?tCM@QJ,$O%,%&%9(B -- $B%k(B
$B%8%c%s%I%k$N@QJ,8x<0$rMQ$$$F9T$&(B. $BHs@~7A9`$r7W;;$9$k:]$K$O(B, $B@h$K3J;RE@(B
$B>e$G$NHs@~7A9`$NCM$r7W;;$7(B, $B$=$NCM$N%9%Z%/%H%k$r5a$a$kJ}K!(B($BJQ49K!(B)$B$rMQ(B
$B$$$k(B. $B;~4V@QJ,$O%;%_%$%s%W%j%7%C%HK!$rMQ$$$F9T$&(B. $B=ENOGH$K4X78$9$k@~7A(B
$B9`$KBP$7$F$OBf7A7?$N1"2rK!(B, $BK`;$9`$KBP$7$F$O%*%$%i!<K!(B, $B$=$NB>$N9`$KBP(B
$B$7$F$O%j!<%W%U%m%C%0K!$rE,MQ$9$k(B. $B7W;;%b!<%I$NA}I}$rM^@)$9$k$?$a(B 
Asselin (1972) $B$N;~4V%U%#%k%?!<$r(B 1 $B%9%F%C%WKh$KE,MQ$9$k(B. $B;~4V%U%#%k%?!<(B
$B$N78?t$NCM$O(B 0.05 $B$H$9$k(B.

$B3J;RE@?t(B, $B;~4V3J;R4V3V(B, $B?tCMG4@-$NM?$(J}$O(B Jakob-Chien {\it et al.}
(1995) $B$K=`$8$k(B. $BHs@~7A9`$N7W;;$K$h$C$F@8$8$k%(%j%"%8%s%0$rKI$0$?$a(B, 
$B7PEY$*$h$S0^EYJ}8~$N3J;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$&$KM?$($k(B. $BD6G4@-$N<!?t(B $N_{d}$ $B$O(B 4 $B$H$9$k(B. $B3J;RE@(B
$B?t$H?eJ?3H;678?t$NCM(B, $B;~4V3J;R4V3V(B $\Delta t$ $B$NM?$(J}$O(B, \Dtabref{$B@Z(B
$BCGGH?t$H3J;RE@?t(B}$B$K$^$H$a$?(B.

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

\section{$B?tCM<B83(B}

$B0J2<3F%F%9%H%1!<%9$N@_Dj$r7k2L$r<($9(B. $BA4$F$N%F%9%H%1!<%9$K4XO"$9$k%Q%i(B
$B%a!<%?$G$"$k(B $a, \Omega, g$ $B$O(B
\begin{eqnarray}
 a &=& 6.37122 \times 10^{6} \mbox{ m} \\
 \Omega &=& 7.292 \times 10^{-5} \mbox{ sec}^{-1} \\
 g &=& 9.80616 \mbox{ msec}^{-2}
\end{eqnarray}
$B$H$9$k(B. $h_{s}$ $B$O%F%9%H%1!<%9(B 5 $B$r=|$-(B $h_{s}=0$ $B$G$"$k(B.

$B?tCM2r$H2r@O2r$^$?$O;2>H2r$H$N8m:9A4BN$N;XI8$H$7$F(B, $B0J2<$N5,3J2=$5$l$?(B
$BA45e8m:9$rMQ$$$k(B. 
\begin{eqnarray}
  l_{1}(h) &=& \frac{I[|h(\lambda, \phi) - h_{T}(\lambda, \Phi)|]}
                    {I[|h_{T}(\lambda, \Phi)|]}, \\
  l_{2}(h) &=& \frac{\sqrt{I[(h(\lambda, \phi) - h_{T}(\lambda, \Phi))^{2}]}}
                    {\sqrt{I[h_{T}(\lambda, \Phi)^{2}]}}, \\
  l_{\infty}(h) &=& \frac{\mbox{max}_{all \lambda, \phi}|(h(\lambda, \phi) - h_{T}(\lambda, \phi)|}
                    {\mbox{max}_{all \lambda, \phi}
                          |h_{T}(\lambda, \Phi)|}
\end{eqnarray}
\begin{eqnarray}
  l_{1}(\Dvect{v}) &=& \frac{I[
        \sqrt{(u(\lambda, \phi) - u_{T}(\lambda, \Phi))^{2}+
              (v(\lambda, \phi) - v_{T}(\lambda, \Phi))^{2}}]}
        {I[\sqrt{u_{T}(\lambda, \Phi)^{2} + v_{T}(\lambda, \Phi)^{2}}]}, \\
  l_{2}(\Dvect{v}) &=& \frac{\sqrt{I[
              (u(\lambda, \phi) - u_{T}(\lambda, \Phi))^{2}+
              (v(\lambda, \phi) - v_{T}(\lambda, \Phi))^{2}]}}
        {\sqrt{I[u_{T}(\lambda, \Phi)^{2} + v_{T}(\lambda, \Phi)^{2}]}}, \\
  l_{\infty}(\Dvect{v}) &=& \frac{\mbox{max}_{all \lambda, \phi}
              [(u(\lambda, \phi) - u_{T}(\lambda, \Phi))^{2}+
              (v(\lambda, \phi) - v_{T}(\lambda, \Phi))^{2}]} 
              {\mbox{max}_{all \lambda, \phi}
              [u_{T}(\lambda, \Phi)^{2} + v_{T}(\lambda, \Phi)^{2}]}
\end{eqnarray}
$B$3$3$G(B $h_{T}(\lambda, \Phi)$ $B$J$I$N2<IU$-E:;z(B $T$ $B$rIU$1$?NL$O2r@O2r(B
$B$^$?$O;2>H2r$rI=$7(B, $I(h)$ $B$O(B $h(\lambda, \phi)$ $B$NA45e@QJ,$J$I$G(B, 
\begin{equation}
  I(h) = \frac{1}{4\pi}\int _{0}^{2\pi}\int _{-\pi/2}^{\pi/2}
          h(\lambda, \phi)\sin \phi \Dd \phi \Dd \lambda
\end{equation}
$B$HDj5A$5$l$k(B. 

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

\subsection{$B%F%9%H%1!<%9(B1: $B6K$r1[$($k(B $\cos$ $B7?$N;3$N0\N.(B}

$B%F%9%H%1!<%9(B 1 $B$O9dBN2sE>$NN.$l>l$K(B cosine $B7?$N;3$rCV$-0\N.$5$;$k<B83(B
$B$G$"$k(B. $B$3$l$O5eLL@u?eJ}Dx<07O$K$*$$$F(B, $u, v$ $B$rDj>o$H$7(B $h$ $B$N<0$r0\(B
$BN.J}Dx<0$H$7$F07$&(B. $u, v$ $B$N=i4|CM$O(B
\begin{eqnarray}
  u &=& u_{0}(\cos \phi \cos \alpha + \sin \phi \cos \lambda \sin \alpha), \\
  v &=& - u_{0}\sin \lambda \sin \alpha 
\end{eqnarray}
$B$HM?$($k(B. $BN.@~4X?t$HB.EY%]%F%s%7%c%k$N=i4|CM$O(B
\begin{eqnarray}
  \psi &=& - a u_{0}
           (\sin \phi \cos \alpha - \cos \lambda \cos \phi \sin \alpha),\\
  \chi &=& 0
\end{eqnarray}
$B$G$"$k(B. $B$3$3$G(B $\alpha $ $B$O5eLL>e$G$NN.$l$NJ}8~$r;XDj$9$k%Q%i%a!<%?$G$"$k(B.
$B=i4|$N;3$NJ,I[$O(B
\begin{equation}
  h = \left\{
\begin{array}{ll}
  (h_{0}/2)( 1 + \cos (\pi r/R) ) & (r < R) \\
  0                               & (r \ge R)
\end{array}
\right.
\end{equation}
$B$H$9$k(B. $B$3$3$G(B
\begin{equation}
  r = a \arccos (\sin \phi _{c}\sin \phi + 
                 \cos \phi _{c}\cos \phi \cos (\lambda -\lambda _{c}))
\end{equation}
$B$G$"$k(B. $BM?$($?%Q%i%a!<%?$O(B\Dtabref{$B%F%9%H%1!<%9(B1$B$N%Q%i%a!<%?(B}$B$K$^$H$a$k(B.
$B7W;;;~4V$O(B 12 $BF|4V$G(B 1 $B%9%F%C%WKh$N%G!<%?$r=PNO$9$k(B. 

\begin{table}[h]
  \begin{center}
    \Dtablab{$B%F%9%H%1!<%9(B1$B$N%Q%i%a!<%?(B}
    \caption{$B%F%9%H%1!<%9(B 1 $B$GMQ$$$?%Q%i%a!<%?(B}
    \begin{tabular}{cc} \hline
      $B%Q%i%a!<%?(B  & $BCM(B \\ \hline
      $\alpha$    & $0, \quad 0.05, \quad \pi/2 - 0.05,\quad \pi/2$ \\
      $u_{0}$     & $2\pi a/(12$$BF|(B) msec${}^{-1}$ \\
      $h_{0}$     & $1000$ m \\
      $\lambda _{c}$ & $3\pi/2$ \\
      $\phi _{c}$ & $0$ \\
      $R$         & $a/3$ \\ \hline
    \end{tabular}
  \end{center}
\end{table}

\begin{table}[h]
  \begin{center}
    \Dtablab{$B%F%9%H%1!<%9(B1$B$N7W;;;~4V(B}
    \caption{$B%F%9%H%1!<%9(B 1 $B$N7W;;;~4V(B (sec)}
    \begin{tabular}{lc|rcccc} \hline
          &   & T42 & T63 & T106 & T213 \\ \hline
                       & real & 1m11.292s &  &  & \\ 
     Intel Pentium III & usr  & 1m07.220s  &  &  & \\ 
     (Coppermine) 1GHz & sys  & 0m04.030s  &  &  & \\ \hline
    \end{tabular}
  \end{center}
\end{table}

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

\subsection{$B%F%9%H%1!<%9(B 2: $BDj>o$JHs@~7ABS>uCO9UN.(B}

$B%F%9%H%1!<%9(B 2 $B$G$OHs@~7A5eLL@u?eJ}Dx<07O$NDj>o2r$H$7$FF@$i$l$k9dBN2s(B
$BE>$NN.$l>l$H(B, $B$=$l$KCO9UN.J?9U$9$k8|$5J,I[$r=i4|$KM?$($k(B.
\begin{eqnarray}
  u &=& u_{0}(\cos \phi \cos \alpha + \sin \phi \cos \lambda \sin \alpha), \\
  v &=& - u_{0}\sin \lambda \sin \alpha, \\
  h &=& h_{0} - \left(a\Omega u_{0} + \frac{u_{0}^{2}}{2}\right)
      (-\cos \lambda \cos \phi \sin \alpha + \sin \phi \cos \alpha)^{2}/g.
\end{eqnarray}
$BN.@~4X?t$HB.EY%]%F%s%7%c%k$N=i4|CM$O%1!<%9(B 1 $B$HF1MM$K(B
\begin{eqnarray}
  \psi &=& - a u_{0}
           (\sin \phi \cos \alpha - \cos \lambda \cos \phi \sin \alpha),\\
  \chi &=& 0
\end{eqnarray}
$B$G$"$k(B. 

$B$3$N7W;;$G$O%3%j%*%j%Q%i%a!<%?(B $f$ $B$O5eLL>e$G$NN.$l$NJ}8~$r;XDj$9$k%Q(B
$B%i%a!<%?(B $\alpha $ $B$K0MB8$9$k(B.
\begin{equation}
  f = 2\Omega(-\cos \lambda \cos \phi \sin \alpha + \sin \phi \cos \alpha).
\end{equation}
$BM?$($?%Q%i%a!<%?$O(B\Dtabref{$B%F%9%H%1!<%9(B2$B$N%Q%i%a!<%?(B}$B$K$^$H$a$k(B.  $B7W;;(B
$B;~4V$O(B 5 $BF|4V$G(B, $B%F%9%H%1!<%9(B 1 $B$HF1MM$K(B 1 $B%9%F%C%WKh$N%G!<%?$r=PNO$9$k(B.

\begin{table}[h]
  \begin{center}
    \Dtablab{$B%F%9%H%1!<%9(B2$B$N%Q%i%a!<%?(B}
    \caption{$B%F%9%H%1!<%9(B 2 $B$GMQ$$$?%Q%i%a!<%?(B}
    \begin{tabular}{cc} \hline
      $B%Q%i%a!<%?(B  & $BCM(B \\ \hline
      $\alpha$    & $0, \quad 0.05, \quad \pi/2 - 0.05, \quad \pi/2$ \\
      $u_{0}$     & $2\pi a/(12$$BF|(B) msec${}^{-1}$ \\
      $h_{0}$     & $2.94\times 10^{4}/g$ m \\ \hline
    \end{tabular}
  \end{center}
\end{table}

\begin{table}[h]
  \begin{center}
    \Dtablab{$B%F%9%H%1!<%9(B2$B$N7W;;;~4V(B}
    \caption{$B%F%9%H%1!<%9(B 2 $B$N7W;;;~4V(B (sec)}
    \begin{tabular}{lc|rccc} \hline
          &   & T42 & T63 & T106 & T213 \\ \hline
                       & real & 0m42.335s &  &  & \\ 
     Intel Pentium III & usr  & 0m40.110s &  &  & \\ 
     (Coppermine) 1GHz & sys  & 0m02.190s  &  &  & \\ \hline
    \end{tabular}
  \end{center}
\end{table}

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

\subsection{$B%F%9%H%1!<%9(B 3: $B6I:_$7$?Hs@~7ABS>uCO9UN.(B}

$B$3$N<B83$O%1!<%9(B 2 $B$HF1MM$KDj>o2r$H$7$FF@$i$l$kBS>u$JN.$l$rM?$($k(B.  $B$3(B
$B$N2r$G$O8B$i$l$?>l=j$G$N$_N.$l$,B8:_$9$k(B. $BN.$l$N<4$rJQ$($?>l9g$N=i4|CM(B
$B$NI=8=$,Fq$7$$$N$G(B, $B$^$:N.$l$,7PEY:BI8$HJ?9T$J7O(B $(\lambda ', \phi')$ 
$B$G$N=i4|CM$r(B $u', v', h'$ $B$HI=$7(B, $B:BI8<4$r(B $\alpha$ $B$@$12sE>$7$?7O(B
$(\lambda, \phi)$ $B$K$*$1$k(B $u, v, h$ $B$XJQ49$9$k(B.

$BJQ49A0$N(B $u', v', h'$ $B$O0J2<$N$h$&$KM?$($i$l$k(B.
\begin{eqnarray}
  u' &=& u_{0}b(x)b(x_{e}-x)e^{4/x_{e}}, \\
  v' &=& 0, \\
  h' &=& h_{0} - \frac{a}{g}\int _{-\pi/2}^{\phi '}
         \left(2\Omega \sin \tau + \frac{u'(\tau)\tan \tau}{a}\right)
         u'(\tau)\Dd \tau.
\end{eqnarray}
$B$3$3$G(B
\[
  b(x) = \left\{
\begin{array}{lc}
0 & x\le 0 \\
e^{-x^{-1}} & 0 < x 
\end{array}
\right.
\]
\[
 x = x_{e}\frac{\phi ' - \phi _{b}}{\phi _{e}-\phi_{b}}
\]
$B$G$"$k(B.

$u', v', h'$ $B$+$i(B $u, v, h$ $B$X$NJQ49$O0J2<$N$h$&$K9T$&(B. $B$^$::BI8$O(B
\begin{eqnarray}
 \sin \phi ' &=& \sin \phi \cos \alpha - \cos \alpha \cos \lambda \sin \alpha, \\
 \sin \lambda '\cos \theta ' &=& \sin \lambda \cos \phi
\end{eqnarray}
$B$K$7$?$,$C$FJQ49$9$k(B. $\lambda '$ $B$r7h$a$k:]$K$O(B
\[
  \lambda ' = \left\{
\begin{array}{lc}
\lambda '_{p} & \cos \alpha \cos \lambda \cos \phi + \sin \alpha \sin \phi \ge 0 \\
\pi - \lambda '_{p} & \cos \alpha \cos \lambda \cos \phi + \sin \alpha \sin \phi < 0
\end{array}
\right.
\]
$B$H$9$k(B. $B$3$3$G(B $\lambda '_{p}$ $B$O(B $\lambda$ $B$N<gCM$G$"$k(B.
$u, v$ $B$O(B
\begin{eqnarray}
 v\cos \phi &=& - u'\sin \alpha \sin \lambda ', \\
 u\cos \lambda &=& v\sin \phi \sin \lambda + u'\cos \lambda '.
\end{eqnarray}
$B$h$j5a$a$k(B. 
$h$ $B$O(B $h'$ $B$N<0$r2sE>8e$N:BI87O$G?tCM@QJ,$9$k$3$H$GF@$i$l$k(B. 

$B%3%j%*%j%Q%i%a!<%?(B $f$ $B$O%F%9%H%1!<%9(B 3 $B$N>l9g$HF1MM$K(B
\begin{equation}
  f = 2\Omega(-\cos \lambda \cos \phi \sin \alpha + \sin \phi \cos \alpha)
\end{equation}
$B$H$9$k(B. 
$BM?$($?%Q%i%a!<%?$O(B\Dtabref{$B%F%9%H%1!<%9(B3$B$N%Q%i%a!<%?(B}$B$K$^$H$a$k(B.  $B7W;;(B
$B;~4V$O(B 5 $BF|4V$G(B, $B%F%9%H%1!<%9(B 1 $B$HF1MM$K(B 1 $B%9%F%C%WKh$N%G!<%?$r=PNO$9$k(B.

\begin{table}[h]
  \begin{center}
    \Dtablab{$B%F%9%H%1!<%9(B3$B$N%Q%i%a!<%?(B}
    \caption{$B%F%9%H%1!<%9(B 3 $B$GMQ$$$?%Q%i%a!<%?(B}
    \begin{tabular}{cc} \hline
      $B%Q%i%a!<%?(B  & $BCM(B                            \\ \hline
      $\alpha$    & $0, \quad \pi/3$              \\
      $u_{0}$     & $2\pi a/(12$$BF|(B) msec${}^{-1}$ \\
      $h_{0}$     & $2.94\times 10^{4}/g$ m       \\ 
      $\phi _{b}$ & $-pi/6$                       \\
      $\phi _{e}$ & $pi/2$                        \\
      $x _{e}   $ & 0.3                           \\ \hline
    \end{tabular}
  \end{center}
\end{table}

\begin{table}[h]
  \begin{center}
    \Dtablab{$B%F%9%H%1!<%9(B3$B$N7W;;;~4V(B}
    \caption{$B%F%9%H%1!<%9(B 3 $B$N7W;;;~4V(B (sec)}
    \begin{tabular}{lc|rccc} \hline
          &   & T42 & T63 & T106 & T213 \\ \hline
                       & real & 0m41.851s &  &  & \\ 
     Intel Pentium III & usr  & 0m39.200s &  &  & \\ 
     (Coppermine) 1GHz & sys  & 0m02.610s  &  &  & \\ \hline
    \end{tabular}
  \end{center}
\end{table}


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

\subsection{$B%F%9%H%1!<%9(B 4: $B0\F0$9$kDc5$05$r;}$D6/@)$5$l$?N.$l(B}

$B$3$N%1!<%9$G$O(B $u, v, h$ $B$rM=JsJQ?t$H$9$k7A$GI=$5$l$?@u?eJ}Dx<07O(B
$B$K6/@)9`$r2C$($k(B. $B6/@)9`$O(B
\begin{eqnarray}
F_{u} &=& \DD{\tilde{u}}{t} - \frac{\tilde{u}\tilde{v}\tan \phi}{a} 
          - f \tilde{v} + \frac{g}{a\cos \phi}\DP{\tilde{h}}{\lambda}, \\
F_{v} &=& \DD{\tilde{v}}{t} + \frac{\tilde{u}\tilde{v}\tan \phi}{a} 
          + f \tilde{v} + \frac{g}{a}\DP{\tilde{h}}{\lambda}, \\
F_{h} &=& \DD{\tilde{h}}{t} + \frac{\tilde{h}}{a\cos \phi}
       \left[\DP{\tilde{u}}{\lambda} + \DP{\tilde{v}\cos \phi}{\phi}
       \right] 
\end{eqnarray}
$B$H$7$FM?$($i$l$k(B. $B$3$3$G(B
\[
\DD{}{t} = \DP{}{t} + \frac{u}{a\cos \phi}\DP{}{\lambda} + 
           \frac{v}{a}\DP{}{\phi} 
\]
$B$G$"$k(B. $B12EYJ}Dx<0(B\Deqref{$B12EYJ}Dx<0(B}$B$HH/;6J}Dx<0(B\Deqref{$BH/;6J}Dx<0(B}$B$K(B
$B$*$1$k6/@)(B $F_{\zeta}, F_{D}$ $B$O(B
\begin{eqnarray}
  F_{\zeta} &=& \frac{1}{a(1-\mu ^{2})}\DP{(F_{v}\cos \phi)}{\lambda} - \frac{1}{a}\DP{(F_{u}\cos \phi)}{\mu}, \\
  F_{D} &=& \frac{1}{a(1-\mu ^{2})}\DP{(F_{u}\cos \phi)}{\lambda} + \frac{1}{a}\DP{(F_{v}\cos \phi)}{\mu}
\end{eqnarray}
$B$h$j7W;;$5$l$k(B.

$\tilde{u}, \tilde{v}, \tilde{h}$ $B$O(B
\begin{eqnarray}
\tilde{u} &=& \overline{u} - \frac{1}{a}\DP{\overline{\psi}}{\phi}, \\
\tilde{v} &=& \frac{1}{a\cos \phi}\DP{\overline{\psi}}{\lambda}, \\
\tilde{h} &=& \overline{h} + \frac{f}{g}\overline{\psi}
\end{eqnarray}
$B$GM?$($i$l(B, $B$3$3$G(B
\begin{eqnarray}
\overline{u} &=& u_{0}\sin ^{14}(2\phi), \\
\overline{h} &=& h_{0} - \frac{a}{g}\int _{-\pi/2}^{\phi}
         \left(2\Omega \sin \tau + \frac{\overline{u}(\tau)\tan \tau}{a}\right)
         \overline{u}(\tau)\Dd \tau, \\
\overline{\psi} &=& \psi _{0}\exp \left(-\sigma \frac{1-C}{1+C}\right),
\end{eqnarray}
\begin{eqnarray}
 \psi _{0} &=& -0.03\frac{gh_{0}}{2\Omega \sin (\pi/4)}, \\
 C &=& \sin \phi _{0}\sin \phi
      + \cos \phi_{0}\cos \phi
      \left(\lambda - \frac{u_{0}}{a}t - \lambda _{0}\right)
\end{eqnarray}
$B$G$"$k(B.

$BM?$($?%Q%i%a!<%?$O(B\Dtabref{$B%F%9%H%1!<%9(B4$B$N%Q%i%a!<%?(B}$B$K$^$H$a$k(B.  $B7W;;(B
$B;~4V$O(B 5 $BF|4V$G(B, $B%F%9%H%1!<%9(B 1 $B$HF1MM$K(B 1 $B%9%F%C%WKh$N%G!<%?$r=PNO$9$k(B.

\begin{table}[h]
  \begin{center}
    \Dtablab{$B%F%9%H%1!<%9(B4$B$N%Q%i%a!<%?(B}
    \caption{$B%F%9%H%1!<%9(B 4 $B$GMQ$$$?%Q%i%a!<%?(B}
    \begin{tabular}{cc} \hline
      $B%Q%i%a!<%?(B  & $BCM(B                 \\ \hline
      $u_{0}$     & $20, \quad 40$ (msec${}^{-1}$)       \\ 
      $h_{0}$     & $10^{5}/g$ m       \\ 
      $\sigma $   & $(12.74244)^{2}$     \\
      $\lambda _{0}$ & 0               \\ 
      $\phi _{0}$ & $\pi/4$           \\ \hline
    \end{tabular}
  \end{center}
\end{table}

\begin{table}[h]
  \begin{center}
    \Dtablab{$B%F%9%H%1!<%9(B4$B$N7W;;;~4V(B}
    \caption{$B%F%9%H%1!<%9(B 4 $B$N7W;;;~4V(B (sec)}
    \begin{tabular}{lc|rccc} \hline
          &   & T42 & T63 & T106 & T213 \\ \hline
                       & real & 0m55.169s &  &  & \\ 
     Intel Pentium III & usr  & 0m51.200s  &  &  & \\ 
     (Coppermine) 1GHz & sys  & 0m03.780s  &  &  & \\ \hline
    \end{tabular}
  \end{center}
\end{table}

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

\subsection{$B%F%9%H%1!<%9(B 5: $B8IN)$7$?;3$r1[$($kBS>uN.(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<$N$h$&$KM?$($k(B.
\begin{equation}
  h_{s} = h_{s0} \left(1 - \frac{1}{R}\sqrt{\mbox{min}[R^{2}, (\lambda -\lambda _{c})^{2}+(\phi - \phi _{c})^{2}]}\right)
\end{equation}
$B=i4|$N>l$O%1!<%9(B 2 $B$N(B $\alpha =0$ $B$N>l9g$HF1$8$G$"$k(B.
\begin{eqnarray}
  u &=& u_{0}\cos \phi, \\
  v &=& 0, \\
  h &=& h_{0} - \left(a\Omega u_{0} + \frac{u_{0}^{2}}{2}\right)
      (\sin \phi)^{2}/g.
\end{eqnarray}
$BN.@~4X?t$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$h$j12EY$HH/;6$N=i4|CM$O(B
\begin{eqnarray}
  \zeta &=& \frac{2u_{0}}{a}\sin \theta, \\
  D &=& 0
\end{eqnarray}
$B$G$"$k(B.

$BM?$($?%Q%i%a!<%?$O(B\Dtabref{$B%F%9%H%1!<%9(B5$B$N%Q%i%a!<%?(B}$B$K$^$H$a$k(B.  $B7W;;(B
$B;~4V$O(B 15 $BF|4V$G(B, $B%F%9%H%1!<%9(B 1 $B$HF1MM$K(B 1 $B%9%F%C%WKh$N%G!<%?$r=PNO$9$k(B.

\begin{table}[h]
  \begin{center}
    \Dtablab{$B%F%9%H%1!<%9(B5$B$N%Q%i%a!<%?(B}
    \caption{$B%F%9%H%1!<%9(B 5 $B$GMQ$$$?%Q%i%a!<%?(B}
    \begin{tabular}{cc} \hline
      $B%Q%i%a!<%?(B     & $BCM(B               \\ \hline
      $u_{0}$        & 20 msec${}^{-1}$ \\ 
      $h_{0}$        & 5960 m           \\ 
      $h_{s0}$       & 2000 m           \\
      $R$            & $\pi$/9          \\
      $\lambda _{c}$ & $\pi$/2         \\ 
      $\phi _{c}$    & $\pi/6$         \\ \hline
    \end{tabular}
  \end{center}
\end{table}

\begin{table}[h]
  \begin{center}
    \Dtablab{$B%F%9%H%1!<%9(B5$B$N7W;;;~4V(B}
    \caption{$B%F%9%H%1!<%9(B 5 $B$N7W;;;~4V(B (sec)}
    \begin{tabular}{lc|cccc} \hline
          &   & T42 & T63 & T106 & T213 \\ \hline
                       & real & 1m26.335 &  &  & \\ 
     Intel Pentium III & usr  & 1m25.770s  &  &  & \\ 
     (Coppermine) 1GHz & sys  & 0m00.550s  &  &  & \\ \hline
    \end{tabular}
  \end{center}
\end{table}

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

\subsection{$B%F%9%H%1!<%9(B 6: $B%m%9%S!<!&%O%&%k%t%#%C%DGH(B}

$B=i4|$KHsH/;6=g0512EYJ}Dx<0$N2r$G$"$k%m%9%S!<!&%O%&%k%t%#%C%DGH$rI=8=$9$k(B
$BN.@~4X?t$rM?$($k(B.
\begin{eqnarray}
  \psi &=& -a^{2}\omega \sin \phi + a^{2}K\cos ^{R}\phi \cos R\lambda, \\
  \chi &=& 0.
\end{eqnarray}
$B=i4|$NB.EY>l$O(B
\begin{eqnarray}
  u &=& a\omega \cos \phi + aK\cos ^{R-1}\phi (R\sin ^{2}\phi - \cos ^{2}\phi)\cos R\lambda, \\
  v &=& -aKR\cos ^{R-1}\phi \sin \phi \sin R\lambda
\end{eqnarray}
$B$G$"$j(B, $B12EY$HH/;6$N=i4|CM$O(B
\begin{eqnarray}
  \zeta &=& 2\omega\sin \phi - K\sin \phi \cos ^{R}\phi (R^{2}+3R+2)\cos R\lambda, \\
  D &=& 0
\end{eqnarray}
$B$G$"$k(B.

$B=i4|$N(B $h$ $B$O(B
\begin{equation}
 h = h_{0} + [a^{2}A(\phi) + a^{2}B(\phi)\cos R\lambda +a^{2}C(\phi)\cos 2R\lambda]/g
\end{equation}
$B$GM?$($i$l$k(B. $B$3$3$G(B
\begin{eqnarray}
  A(\phi) &=&
    \frac{\omega}{2}(2\Omega + \omega)\cos^{2} \phi \nonumber \\ 
  &&+ \frac{1}{4}K^{2}\cos ^{2R}[(R+1)\cos^{2}\phi 
    + (2R^{2} - R - 2) - 2R^{2}cos^{-2}\phi], \\
  B(\phi) &=& \frac{2(\Omega + \omega)K}{(R+1)(R+2)}\cos ^{R}\phi 
              [(R^{2} + 2R +2) - (R + 1)^{2}\cos ^{2}\phi], \\
  C(\phi) &=& \frac{1}{4}K^{2}\cos ^{2R}\phi[(R + 1)\cos ^{2}\phi - (R + 2)]
\end{eqnarray}
$B$G$"$k(B. 

$BM?$($?%Q%i%a!<%?$O(B\Dtabref{$B%F%9%H%1!<%9(B5$B$N%Q%i%a!<%?(B}$B$K$^$H$a$k(B.  $B7W;;(B
$B;~4V$O(B 15 $BF|4V$G(B, $B%F%9%H%1!<%9(B 1 $B$HF1MM$K(B 1 $B%9%F%C%WKh$N%G!<%?$r=PNO$9$k(B.

\begin{table}[h]
  \begin{center}
    \Dtablab{$B%F%9%H%1!<%9(B5$B$N%Q%i%a!<%?(B}
    \caption{$B%F%9%H%1!<%9(B 5 $B$GMQ$$$?%Q%i%a!<%?(B}
    \begin{tabular}{cc} \hline
      $B%Q%i%a!<%?(B     & $BCM(B               \\ \hline
      $h_{0}$  & 8000 m           \\ 
      $R$      & 4               \\
      $\omega$ & $7.848\times 10^{-6}$ sec${}^{-1}$ \\ 
      $K$      & $7.848\times 10^{-6}$ sec${}^{-1}$ \\ \hline
    \end{tabular}
  \end{center}
\end{table}

\begin{table}[h]
  \begin{center}
    \Dtablab{$B%F%9%H%1!<%9(B6$B$N7W;;;~4V(B}
    \caption{$B%F%9%H%1!<%9(B 6 $B$N7W;;;~4V(B (sec)}
    \begin{tabular}{lc|cccc} \hline
          &   & T42 & T63 & T106 & T213 \\ \hline
                       & real & 1m35.644s &  &  & \\ 
     Intel Pentium III & usr  & 1m32.210s &  &  & \\ 
     (Coppermine) 1GHz & sys  & 0m03.410s &  &  & \\ \hline
    \end{tabular}
  \end{center}
\end{table}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\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, 2004:
       $B%9%Z%/%H%kK!$K$h$k?tCM7W;;F~Lg(B, $BEl5~Bg3X=PHG2q(B

 \item Jakob-Chien, R., J. J. Hack, and D. L. Williamson, 1995:
       Spectral Transform Solutions to the Shallow Water Test Set,
       {\it J. Comp. Phys.}, {\bf 119}, 164--187.

 \item Jacob, R., 1992:
       STSWM (NCAR Spectral Transform Shallow Water Model),
	\htmladdnormallink{
        http://www.csm.ornl.gov/chammp/stswm/}
        {http://www.csm.ornl.gov/chammp/stswm/}

 \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),
       \htmladdnormallink{
       http://www.gfd-dennou.org/arch/spmodel/}
       {http://www.gfd-dennou.org/arch/spmodel/}, $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

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\begin{center}
 http:\slash \slash www.gfd-dennou.org\slash arch\slash spmodel\slash 
\end{center}
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\[
 \mbox{spmodel@gfd-dennou.org}
\]
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