\section{$BN%;62=(B}

\subsection{$B1tD>J}8~$NN%;62=(B}

$B1tD>J}8~$NN%;62=$K%m!<%l%s%D3J;R$rMQ$$$k(B. $B$9$J$o$A1tD>:BI8(B, $BG.%U%i%C%/%9(B
$B$r@0?t3J;RE@$K$*$-(B, $BL)EY(B, $B290L(B, $B29EY(B, $B3H;678?t(B($BMpN.%(%M%k%.!<(B)$B$OH>@0?t3J(B
$B;RE@$KCV$/(B. $B@0?t3J;RE@4V3V$r(B $\Delta z_{i+\frac{1}{2}} \equiv z_{i+1} -
z_{i}$, $BH>@0?t3J;RE@4V3V$r(B $\Delta z_{i} \equiv z_{i+\frac{1}{2}} -
z_{i-\frac{1}{2}}$ $B$H$9$k(B. $BJ|<M2CG.9`(B $Q_{rad}$, $BCOI=LL29EY(B $T_{g}$ $B$N7W(B
$B;;J}K!$O!V2P@1Bg5$$NJ|<M%b%G%k!W$*$h$S!V2P@1COI=G.<};Y%b%G%k!W$r;2>H$N$3(B
$B$H(B.

\begin{eqnarray}
  \DP{\theta _{i+\frac{1}{2}}}{t} 
  &=& \frac{1}{\rho _{i+\frac{1}{2}}c_{p}}
      \frac{\theta _{i+\frac{1}{2}}}{T_{i+\frac{1}{2}}}Q_{rad,i+\frac{1}{2}} 
    + \frac{1}{\rho _{i+\frac{1}{2}}}
      \frac{F_{turb,i+1} - F_{turb,i}}{\Delta z_{i+\frac{1}{2}}}, \\
  F_{turb,i} 
  &=& \rho _{i}K_{h,i}\frac{\theta _{i+\frac{1}{2}}-\theta _{i-\frac{1}{2}}}
    {\Delta z_{i}},\\
  K_{h,i}
  &=& kz_{i}^{2}\sqrt{\left|\frac{\theta _{i}}{g}
      \frac{\theta _{i+\frac{1}{2}}-\theta _{i-\frac{1}{2}}}
      {\Delta z_{i}}\right|}, \\
  & & \nonumber \\
  H
  &=& \rho _{\frac{1}{2}}c_{p}C_{d}|U|(T_{g} - T_{\frac{1}{2}})
\end{eqnarray} 

\subsection{$B;~4VJ}8~$NN%;62=(B}

$B;~4VJ}8~$NN%;62=$OA0?J:9J,$G9T$J$&(B. $B$3$3$G;~9o(B $n\Delta t$ $B$K$*$1$kJ*(B
$BM}NL(B $A$ $B$NCM$r(B $A^{n}$ $B$HI=$9(B. $BJ|<M9`$K$D$$$F$OM[2rK!$G(B, $B3H;69`$K$D$$(B
$B$F$O1"2rK!(B(Crank-Nicolson $BK!(B)$B$G2r$/(B\footnote{Crank-Nicolson $BK!$K$D$$$F(B
$B$OJL;f2r@b$r;2>H$N$3$H(B}.

\begin{eqnarray}
  \theta _{i+\frac{1}{2}}^{n+1}
  &=& \theta _{i+\frac{1}{2}}^{n}+\Delta t \cdot
      \left\{
      \frac{1}{\rho _{i+\frac{1}{2}}^{n}c_{p}}
      \frac{\theta _{i+\frac{1}{2}}^{n}}
           {T_{i+\frac{1}{2}}^{n}}Q_{rad, i+\frac{1}{2}}^{n} 
      \right. \nonumber \\ 
  && \left.+\frac{1}{2}\left[
      \frac{1}{\rho _{i+\frac{1}{2}}^{n+1}}
      \frac{F_{turb,i+1}^{n+1} - F_{turb,i}^{n+1}}
           {\Delta z_{i+\frac{1}{2}}}\right]
     +\frac{1}{2}\left[
      \frac{1}{\rho _{i+\frac{1}{2}}^{n}}
      \frac{F_{turb,i+1}^{n} - F_{turb,i}^{n}}
           {\Delta z_{i+\frac{1}{2}}}\right]
      \right\}. 
\end{eqnarray}     

