\batchmode

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\usepackage{Dennou6}
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\DoffJ


\Dtitle[\DselJ{deepconv-mars: Υ����ǥ�}{deepconv-mars:}]
{\DselJ{
  2 ����������ή�Υ�ǥ� deepconv-mars \\�� 2 ��: Υ����ǥ����} 
  {Two dimensional anelastic model deepconv-mars: \\Part II, Finite difference equations of the model}}


\Dauthor{\DselJ{��������}{Masatsugu Odaka}}
\Ddate{\DselJ{2001 ǯ 11 �� 1 ��}{2001/11/01}}




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$\displaystyle \left.
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\right]
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4232}%
$\displaystyle + \frac{(\Delta x)^{2}}{\rho _{0,j}\Delta z_{j}}
\left[ \left.
\rho _{0,j+1}K_{i,j+1}^{n}
\left(w_{i,j+1}^{n}-w_{i,j}^{n}\right)
\right/\Delta z_{j+1} -
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4233}%
$\displaystyle \left.
\left.
\left. \rho _{0,j}K_{i,j}^{n}
\left(w_{i,j+\frac{1}{2}}^{n}-w_{i,j-\frac{1}{2}}^{n}\right)
\right/\Delta z_{j-1}
\right] \right\}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4235}%
$\displaystyle \mbox{DUNLV}_{i+\frac{1}{2},j}^{n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4237}%
$\displaystyle \left\{
\left[
\left(u_{i+\frac{3}{2},j}^{n}-u_{i+\frac{1}{2},j}^{n} \right)^{3}
-\left(u_{i+\frac{1}{2},j}^{n}-u_{i-\frac{1}{2},j}^{n} \right)^{3}
\right]
+ 0.1
\left[ \left(u_{i+\frac{1}{2},j+1}^{n}-u_{i+\frac{1}{2},j}^{n}
\right)^{3} \right. \right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4238}%
$\displaystyle \left.
\left.
\left. - \left(u_{i+\frac{1}{2},j}^{n}-u_{i+\frac{1}{2},j-1}^{n}
\right)^{3}
\right]
\right\}
\right/
(16.0 \cdot 10^{3} \cdot \rho _{0,j}\Delta z_{j}/\Delta x ),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4239}%
$\displaystyle \mbox{DVNLV}_{i+\frac{1}{2},j}^{n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4241}%
$\displaystyle \left\{
\left[
\left(v_{i+\frac{3}{2},j}^{n}-v_{i+\frac{1}{2},j}^{n}\right)^{3}
-\left(v_{i+\frac{1}{2},j}^{n}-v_{i-\frac{1}{2},j}^{n}\right)^{3}
\right]
+ 0.1
\left[ \left(v_{i+\frac{1}{2},j+1}^{n}-v_{i+\frac{1}{2},j}^{n}
\right)^{3} \right.
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4242}%
$\displaystyle \left.
\left.
\left. - \left(v_{i+\frac{1}{2},j}^{n}-v_{i+\frac{1}{2},j-1}^{n}
\right)^{3}
\right]
\right\}
\right/
(16.0 \cdot 10^{3} \cdot \rho _{0,j}\Delta z_{j}/\Delta x ),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4243}%
$\displaystyle \mbox{DWNLV}_{i,j+\frac{1}{2}}^{n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4245}%
$\displaystyle \left\{
\left[
\left(w_{i+1,j+\frac{1}{2}}^{n}-w_{i,j+\frac{1}{2}}^{n}\right)^{3}
-\left(w_{i,j+\frac{1}{2}}^{n}-w_{i-1,j+\frac{1}{2}}^{n}\right)^{3}
\right]
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4246}%
$\displaystyle \left.
\left.
+ 0.1
\left[ \left(w_{i,j++\frac{3}{2}}^{n}-w_{i,j+\frac{1}{2}}^{n}\right)^{3}
- \left(w_{i,j+\frac{1}{2}}^{n}-w_{i,j-\frac{1}{2}}^{n}\right)^{3}
\right]
\right\}
\right/$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4247}%
$\displaystyle (16.0 \cdot 10^{3} \cdot \rho _{0,j+\frac{1}{2}}
\Delta z_{j+\frac{1}{2}}/\Delta x ),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4248}%
$\displaystyle \mbox{BUOY}_{i,j+\frac{1}{2}}^{n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4250}%
$\displaystyle \frac{g}{\Theta _{0,j+\frac{1}{2}}}
\theta _{i,j+\frac{1}{2}}^{n},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4251}%
$\displaystyle \mbox{DUCOLI}_{i+\frac{1}{2},j}^{n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4253}%
$\displaystyle - f v_{i+\frac{1}{2},j}^{n},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4254}%
$\displaystyle \mbox{DVCOLI}_{i+\frac{1}{2},j}^{n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4256}%
$\displaystyle + f u_{i+\frac{1}{2},j}^{n}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar747}%
\begin{eqnarray*}
 && u_{i+\frac{1}{2},j+\frac{1}{2}}^{n} =
 0.5\left(u_{i+\frac{1}{2},j+1}^{n} + u_{i+\frac{1}{2},j}^{n}\right), 
 \quad 
 u_{i,j}^{n} =
 0.5\left(u_{i+\frac{1}{2},j}^{n} + u_{i-\frac{1}{2},j}^{n}\right), \\
 && v_{i+\frac{1}{2},j+\frac{1}{2}}^{n} =
 0.5\left(v_{i+\frac{1}{2},j+1}^{n} + v_{i+\frac{1}{2},j-1}^{k}\right), 
 \quad
 v_{i,j}^{n} =
 0.5\left(v_{i+\frac{1}{2},j}^{n} + v_{i-\frac{1}{2},j}^{n}\right), \\
 &&
 w_{i+\frac{1}{2},j+\frac{1}{2}}^{n} =
 0.5\left(w_{i+1,j+\frac{1}{2}}^{n} + w_{i,j+\frac{1}{2}}^{n}\right), 
 \quad
 w_{i,j}^{n} =
 0.5\left(w_{i,j+\frac{1}{2}}^{n} + w_{i,j-\frac{1}{2}}^{n}\right), \\
 && 
 \theta _{i,j+\frac{1}{2}} =
 \left( -\frac{1}{16}\theta _{i,j+2}^{n}
        +\frac{9}{16}\theta _{i,j+1}^{n}
        +\frac{9}{16}\theta _{i,j-1}^{n}
        -\frac{1}{16}\theta _{i,j-2}^{n} \right) , \\
 && 
 K_{i+\frac{1}{2},j+\frac{1}{2}}^{n} =
 0.25\left(K_{i+1,j+1}^{n} + K_{i+1,j}^{n} + 
           K_{i,j+1}^{n}   + K_{i,j}^{n}\right), \\
 && \\
 && 
 \Theta _{0,j+\frac{1}{2}} =
 0.5\left(\Theta _{0,j+1}+\Theta _{0,j+1}\right), \quad
 \rho  _{0,j+\frac{1}{2}} =
 0.5\left(\rho _{0,j+1}+\rho _{0,j+1}\right), \\
 && \\
 && 
 (\Ddiv \rho _{0}\Dvect{v}/\rho _{0})_{i+\frac{1}{2},j}^{n}
 = \frac{u_{i+1,j}^{n} - u_{i,j}^{n}}{\Delta x}
 + \frac{\rho _{0,j+\frac{1}{2}}w_{i+\frac{1}{2},j+\frac{1}{2}}^{n} -
         \rho _{0,j-\frac{1}{2}}w_{i+\frac{1}{2},j-\frac{1}{2}}^{n}}
   {\rho _{0,j}\Delta z_{j}}, \\
 &&
 (\Ddiv \rho _{0}\Dvect{v}/\rho _{0})_{i,j+\frac{1}{2}}^{n}
 = \frac{u_{i+\frac{1}{2},j+\frac{1}{2}}^{n} - 
         u_{i-\frac{1}{2},j+\frac{1}{2}}^{n}}{\Delta x}
 + \frac{\rho _{0,j+1}w_{i,j+1}^{n} - \rho _{0,j}w_{i,j}^{n}}
   {\rho _{0,j+\frac{1}{2}}\Delta z_{j+\frac{1}{2}}}.
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1866}%
$[\mbox{DTADV}]_{i,j}^{n}, [\mbox{DTAD0}]_{i,j}^{n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1868}%
$[\mbox{DTDIF}]_{i,j}^{N}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1870}%
$[\mbox{DTDI0}]_{i,j}^{N}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1872}%
$Q_{rad,i,j}^{N}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1874}%
$Q_{dis,i,j}^{N}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4270}%
$\displaystyle \theta _{i,j}^{n+1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4272}%
$\displaystyle \theta _{i,j}^{N} +
dt \left\{
\frac{\Theta _{0,j}}{T_{0,j}}(Q_{rad,i,j}^{N} + Q_{dis,i,j}^{N})
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4273}%
$\displaystyle + \left.
[\mbox{DTADV}]_{i,j}^{n} +
[\mbox{DTAD0}]_{i,j}^{n} +
[\mbox{DTDIF}]_{i,j}^{N} +
[\mbox{DTDI0}]_{i,j}^{N} \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath959}%
\begin{displaymath}
  Q_{dis,i,j}^{N} = \frac{C_{\epsilon}}{lc_{p}}
  (\varepsilon _{i,j}^{N})^{\frac{3}{2}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4276}%
$\displaystyle \mbox{DTADV}_{i,j}^{n}
= - \left\{
\frac{1}{\rho _{0,j}\Delta x}\left[
- \frac{1}{24}F\theta _{x(i+\frac{3}{2},j)}^{n}
+ \frac{9}{8} F\theta _{x(i+\frac{1}{2},j)}^{n}
- \frac{9}{8} F\theta _{x(i-\frac{1}{2},j)}^{n}
+ \frac{1}{24}F\theta _{x(i-\frac{3}{2},j)}^{n} \right]
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4277}%
$\displaystyle +  \left.
\frac{1}{\rho _{0,j}\Delta z_{j}}\left[
- \frac{1}{24}F\theta _{z(i,j+\frac{3}{2})}^{n}
+ \frac{9}{8} F\theta _{z(i,j+\frac{1}{2})}^{n}
- \frac{9}{8} F\theta _{z(i,j-\frac{1}{2})}^{n}
+ \frac{1}{24}F\theta _{z(i,j-\frac{3}{2})}^{n} \right] \right\},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4278}%
$\displaystyle F\theta _{x(i+\frac{1}{2},j)}^{n}
=
\rho _{0,j}u_{i+\frac{1}{2},j}^{n}
\left( - \frac{1}{16}\theta _{i+2,j}^{n}
+ \frac{9}{16}\theta _{i+1,j}^{n}
+ \frac{9}{16}\theta _{i,j}^{n}
- \frac{1}{16}\theta _{i-1,j}^{n}  \right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4279}%
$\displaystyle F\theta _{z(i,j+\frac{1}{2})}^{n}
=
\rho _{0,j+\frac{1}{2}}w_{i,j+\frac{1}{2}}^{n}
\left( - \frac{1}{16}\theta _{i,j+2}^{n}
+ \frac{9}{16}\theta _{i,j+1}^{n}
+ \frac{9}{16}\theta _{i,j}^{n}
- \frac{1}{16}\theta _{i,j-1}^{n}  \right).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4281}%
$\displaystyle \mbox{DTAD0}_{i,j}^{n}
= - \left\{
\frac{1}{\rho _{0,j}\Delta x}\Theta _{0,j}\left[
- \frac{1}{24}F_{x(i+\frac{3}{2},j)}^{n}
+ \frac{9}{8} F_{x(i+\frac{1}{2},j)}^{n}
- \frac{9}{8} F_{x(i-\frac{1}{2},j)}^{n}
+ \frac{1}{24}F_{x(i-\frac{3}{2},j)}^{n} \right]
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4282}%
$\displaystyle + \left.
\frac{1}{\rho _{0,j}\Delta z_{j}}\left[
- \frac{1}{24}F\Theta _{0,z(j+\frac{3}{2})}^{n}
+ \frac{9}{8} F\Theta _{0,z(j+\frac{1}{2})}^{n}
- \frac{9}{8} F\Theta _{0,z(j-\frac{1}{2})}^{n}
+ \frac{1}{24}F\Theta _{0,z(j-\frac{3}{2})}^{n} \right] \right\},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4283}%
$\displaystyle F_{x(i+\frac{1}{2},j)}^{n}
=
\rho _{0,j}u_{i+\frac{1}{2},j}^{n},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4284}%
$\displaystyle F\Theta _{0,z(j+\frac{1}{2})}^{n}
=
\rho _{0,j+\frac{1}{2}}w_{i,j+\frac{1}{2}}^{n}
\left( - \frac{1}{16}\Theta _{0,j+2}
+ \frac{9}{16}\Theta _{0,j+1}
+ \frac{9}{16}\Theta _{0,j}
- \frac{1}{16}\Theta _{0,j-1} \right).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4286}%
$\displaystyle \mbox{DTDIF}_{i,j}^{n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4288}%
$\displaystyle \frac{1}{(\Delta x)^{2}}
\left[
\tilde{K}_{i+\frac{1}{2},j}^{n}(\theta _{i+1,j}^{n}-\theta _{i,j}^{n})
-\tilde{K}_{i-\frac{1}{2},j}^{n}(\theta _{i,j}^{n}  -\theta _{i-1,j}^{n})
\right] +$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4289}%
$\displaystyle \frac{1}{\rho _{0,j}\Delta z_{j}}
\left[ \rho _{0,j+\frac{1}{2}}
\tilde{K}_{i,j+\frac{1}{2}}^{n}
\frac{
(\theta _{i,j+1}^{n}-\theta _{i,j}^{n})}{\Delta z_{j+\frac{1}{2}}}
- \rho _{0,j-\frac{1}{2}}
\tilde{K}_{i,j-\frac{1}{2}}^{n}
\frac{
(\theta _{i,j}^{n}  -\theta _{i,j-1}^{n})}{\Delta z_{j-\frac{1}{2}}}
\right],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1196}%
\begin{displaymath}
 \mbox{DTDI0}_{i,j}^{n}
 =
 \frac{1}{\rho _{0,j}\Delta z_{j}}
 \left[
     \rho _{0,j+\frac{1}{2}}\tilde{K}_{i,j+\frac{1}{2}}^{n}
     \frac{
     (\Theta _{0,j+1}^{n}-\Theta _{0,j}^{n})}{\Delta z_{j+\frac{1}{2}}}
   - \rho _{0,j-\frac{1}{2}}\tilde{K}_{i,j-\frac{1}{2}}^{n}
     \frac{
     (\Theta _{0,j}^{n}  -\Theta _{0,j-1}^{n})}{\Delta z_{j-\frac{1}{2}}}
 \right],
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1834}%
\begin{displaymath}
 \tilde{K}_{i+\frac{1}{2},j}^{n} 
 = 0.5(\tilde{K}_{i+1,j}^{n} +\tilde{K}_{i,j}^{n} ), \quad
 \tilde{K}_{i,j+\frac{1}{2}}^{n} 
 = 0.5(\tilde{K}_{i,j+1}^{n} +\tilde{K}_{i,j}^{n} ).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath1835}%
\begin{displaymath}
  \left(\DP[2]{}{x} +\frac{1}{\rho _{0}}\DP{}{z}\rho _{0}\DP{}{z}\right)
  P = \DP{}{t}\left(\frac{1}{\rho _{0}}\Ddiv \rho _{0}\Dvect{v}\right) 
  + \DP{}{x}\alpha ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1273}%
\begin{displaymath}
   \Dvect{D_{x}P} + \Dvect{D_{z}P} = \Dvect{S}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1886}%
$\Dvect{P}, \Dvect{D_{x}}, \Dvect{D_{z}},
\Dvect{S}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1836}%
\begin{displaymath}
  \hat{P}, \quad
  \DP[2]{}{x}, \quad
  \frac{1}{\rho _{0}}\DP{}{z}\left(\rho _0\DP{}{z}\right), \quad
  \DP{}{t}\left(\frac{1}{\rho _{0}}\Ddiv \Dvect{v}\right) 
  + \DP{}{x}\alpha ,      
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1890}%
$\Dvect{D_{z}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1892}%
$\lambda_{i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1894}%
$V_{i}(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1896}%
$\Dvect{V}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1900}%
$\Dvect{\Lambda }$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1902}%
$\Dvect{D_{z}V} = \Dvect{V\Lambda }$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1904}%
$\Dvect{P} = \Dvect{V}\cdot
\Dvect{H}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1837}%
\begin{displaymath}
  \Dvect{V}\Dvect{D_{x}H} + \Dvect{V\Lambda H} = \Dvect{S}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1328}%
\begin{displaymath}
  \left(\Dvect{D_{x}} + \Dvect{\Lambda }\right) \Dvect{H}
  = \Dvect{V}^{-1}\Dvect{S},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1920}%
$z$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1922}%
$\Dvect{D}_{z}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1838}%
\begin{displaymath}
  \frac{1}{\rho _{0}}\DP{}{z}\rho _{0}\DP{}{z} \pi 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1926}%
$A_{ij}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1930}%
$A_{i,j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4323}%
$\displaystyle A_{i,i+2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4325}%
$\displaystyle -\frac{1}{\rho _{0}\Delta z_{i}}\left(
\frac{1}{24\Delta z_{i+\frac{3}{2}}}\frac{(\rho _
{0,i+2}+\rho _{0,i+1})}{2}\right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4326}%
$\displaystyle A_{i,i+1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4328}%
$\displaystyle \frac{1}{\rho _{0}\Delta z_{i}}\left(
\frac{1}{24\Delta z_{i+\frac{3}{2}}}\frac{(\rho _
{0,i+2}+\rho _{0,i+1})}{2} +
\frac{9}{8\Delta m_{i+\frac{1}{2}}}\frac{(\rho _
{0,i+1}+\rho _{0,i})}{2}\right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4329}%
$\displaystyle A_{i,i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4331}%
$\displaystyle - \frac{1}{\rho _{0}\Delta z_{i}}\left(
\frac{9}{8\Delta zm_{i+\frac{1}{2}}}\frac{(\rho _
{0,i+1}+\rho _{0,i})}{2}
+ \frac{9}{8\Delta z_{i-\frac{1}{2}}}\frac{(\rho _
{0,i}+\rho _{0,i-1})}{2}\right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4332}%
$\displaystyle A_{i+1,i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4334}%
$\displaystyle \frac{1}{\rho _{0}\Delta z_{i}}\left(
\frac{1}{24\Delta z_{i-\frac{3}{2}}}\frac{(\rho _
{0,i-1}+\rho _{0,i-2})}{2} +
\frac{9}{8\Delta z_{i-\frac{1}{2}}}\frac{(\rho _
{0,i}+\rho _{0,i-1})}{2}\right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4335}%
$\displaystyle A_{i+2,i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4337}%
$\displaystyle -\frac{1}{\rho _{0}\Delta z_{i}}\left(
\frac{1}{24\Delta z_{i-\frac{3}{2}}}\frac{(\rho _
{0,i-1}+\rho _{0,i-2})}{2} \right).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1932}%
$\DP{}{z}=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1936}%
$x$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4342}%
$\displaystyle \Dvect{H}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4344}%
$\displaystyle \sum_{k=1}^{NX/2-1}
\left[\Dvect{H}\right]_{k_{x}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4345}%
$\displaystyle \Dvect{V}^{-1}\Dvect{S}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4347}%
$\displaystyle \sum_{k=1}^{NX/2-1}
\left[\Dvect{V}^{-1}\Dvect{S}\right]_{k_{x}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4348}%
$\displaystyle \left(\Dvect{D_{x}} + \Dvect{\Lambda }\right)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4350}%
$\displaystyle \sum_{k_{x}=1}^{NX/2-1}
\left[\Dvect{D_{x}} + \Dvect{\Lambda }\right]_{k_{x}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1454}%
\begin{displaymath}
      \left[\Dvect{H}\right]_{k_{x}} = 
      \left[\Dvect{D_{x}} + \Dvect{\Lambda }\right]_{k_{x}}^{-1}
      \left[\Dvect{V}^{-1}\Dvect{S}\right]_{k_{x}}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1938}%
$T_{j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1940}%
$P_{0,j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1942}%
$\rho _{0,j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1948}%
$T_{0,j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4360}%
$\displaystyle \ln P_{0,j} = \ln P_{00}
- \sum _{j=1}^{j}\frac{g}{RT_{0,j}}\Delta z_{j},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4361}%
$\displaystyle \rho _{0,j} = \frac{P_{0,j}}{RT_{0,j}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1950}%
$P_{0,j}, \rho _{0,j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1952}%
$\Pi _{0,j}, \Theta _{0,j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1954}%
$\Pi_{0,j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1956}%
$\Theta _{0,j}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4369}%
$\displaystyle \Pi _{0,j}    = \left(\frac{P_{0,j}}{P_00}\right)^{\kappa },$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4370}%
$\displaystyle \Theta _{0,j} = \frac{T_{0,j}}{\Pi _{0,j}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2388}%
$[\mbox{DKADV}]_{i,j}^{n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2390}%
$[\mbox{DKDIF}]_{i,j}^{N}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2392}%
$[\mbox{DKNLD}]_{i,j}^{N}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4381}%
$\displaystyle \varepsilon _{i,j}^{n+1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4383}%
$\displaystyle \varepsilon _{i,j}^{N} + dt \left\{
[\mbox{DKADV}]_{i,j}^{n} +
[\mbox{DKDIF}]_{i,j}^{N} +
[\mbox{DKNLD}]_{i,j}^{N} \right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4384}%
$\displaystyle + \left.
[\mbox{DKBP}]_{i,j}^{n} +
[\mbox{DKSP}]_{i,j}^{n} -
\frac{C_{\epsilon}}{l}(\varepsilon _{i,j}^{N})^{\frac{3}{2}} \right\}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4386}%
$\displaystyle \mbox{DKNLD}_{i,j}^{n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4388}%
$\displaystyle \frac{1}{(\Delta x)^{2}}
\left[
K_{NLD,i+\frac{1}{2},j}^{n}(\varepsilon_{i+1,j}^{n}-\varepsilon_{i,j}^{n})
-K_{NLD,i-\frac{1}{2},j}^{n}(\varepsilon_{i,j}^{n}  -\varepsilon_{i-1,j}^{n})
\right] + \frac{1}{\rho _{0,j}\Delta z_{j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4389}%
$\displaystyle \left[ \rho _{0,j+\frac{1}{2}}
K_{NLD,i,j+\frac{1}{2}}^{n}
\frac{
(\varepsilon_{i,j+1}^{n}-\varepsilon_{i,j}^{n})}{\Delta z_{j+\frac{1}{2}}}
- \rho _{0,j-\frac{1}{2}}
K_{NLD,i,j-\frac{1}{2}}^{n}
\frac{
(\varepsilon_{i,j}^{n}-\varepsilon_{*i,j-1}^{n})}{\Delta z_{j-\frac{1}{2}}}
\right],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar2111}%
\begin{eqnarray*}
 K_{NLD,i+\frac{1}{2},j}^{n} 
 &=& 
 \mbox{MIN}
 \left[ K_{NLD,max}, \quad
        0.01\frac{(\Delta x)^{2}}{\Delta t}
        \frac{{\cal L}(\varepsilon)_{i+1,j}^{n}
              +{\cal L}(\varepsilon)_{i,j}^{n}}{2} \right], \\
 K_{NLD,i,j+\frac{1}{2}}^{n} 
 &=&
 \mbox{MIN}
 \left[ K_{NLD,max}, \quad
        0.01\frac{(\Delta x)^{2}}{\Delta t}
        \frac{{\cal L}(\varepsilon)_{i,j+1}^{n}
              +{\cal L}(\varepsilon)_{i,j}^{n}}{2} \right], \\
 {\cal L}(\varepsilon)_{i,j}^{n}
 &=& \left. \left(
 3\left|\varepsilon_{i+1,j}^{n} + 
        \varepsilon_{i-1,j}^{n} - 2\varepsilon_{i,j}^{n}\right|
 +\left|\varepsilon_{i,j+1}^{n} + 
        \varepsilon_{i,j-1}^{n} - 2\varepsilon_{i,j}^{n}\right|
 \right)\right /2000, \\
 K_{NLD,max} &=& 0.2\frac{(\Delta x)^{2}}{\Delta t}.
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4392}%
$\displaystyle \mbox{DKBP}_{i,j}^{n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4394}%
$\displaystyle -\frac{g}{\Theta _{0,j}}K_{i,j}^{n}
\frac{1}{\Delta z_{j}}\left[
(\theta _{i,j+\frac{1}{2}}+\Theta _{0,j+\frac{1}{2}}) -
(\theta _{i,j-\frac{1}{2}}+\Theta _{0,j-\frac{1}{2}}) \right],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4395}%
$\displaystyle \mbox{DKSP}_{i,j}^{n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4397}%
$\displaystyle 2K_{i,j}^{n}\left[
\left(
\frac{u_{i+\frac{1}{2},j}^{n}-u_{i-\frac{1}{2},j}^{n}}{\Delta x}
\right)^{2}
+ \left(
\frac{w_{i,j+\frac{1}{2}}^{n}-w_{i,j-\frac{1}{2}}^{n}}{\Delta z_{j}}
\right)^{2}
\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4398}%
$\displaystyle + \frac{2}{3}\varepsilon _{i,j}^{n} \left[
\frac{u_{i,j+\frac{1}{2}}^{n}-u_{i,j-\frac{1}{2}}^{n}}{\Delta z_{j}} +
\frac{w_{i+\frac{1}{2},j}^{n}-w_{i-\frac{1}{2},j}^{n}}{\Delta x}\right]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4399}%
$\displaystyle + K_{i,j}^{n}
\left[
\frac{u_{i,j+\frac{1}{2}}^{n}-u_{i,j-\frac{1}{2}}^{n}}{\Delta z_{j}} +
\frac{w_{i+\frac{1}{2},j}^{n}-w_{i-\frac{1}{2},j}^{n}}{\Delta x}\right]^{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2386}%
\begin{displaymath}
 u_{i,j+\frac{1}{2}}^{n} =
 0.5\left(u_{i+\frac{1}{2},j+\frac{1}{2}}^{n} + 
          u_{i-\frac{1}{2},j+\frac{1}{2}}^{n}\right), 
 \quad 
 w_{i+\frac{1}{2},j}^{n} =
 0.5\left(w_{i+\frac{1}{2},j+\frac{1}{2}}^{n} + 
          w_{i+\frac{1}{2},j-\frac{1}{2}}^{n}\right).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4403}%
$\displaystyle F_{u,i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4405}%
$\displaystyle - \rho _{0}C_{D,i}|u_{i,\frac{1}{2}}|u_{i,\frac{1}{2}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4406}%
$\displaystyle F_{\theta,i}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4408}%
$\displaystyle \rho _{0}C_{D,i}|u_{i,\frac{1}{2}}|(T_{sfc,i}-T_{i,1}).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2282}%
\begin{displaymath}
  C_{D,i} = \left\{
  \begin{array}{lcl}
  C_{Dn}\left( 1 -
  	\frac{a\mbox{Ri}_{B,i}}{1+c|\mbox{Ri}_{B,i}|^{1/2}} \right) & 
  	for & \mbox{Ri}_{B,i} < 0,  \\
  C_{Dn}\frac{1}{(1+b\mbox{Ri}_{B,i})^{2}}& for &  \mbox{Ri}_{B,i} \geq 0,
  \end{array}\right. 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2305}%
\begin{displaymath}
  \mbox{Ri}_{B,i} \equiv \frac{gz_{1}(\Theta _{sfc,i}-\Theta _
  {i,1})}{\overline{\Theta }_{0,1}u_{i,\frac{1}{2}}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2536}%
$[\mbox{DQADV}]_{i,j}^{n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2538}%
$[\mbox{DQFALL}]_{i,j}^{N}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2540}%
$[\mbox{DQDIF}]_{i,j}^{N}, [\mbox{DQNLD}]_{i,j}^{N}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2544}%
$[\mbox{DQDIF}]_{i,j}^{N}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2546}%
$[\mbox{DQNLD}]_{i,j}^{N}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2478}%
\begin{displaymath}
 q_{i,j}^{n+1} 
 = q_{i,j}^{N} + dt \left\{
  [\mbox{DQADV}]_{i,j}^{n} +
  [\mbox{DQDIF}]_{i,j}^{N} +
  [\mbox{DQFALL}]_{i,j}^{N}+
  [\mbox{DQNLD}]_{i,j}^{N} \right\}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4428}%
$\displaystyle \mbox{DQFALL}_{i,j}^{n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4430}%
$\displaystyle - \frac{1}{\rho _{0,j}\Delta z_{j}}
\left\{ FQf_{z(i,j+\frac{1}{2})}^{n}-FQf_{z(i,j-\frac{1}{2})}^{n}
\right\},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4431}%
$\displaystyle FQf_{z(i,j-\frac{1}{2})}^{n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4433}%
$\displaystyle - \frac{4\rho _{d}gr_{mod}^{2}}{18\eta }\left( 1 +
2\frac{\lambda _{r}}{r_{mod}}\frac{p_{r}}{P_{0,j}}\right)
\rho _{0,j}q_{i,j}^{n},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3401}%
$Q_{rad,i,j}^{n}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4437}%
$\displaystyle Q_{rad,i,j}^{n}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4439}%
$\displaystyle Q_{rad,IR,i,j}^{n} + Q_{rad,NIR,i,j}^{n} +
Q_{rad,dust,SR,i,j}^{n} + Q_{rad,dust,IR,i,j}^{n},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4440}%
$\displaystyle Q_{rad,*,i,j}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4442}%
$\displaystyle - \frac{g}{c_{p}}
\frac{F_{*,net,i,j+\frac{1}{2}} -
F_{*,net,i,j-\frac{1}{2}}}
{\Delta P _{0,j}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3389}%
\begin{displaymath}
  F_{*,net,i,j+\frac{1}{2}} =
                 F_{IR,i,j+\frac{1}{2}}^{\uparrow} - 
                 F_{IR,i,j+\frac{1}{2}}^{\downarrow}, \quad
  \Delta P_{0,j} = P_{0,j+\frac{1}{2}} - P_{0,j-\frac{1}{2}}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3405}%
$m$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4452}%
$\displaystyle F_{IR,i,j+\frac{1}{2}}^{\uparrow}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4454}%
$\displaystyle \sum _{m}\Delta \nu _{m}\left\{
\pi B_{\nu _{i},T_{sfc,i}}{\cal T}_{i}(0,z_{j+\frac{1}{2}})
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4455}%
$\displaystyle \left.
+  \sum _{j'=1}^{j} \pi B_{\nu _{m},T_{i,j'}}
\frac{ {\cal T }_{m}(z_{j+\frac{1}{2}},z_{j'+\frac{1}{2}}) -
{\cal T }_{m}(z_{j+\frac{1}{2}},z_{j'-\frac{1}{2}}) }
{ \Delta z_{j'} } \right\},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4456}%
$\displaystyle F_{IR,i,j+\frac{1}{2}}^{\downarrow}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4458}%
$\displaystyle \sum _{m}\Delta \nu _{m}\left\{
\sum _{j'=j}^{J}\pi B_{\nu _{m},T_{i,j'}}
\frac{ {\cal T }_{m}(z_{j+\frac{1}{2}},z_{j'+\frac{3}{2}}) -
{\cal T }_{m}(z_{j+\frac{1}{2}},z_{j'+\frac{1}{2}}) }
{ \Delta z_{j'} }
\right\} ,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4459}%
$\displaystyle B_{\nu _{m},T_{i,j}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4461}%
$\displaystyle \frac{1.19\times 10^{-8}\nu _{m}^{3}}
{e^{1.4387\nu_{i}/T_{i,j}}-1},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4462}%
$\displaystyle T_{i,j}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4464}%
$\displaystyle \Pi _{0,j}(\theta _{i,j}+\Theta _{0,j})$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3390}%
\begin{displaymath}
  {\cal T}_{m}(z_{j+\frac{1}{2}},z_{j'+\frac{1}{2}}) = 
  \exp ( - W_{m,j,j'}/\Delta \nu _{m}),
  \quad
  W_{m,j,j'} = \frac{S_{m} u(z_{j+\frac{1}{2}},z_{j'+\frac{1}{2}})}
  {\sqrt{ 1 + S_{m}u^{*}(z_{j+\frac{1}{2}},z_{j'+\frac{1}{2}})/
   \alpha ^{*}_{m}}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3391}%
\begin{displaymath}
  u(z_{j+\frac{1}{2}},z_{j'+\frac{1}{2}}) = 1.67 
  g | P_{0,j+\frac{1}{2}} - P_{0,j'+\frac{1}{2}} |,
  \quad
  \alpha ^{*}_{m}=\alpha _{m} \frac{\overline{p}_{jj'}}{p_{0}}, 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3392}%
\begin{displaymath}
  P_{0,j+\frac{1}{2}} = 0.5(P_{0,j}+P_{0,j+1}),
  \quad
  \overline{p}_{jj'} = 
  \sum _{l=j}^{j'-1} \frac{P_{0,l+1}\cdot 1.67
  g|P_{0,l+\frac{3}{2}}-P_{0,l+\frac{1}{2}}|}
  {u(z_{j+\frac{1}{2}},z_{j'+\frac{1}{2}})},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2738}%
\begin{displaymath}
  F_{NIR,i,j+\frac{1}{2}}^{\downarrow} = \sum _{m}\Delta \nu _{m}\left\{
      S_{\nu _{m}}{\cal T}_{i}(z_{j+\frac{1}{2}},z_{J+\frac{3}{2}})\cos \zeta 
      \right\}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3393}%
\begin{displaymath}
  u(z_{j+\frac{1}{2}},z_{J+\frac{3}{2}}) = 
  \frac{1.67 g | P_{0,j+\frac{1}{2}} - P_{0,J+\frac{3}{2}} |}
  {\mbox{MAX}(\cos \zeta, \epsilon )}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3417}%
$\epsilon $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3421}%
$u = 0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3423}%
$\cos \zeta =0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4477}%
$\displaystyle F_{dif,\nu_{m},i,j+\frac{1}{2}}^{\uparrow}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4479}%
$\displaystyle F_{dif,\nu_{m},i,j-\frac{1}{2}}^{\uparrow} -
\Delta \tau _{\nu_{m},j}\left[
\gamma _{1,\nu_{m}}\frac{F_{dif,\nu_{m},i,j+\frac{1}{2}}^{\uparrow} +
F_{dif,\nu_{m},i,j-\frac{1}{2}}^{\uparrow}}{2}
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4480}%
$\displaystyle - \left.
\gamma _{2,\nu_{m}}\frac{F_{dif,\nu_{m},i,j+\frac{1}{2}}^{\downarrow} +
F_{dif,\nu_{m},i,j-\frac{1}{2}}^{\downarrow}}{2}
-\gamma _{3,\nu_{m}}\tilde{\omega}_{\nu_{m}}^{*}
S_{0}e^{-\tau _{\nu_{m},j+\frac{1}{2}}^{*}
/\mu_{0}} \right],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4481}%
$\displaystyle F_{dif,\nu_{m},i,j-\frac{1}{2}}^{\downarrow}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4483}%
$\displaystyle F_{dif,\nu_{m},i,j+\frac{1}{2}}^{\downarrow} +
\Delta \tau _{\nu_{m},j}\left[
\gamma _{2,\nu_{m}}\frac{F_{dif,\nu_{m},i,j+\frac{1}{2}}^{\uparrow} +
F_{dif,\nu_{m},i,j-\frac{1}{2}}^{\uparrow}}{2}
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4484}%
$\displaystyle - \left.
\gamma _{1,\nu_{m}}\frac{F_{dif,\nu_{m},i,j+\frac{1}{2}}^{\downarrow} +
F_{dif,\nu_{m},i,j-\frac{1}{2}}^{\downarrow}}{2}
+(1-\gamma _{3,\nu_{m}})\tilde{\omega}_{\nu_{m}}^{*}
S_{0}e^{-\tau _{\nu_{m},j+\frac{1}{2}} ^{*}/\mu_{0}}
\right],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3394}%
\begin{displaymath}
 \Delta \tau _{\nu_{m}, j}= \frac{\overline{Q}_{e,\nu_{m}}}{r_{eff}}
     \frac{3\rho _{0,j}q_{i,j}}{4\pi \rho _{s}} \Delta z_{j}, \quad
 \tau _{\nu_{m},j+\frac{1}{2}} = \sum _{j'=j+1}^{J+1}\Delta \tau _{\nu_{m},j'}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3425}%
$\Dvect{F}_{dif,\nu_{m}}^{\uparrow}=(
F_{dif,\nu_{m},i,\frac{1}{2}}^{\uparrow},
F_{dif,\nu_{m},i,\frac{3}{2}}^{\uparrow},...,
F_{dif,\nu_{m},i,J+\frac{1}{2}}^{\uparrow})^{T}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4488}%
$\displaystyle \Dvect{F}_{dif,\nu_{m}}^{\uparrow}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4490}%
$\displaystyle \Dvect{A}\Dvect{F}_{dif,\nu_{m}}^{\uparrow} +
\Dvect{B}\Dvect{F}_{dif,\nu_{m}}^{\downarrow} + \Dvect{R},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4491}%
$\displaystyle \Dvect{F}_{dif,\nu_{m}}^{\downarrow}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4493}%
$\displaystyle \Dvect{C}\Dvect{F}_{dif,\nu_{m}}^{\uparrow} +
\Dvect{D}\Dvect{F}_{dif,\nu_{m}}^{\downarrow} + \Dvect{S}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3427}%
$0\leq j \leq J$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar2934}%
\begin{eqnarray*}
 A_{jk} &=& \left\{
 \begin{array}{cl}
 - \frac{1}{2}\Delta \tau _{\nu_{m},j}\gamma_{1,\nu_{m}} & k=j, j\geq 1\\
 1 - \frac{1}{2}\Delta \tau _{\nu_{m},j}\gamma_{1,\nu_{m}} & k=j-1, j\geq 1\\
 0 & \mbox{others}
 \end{array}
 \right. \\
 B_{jk} &=& \left\{
 \begin{array}{cl}
 A & j=k=0 \\
 \frac{1}{2}\Delta \tau _{\nu_{m},j}\gamma_{2,\nu_{m}}& k=j, j-1 ,j\geq 1\\
 0 & \mbox{others}
 \end{array}
 \right. \\
 C_{jk} &=& \left\{
 \begin{array}{cl}
  \frac{1}{2}\Delta \tau _{\nu_{m},j+1}\gamma _{2,\nu_{m}} & k=j,j+1, j\leq J-1
 \\
 0 & \mbox{others}
 \end{array}
 \right. \\
D_{jk} &=& \left\{
 \begin{array}{cl}
  - \frac{1}{2}\Delta \tau _{\nu_{m},j+1}\gamma_{1,\nu_{m}} & k=j,j\leq J-1 \\
 1 - \frac{1}{2}\Delta \tau _{\nu_{m},j+1}\gamma_{1,\nu_{m}} & k=j+1 \\
 0 & \mbox{others}
 \end{array}
 \right. \\
R_{j} &=& \left\{
 \begin{array}{cl}
 A S_{0}e^{-\tau _{\nu_{m},\frac{1}{2}}^{*}/\mu_{0}} & j=0 \\
 \Delta \tau _{\nu_{m},j}
 \gamma _{3,\nu_{m}}\tilde{\omega}_{\nu_{m}}^{*}
            S_{0}e^{-\tau _{\nu_{m},j+\frac{1}{2}}^{*}/\mu_{0}}
 & j\geq 1 
 \end{array}
 \right. \\
S_{j} &=& \left\{
 \begin{array}{cl}
 \Delta \tau _{\nu_{m},j+1}(1-\gamma _{3,\nu_{m}})
  \tilde{\omega}_{\nu_{m}}^{*}S_{0}e^{-\tau _{\nu_{m},j+\frac{3}{2}}^{*}
  /\mu_{0}} &
 j\leq J-1 \\
 0 & j=J
 \end{array}
 \right.
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4498}%
$\displaystyle F_{IR,\nu_{m},i,j+\frac{1}{2}}^{\uparrow}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4500}%
$\displaystyle F_{IR,\nu_{m},i,j-\frac{1}{2}}^{\uparrow} -
\Delta \tau _{\nu_{m},j}\left[
\gamma _{1,\nu_{m}}\frac{F_{IR,\nu_{m},i,j+\frac{1}{2}}^{\uparrow} +
F_{IR,\nu_{m},i,j-\frac{1}{2}}^{\uparrow}}{2}
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4501}%
$\displaystyle - \left.
\gamma _{2,\nu_{m}}\frac{F_{IR,\nu_{m},i,j+\frac{1}{2}}^{\downarrow} +
F_{IR,\nu_{m},i,j-\frac{1}{2}}^{\downarrow}}{2}
-2\pi (1-\tilde{\omega}_{\nu_{m}}^{*})B_{\nu_{m},T_{i,j}}
\right],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4502}%
$\displaystyle F_{IR,\nu_{m},i,j-\frac{1}{2}}^{\downarrow}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4504}%
$\displaystyle F_{IR,\nu_{m},i,j+\frac{1}{2}}^{\downarrow} +
\Delta \tau _{\nu_{m},j}\left[
\gamma _{2,\nu_{m}}\frac{F_{IR,\nu_{m},i,j+\frac{1}{2}}^{\uparrow} +
F_{IR,\nu_{m},i,j-\frac{1}{2}}^{\uparrow}}{2}
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4505}%
$\displaystyle - \left.
\gamma _{1,\nu_{m}}\frac{F_{IR,\nu_{m},i,j+\frac{1}{2}}^{\downarrow} +
F_{IR,\nu_{m},i,j-\frac{1}{2}}^{\downarrow}}{2}
+2\pi (1-\tilde{\omega}_{\nu_{m}}^{*})B_{\nu_{m},T_{i,j}}
\right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3431}%
$\Dvect{F}_{IR,\nu_{m}}^{\uparrow}=(F_{IR,\nu_{m},i,\frac{1}{2}}^{\uparrow},
F_{IR,\nu_{m},i,\frac{3}{2}}^{\uparrow},...,
F_{IR,\nu_{m},i,J+\frac{1}{2}}^{\uparrow})^{T}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4508}%
$\displaystyle \Dvect{F}_{IR,\nu_{m}}^{\uparrow}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4510}%
$\displaystyle \Dvect{A}\Dvect{F}_{IR,\nu_{m}}^{\uparrow} +
\Dvect{B}'\Dvect{F}_{IR,\nu_{m}}^{\downarrow} + \Dvect{R}',$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4511}%
$\displaystyle \Dvect{F}_{IR,\nu_{m}}^{\downarrow}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4513}%
$\displaystyle \Dvect{C}\Dvect{F}_{IR,\nu_{m}}^{\uparrow} +
\Dvect{D}\Dvect{F}_{IR,\nu_{m}}^{\downarrow} + \Dvect{S}'.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar3159}%
\begin{eqnarray*}
 B'_{jk} &=& \left\{
 \begin{array}{cl}
 0      & j=k=1 \\
 B_{jk} & \mbox{others}
 \end{array}
 \right. \\
R'_{j} &=& \left\{
 \begin{array}{cl}
 \pi B_{\nu_{m}, T_{sfc,i}} & j=0 \\
  2\pi \Delta \tau _{\nu_{m},j}( 1 - \tilde{\omega }^{*})
  B_{\nu_{m}, T_{i,j}} & j\geq 1 \\
 \end{array}
 \right.\\
S'_{j} &=& \left\{
 \begin{array}{cl}
 2\pi \Delta \tau _{\nu_{m},j}( 1 - \tilde{\omega }^{*})
  B_{\nu_{m}, T_{i,j}} & j\leq J-1 \\
 0 & i=N
 \end{array}
 \right. 
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3824}%
$J'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3826}%
$j=1,2,...J'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3828}%
$T_{i,J'}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3830}%
$T_{sfc,i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3834}%
$j = 1$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4526}%
$\displaystyle \frac{T_{i,j}^{n+1}-T_{i,j}^{n}}{\Delta t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4528}%
$\displaystyle \frac{\kappa}{4\Delta z_{j}}
\left( \frac{T_{i,j+1}^{n+1} - T_{i,j}^{n+1}}
{\Delta z_{j+1}+\Delta z_{j}} -
\frac{T_{i,j}^{n+1} - T_{i,j-1}^{n+1}}
{\Delta z_{j}+\Delta z_{j-1}}
\right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4529}%
$\displaystyle +
\left. \frac{T_{i,j+1}^{n} - T_{i,j+1}^{n}}
{\Delta z_{j+1}+\Delta z_{j}} -
\frac{T_{i,j}^{n} - T_{i,j-1}^{n}}
{\Delta z_{j}+\Delta z_{j-1}}
\right).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3840}%
$\kappa = k_{g}/\rho _{g}c_{p,g}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3842}%
$(n+1)\Delta t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3844}%
$n\Delta t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4534}%
$\displaystyle - \frac{\kappa \Delta t}{\Delta z_{j}}
\frac{T_{i,j-1}^{n+1}}
{\overline{\Delta z}_{i}}
+ \left[
4 + \frac{\kappa \Delta t}{\Delta z_{i,j}}
\left(
\frac{1}{\overline{\Delta z}_{j+\frac{1}{2}}}+
\frac{1}{\overline{\Delta z}_{j-\frac{1}{2}}}
\right)
\right]T_{i,j}^{n+1}
- \frac{\kappa \Delta t}{\Delta z_{j}}
\frac{T_{i,j+1}^{n+1}}
{\overline{\Delta z}_{j+\frac{1}{2}}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4536}%
$\displaystyle + \frac{\kappa \Delta t}{\Delta z_{j}}
\frac{T_{i,j-1}^{n}}
{\overline{\Delta z}_{j-\frac{1}{2}}}
+ \left[
4 - \frac{\kappa \Delta t}{\Delta z_{j}}
\left(
\frac{1}{\overline{\Delta z}_{j+\frac{1}{2}}}+
\frac{1}{\overline{\Delta z}_{j-\frac{1}{2}}}
\right)
\right]T_{i,j}^{n}
+ \frac{\kappa \Delta t}{\Delta z_{j}}
\frac{T_{i,j+1}^{n+1}}
{\overline{\Delta z}_{j+\frac{1}{2}}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3846}%
$\overline{\Delta z}_{j+\frac{1}{2}}=(\Delta z_{j+1}+\Delta
z_{j})/2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3848}%
$\Dvect{T}^{n}=(..., T_{i,j}^{n}, T_{i,j+1}^{n},
T_{i,j+2}^{n}, ...)^{T}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3579}%
\begin{displaymath}
  \Dvect{A}\cdot \Dvect{T}^{n+1} = \Dvect{B}\cdot \Dvect{T}^{n},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3852}%
$\Dvect{A},\Dvect{B}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3856}%
$\Dvect{A}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3858}%
$\Dvect{B}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar3601}%
\begin{eqnarray*}
&&
 A_{jj}=4 + \frac{\kappa \Delta t}{\Delta z_{j}}
  \left( \frac{1}{\overline{\Delta z}_{j+\frac{1}{2}}}+
         \frac{1}{\overline{\Delta z}_{j-\frac{1}{2}}}
  \right),
 A_{j,j+1}= - \frac{\kappa \Delta t}{\Delta z_{i}}
  \frac{1}{\overline{\Delta z}_{i+\frac{1}{2}}},
 A_{j,j-1}= - \frac{\kappa \Delta t}{\Delta z_{i}}
  \frac{1}{\overline{\Delta z}_{i-\frac{1}{2}}}, \\
&&
 B_{jj}=4 - \frac{\kappa \Delta t}{\Delta z_{j}}
  \left( \frac{1}{\overline{\Delta z}_{i+\frac{1}{2}}}+
         \frac{1}{\overline{\Delta z}_{i-\frac{1}{2}}}
  \right),
 B_{j,j+1}= + \frac{\kappa \Delta t}{\Delta z_{i}}
  \frac{1}{\overline{\Delta z}_{i+\frac{1}{2}}},
 B_{j,j-1}= + \frac{\kappa \Delta t}{\Delta z_{i}}
  \frac{1}{\overline{\Delta z}_{i-\frac{1}{2}}},
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3860}%
$J'\times J'$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3657}%
\begin{displaymath}
  \Dvect{A}\cdot \Dvect{T}^{n+1} = \Dvect{B}\cdot \Dvect{T}^{n} + 
                                   \Dvect{S}
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3668}%
\begin{displaymath}
  \Dvect{T}^{n+1} = \Dvect{A}^{-1} \cdot 
                    (\Dvect{B}\cdot \Dvect{T}^{n} + \Dvect{S}),
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar3682}%
\begin{eqnarray*}
&&
 A_{11}=4 + \frac{\kappa \Delta t}{\Delta z_{1}}
  \left( \frac{1}{\overline{\Delta z}_{\frac{3}{2}}} \right),
 B_{11}=4 - \frac{\kappa \Delta t}{\Delta z_{1}}
  \left( \frac{1}{\overline{\Delta z}_{\frac{3}{2}}} \right), \\
&&
 A_{J'J'}=4 + \frac{\kappa \Delta t}{\Delta z_{J'}}
  \left( \frac{1}{\overline{\Delta z}_{J'-\frac{1}{2}}} \right),
 B_{J'J'}=4 - \frac{\kappa \Delta t}{\Delta z_{J'}}
  \left( \frac{1}{\overline{\Delta z}_{J'-\frac{1}{2}}} \right),
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3870}%
$\Dvect{S}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3822}%
\begin{displaymath}
 S_{j} = \left\{
 \begin{array}{ll}
   \frac{\Delta t}{\rho _{g}c_{p,g}\Delta z_{J'}}
        [- F_{s}(1-A) + F_{IR,net} + H], & j=J' \\
  0, & j\neq J'
 \end{array}
\right.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}


\end{document}
