# LaTeX2HTML 2002-2-1 (1.70)
# Associate images original text with physical files.


$key = q/displaystyleu_{i+frac{1}{2},j}^{N}+dtleft{frac{hat{P}_{i+1,j}-hat{P}_{i,j}}{Deltax}+alpha_{i+frac{1}{2},j}right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="297" HEIGHT="71" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$\displaystyle u_{i+\frac{1}{2},j}^{N} + dt \left\{
\frac{\hat{P}_{i+1,j}-\hat{P}_{i,j}}{\Delta x}
+ \alpha _{i+\frac{1}{2},j} \right\},$">|; 

$key = q/{eqnarraystar}B'_{jk}&=&left{array{{cl}0&j=k=1B_{jk}&mbox{others}array{right.R'_nu_{m},T_{i,j}}&jleqJ-10&i=Narray{right.{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="177" BORDER="0"
 SRC="|."$dir".q|img224.png"
 ALT="\begin{eqnarray*}
B'_{jk} &amp;=&amp; \left\{
\begin{array}{cl}
0 &amp; j=k=1 \\\\
B_{jk}...
...\nu_{m}, T_{i,j}} &amp; j\leq J-1 \\\\
0 &amp; i=N
\end{array} \right.
\end{eqnarray*}">|; 

$key = q/displaystylembox{DWVIS}_{i,j+frac{1}{2}}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\displaystyle \mbox{DWVIS}_{i,j+\frac{1}{2}}^{n}$">|; 

$key = q/displaystyletheta_{i,j}^{n+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$\displaystyle \theta _{i,j}^{n+1}$">|; 

$key = q/rho_{0,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$\rho _{0,j}$">|; 

$key = q/displaystyleB_{nu_{m},T_{i,j}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="$\displaystyle B_{\nu _{m},T_{i,j}}$">|; 

$key = q/Dvect{D}_{z};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$\Dvect{D}_{z}$">|; 

$key = q/{displaymath}left[Dvect{H}right]_{k_{x}}=left[Dvect{D_{x}}+Dvect{Lambda}right]_{x}}^{-1}left[Dvect{V}^{-1}Dvect{S}right]_{k_{x}}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="245" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="\begin{displaymath}
\left[\Dvect{H}\right]_{k_{x}} =
\left[\Dvect{D_{x}} + \D...
...ht]_{k_{x}}^{-1}
\left[\Dvect{V}^{-1}\Dvect{S}\right]_{k_{x}}
\end{displaymath}">|; 

$key = q/Dvect{A},Dvect{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img241.png"
 ALT="$\Dvect{A},\Dvect{B}$">|; 

$key = q/displaystyleFTheta_{0,z(j+frac{1}{2})}^{n}=rho_{0,j+frac{1}{2}}w_{i,j+frac{1}{2}0,j+1}+frac{9}{16}Theta_{0,j}-frac{1}{16}Theta_{0,j-1}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="597" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$\displaystyle F\Theta _{0,z(j+\frac{1}{2})}^{n}
=
\rho _{0,j+\frac{1}{2}}w_{i,j...
...eta _{0,j+1}
+ \frac{9}{16}\Theta _{0,j}
- \frac{1}{16}\Theta _{0,j-1} \right).$">|; 

$key = q/displaystyleleft(Dvect{D_{x}}+Dvect{Lambda}right);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$\displaystyle \left(\Dvect{D_{x}} + \Dvect{\Lambda }\right)$">|; 

$key = q/displaystyle-frac{g}{Theta_{0,j}}K_{i,j}^{n}frac{1}{Deltaz_{j}}left[(theta_{i,j+}{2}})-(theta_{i,j-frac{1}{2}}+Theta_{0,j-frac{1}{2}})right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="440" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$\displaystyle -\frac{g}{\Theta _{0,j}}K_{i,j}^{n}
\frac{1}{\Delta z_{j}}\left[
...
...+\frac{1}{2}}) -
(\theta _{i,j-\frac{1}{2}}+\Theta _{0,j-\frac{1}{2}}) \right],$">|; 

$key = q/displaystyleDvect{C}Dvect{F}_{IR,nu_{m}}^{uparrow}+Dvect{D}Dvect{F}_{IR,nu_{m}}^{downarrow}+Dvect{S}'.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img223.png"
 ALT="$\displaystyle \Dvect{C}\Dvect{F}_{IR,\nu_{m}}^{\uparrow} +
\Dvect{D}\Dvect{F}_{IR,\nu_{m}}^{\downarrow} + \Dvect{S}'.$">|; 

$key = q/displaystyle-left.gamma_{2,nu_{m}}frac{F_{dif,nu_{m},i,j+frac{1}{2}}^{downarrow}^{*}S_{0}e^{-tau_{nu_{m},j+frac{1}{2}}^{*}slashmu_{0}}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="498" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="$\displaystyle - \left.
\gamma _{2,\nu_{m}}\frac{F_{dif,\nu_{m},i,j+\frac{1}{2}}...
...ga}_{\nu_{m}}^{*}
S_{0}e^{-\tau _{\nu_{m},j+\frac{1}{2}}^{*}
/\mu_{0}} \right],$">|; 

$key = q/displaystyle+left.[mbox{DKBP}]_{i,j}^{n}+[mbox{DKSP}]_{i,j}^{n}-frac{C_{epsilon}}{l}(varepsilon_{i,j}^{N})^{frac{3}{2}}right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="$\displaystyle + \left.
[\mbox{DKBP}]_{i,j}^{n} +
[\mbox{DKSP}]_{i,j}^{n} -
\frac{C_{\epsilon}}{l}(\varepsilon _{i,j}^{N})^{\frac{3}{2}} \right\}$">|; 

$key = q/displaystyleQ_{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},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="454" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="$\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},$">|; 

$key = q/Dvect{B};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img243.png"
 ALT="$\Dvect{B}$">|; 

$key = q/displaystyleleft.left.left.-left(u_{i+frac{1}{2},j}^{n}-u_{i+frac{1}{2},j-1}^{n}rightslash(16.0cdot10^{3}cdotrho_{0,j}Deltaz_{j}slashDeltax),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="429" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$\displaystyle \left.
\left.
\left. - \left(u_{i+\frac{1}{2},j}^{n}-u_{i+\frac{1...
...]
\right\}
\right/
(16.0 \cdot 10^{3} \cdot \rho _{0,j}\Delta z_{j}/\Delta x ),$">|; 

$key = q/displaystylesum_{k=1}^{NXslash2-1}left[Dvect{H}right]_{k_{x}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="116" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$\displaystyle \sum_{k=1}^{NX/2-1}
\left[\Dvect{H}\right]_{k_{x}},$">|; 

$key = q/coszeta=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="$\cos \zeta =0$">|; 

$key = q/displaystylefrac{1}{rho_{0}Deltaz_{i}}left(frac{1}{24Deltaz_{i+frac{3}{2}}}frac{Deltam_{i+frac{1}{2}}}frac{(rho_{0,i+1}+rho_{0,i})}{2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="498" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$\displaystyle \frac{1}{\rho _{0}\Delta z_{i}}\left(
\frac{1}{24\Delta z_{i+\fra...
...rac{9}{8\Delta m_{i+\frac{1}{2}}}\frac{(\rho _
{0,i+1}+\rho _{0,i})}{2}\right),$">|; 

$key = q/n,N;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$n, N$">|; 

$key = q/displaystylePi_{0,j}=left(frac{P_{0,j}}{P_00}right)^{kappa},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="135" HEIGHT="62" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="$\displaystyle \Pi _{0,j} = \left(\frac{P_{0,j}}{P_00}\right)^{\kappa },$">|; 

$key = q/displaystyleleft.+sum_{j'=1}^{j}piB_{nu_{m},T_{i,j'}}frac{{calT}_{m}(z_{j+frac{1_{m}(z_{j+frac{1}{2}},z_{j'-frac{1}{2}})}{Deltaz_{j'}}right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="423" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="$\displaystyle \left.
+ \sum _{j'=1}^{j} \pi B_{\nu _{m},T_{i,j'}}
\frac{ {\cal ...
...cal T }_{m}(z_{j+\frac{1}{2}},z_{j'-\frac{1}{2}}) }
{ \Delta z_{j'} } \right\},$">|; 

$key = q/displaystyle+left.left(rho_{0,j+1}w_{i,j+1}^{n}w_{i,j+1}^{n}-rho_{0,j}w_{i,j}^{nt)Deltaxrightslash(rho_{0,j+frac{1}{2}}Deltaz_{j+frac{1}{2}});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="446" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$\displaystyle + \left.
\left( \rho _{0,j+1}w_{i,j+1}^{n}w_{i,j+1}^{n}
- \rho _{...
...^{n}
\right)
\Delta x \right/
(\rho _{0,j+\frac{1}{2}}\Delta z_{j+\frac{1}{2}})$">|; 

$key = q/[mbox{DTADV}]_{i,j}^{n},[mbox{DTAD0}]_{i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="196" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$[\mbox{DTADV}]_{i,j}^{n}, [\mbox{DTAD0}]_{i,j}^{n}$">|; 

$key = q/displaystylew_{i,j+frac{1}{2}}^{N}+dtfrac{hat{P}_{i,j+1}-hat{P}_{i,j}}{Deltaz_{j+frac{1}{2}}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="197" HEIGHT="71" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\displaystyle w_{i,j+\frac{1}{2}}^{N} + dt
\frac{\hat{P}_{i,j+1}-\hat{P}_{i,j}}{\Delta z_{j+\frac{1}{2}}}.$">|; 

$key = q/T_{0,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$T_{0,j}$">|; 

$key = q/displaystyle+left.frac{T_{i,j+1}^{n}-T_{i,j+1}^{n}}{Deltaz_{j+1}+Deltaz_{j}}-frac{T_{i,j}^{n}-T_{i,j-1}^{n}}{Deltaz_{j}+Deltaz_{j-1}}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img232.png"
 ALT="$\displaystyle +
\left. \frac{T_{i,j+1}^{n} - T_{i,j+1}^{n}}
{\Delta z_{j+1}+\De...
...j}} -
\frac{T_{i,j}^{n} - T_{i,j-1}^{n}}
{\Delta z_{j}+\Delta z_{j-1}}
\right).$">|; 

$key = q/A_{ij};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$A_{ij}$">|; 

$key = q/P_{0,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$P_{0,j}$">|; 

$key = q/displaystyleQ_{rad,*,i,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="$\displaystyle Q_{rad,*,i,j}$">|; 

$key = q/displaystyleF_{x(i+frac{1}{2},j)}^{n}=rho_{0,j}u_{i+frac{1}{2},j}^{n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$\displaystyle F_{x(i+\frac{1}{2},j)}^{n}
=
\rho _{0,j}u_{i+\frac{1}{2},j}^{n},$">|; 

$key = q/Q_{dis,i,j}^{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$Q_{dis,i,j}^{N}$">|; 

$key = q/u=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="$u = 0$">|; 

$key = q/displaystyle-(gamma_{i+1,j}-gamma_{i,j})+[mbox{DUADV}]_{i+frac{1}{2},j}^{n}+[mboRS}]_{i+frac{1}{2},j}^{n}+[mbox{DUCOLI}]_{i+frac{1}{2},j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="542" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$\displaystyle - ( \gamma _{i+1,j} - \gamma _{i,j})
+ [\mbox{DUADV}]_{i+\frac{1}...
...
+ [\mbox{DUPRS}]_{i+\frac{1}{2},j}^{n}
+ [\mbox{DUCOLI}]_{i+\frac{1}{2},j}^{n}$">|; 

$key = q/{displaymath}Dvect{A}cdotDvect{T}^{n+1}=Dvect{B}cdotDvect{T}^{n}+Dvect{S}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="33" BORDER="0"
 SRC="|."$dir".q|img246.png"
 ALT="\begin{displaymath}
\Dvect{A}\cdot \Dvect{T}^{n+1} = \Dvect{B}\cdot \Dvect{T}^{n} +
\Dvect{S}
\end{displaymath}">|; 

$key = q/displaystyleTheta_{0,j}=frac{T_{0,j}}{Pi_{0,j}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$\displaystyle \Theta _{0,j} = \frac{T_{0,j}}{\Pi _{0,j}}.$">|; 

$key = q/displaystylesum_{m}Deltanu_{m}left{sum_{j'=j}^{J}piB_{nu_{m},T_{i,j'}}frac{{calT_{m}(z_{j+frac{1}{2}},z_{j'+frac{1}{2}})}{Deltaz_{j'}}right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="484" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$\displaystyle \sum _{m}\Delta \nu _{m}\left\{
\sum _{j'=j}^{J}\pi B_{\nu _{m},T...
...al T }_{m}(z_{j+\frac{1}{2}},z_{j'+\frac{1}{2}}) }
{ \Delta z_{j'} }
\right\} ,$">|; 

$key = q/textstyle=;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$\textstyle =$">|; 

$key = q/displaystylembox{DUCOLI}_{i+frac{1}{2},j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$\displaystyle \mbox{DUCOLI}_{i+\frac{1}{2},j}^{n}$">|; 

$key = q/{displaymath}Dvect{A}cdotDvect{T}^{n+1}=Dvect{B}cdotDvect{T}^{n},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img240.png"
 ALT="\begin{displaymath}
\Dvect{A}\cdot \Dvect{T}^{n+1} = \Dvect{B}\cdot \Dvect{T}^{n},
\end{displaymath}">|; 

$key = q/displaystyleleft.left.left.-left(v_{i+frac{1}{2},j}^{n}-v_{i+frac{1}{2},j-1}^{n}rightslash(16.0cdot10^{3}cdotrho_{0,j}Deltaz_{j}slashDeltax),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="426" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$\displaystyle \left.
\left.
\left. - \left(v_{i+\frac{1}{2},j}^{n}-v_{i+\frac{1...
...]
\right\}
\right/
(16.0 \cdot 10^{3} \cdot \rho _{0,j}\Delta z_{j}/\Delta x ),$">|; 

$key = q/Pi_{0,j},Theta_{0,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$\Pi _{0,j}, \Theta _{0,j}$">|; 

$key = q/displaystyle+left.left(rho_{0,j+frac{1}{2}}v_{i+frac{1}{2},j+frac{1}{2}}^{n}w_{i,j-frac{1}{2}}^{n}right)Deltaxrightslash(rho_{0,j}Deltaz_{j});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="547" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$\displaystyle +
\left.
\left(
\rho _{0,j+\frac{1}{2}}
v_{i+\frac{1}{2},j+\frac{...
...\frac{1}{2},j-\frac{1}{2}}^{n}
\right)
\Delta x\right/(\rho _{0,j}\Delta z_{j})$">|; 

$key = q/displaystylembox{DUVIS}_{i+frac{1}{2},j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$\displaystyle \mbox{DUVIS}_{i+\frac{1}{2},j}^{n}$">|; 

$key = q/displaystyleDvect{F}_{IR,nu_{m}}^{downarrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img222.png"
 ALT="$\displaystyle \Dvect{F}_{IR,\nu_{m}}^{\downarrow}$">|; 

$key = q/Dvect{A};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img242.png"
 ALT="$\Dvect{A}$">|; 

$key = q/displaystyleDvect{A}Dvect{F}_{IR,nu_{m}}^{uparrow}+Dvect{B}'Dvect{F}_{IR,nu_{m}}^{downarrow}+Dvect{R}',;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img221.png"
 ALT="$\displaystyle \Dvect{A}\Dvect{F}_{IR,\nu_{m}}^{\uparrow} +
\Dvect{B}'\Dvect{F}_{IR,\nu_{m}}^{\downarrow} + \Dvect{R}',$">|; 

$key = q/T_{sfc,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img228.png"
 ALT="$T_{sfc,i}$">|; 

$key = q/nDeltat;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img235.png"
 ALT="$n\Delta t$">|; 

$key = q/displaystylembox{DVCOLI}_{i+frac{1}{2},j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$\displaystyle \mbox{DVCOLI}_{i+\frac{1}{2},j}^{n}$">|; 

$key = q/displaystyleleft.left.+0.1left[left(w_{i,j++frac{3}{2}}^{n}-w_{i,j+frac{1}{2}}^{}}^{n}-w_{i,j-frac{1}{2}}^{n}right)^{3}right]right}rightslash;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="425" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$\displaystyle \left.
\left.
+ 0.1
\left[ \left(w_{i,j++\frac{3}{2}}^{n}-w_{i,j+...
...,j+\frac{1}{2}}^{n}-w_{i,j-\frac{1}{2}}^{n}\right)^{3}
\right]
\right\}
\right/$">|; 

$key = q/[mbox{DQDIF}]_{i,j}^{N},[mbox{DQNLD}]_{i,j}^{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="$[\mbox{DQDIF}]_{i,j}^{N}, [\mbox{DQNLD}]_{i,j}^{N}$">|; 

$key = q/T_{i,J'};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img227.png"
 ALT="$T_{i,J'}$">|; 

$key = q/Dvect{T}^{n}=(...,T_{i,j}^{n},T_{i,j+1}^{n},T_{i,j+2}^{n},...)^{T};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img239.png"
 ALT="$\Dvect{T}^{n}=(..., T_{i,j}^{n}, T_{i,j+1}^{n},
T_{i,j+2}^{n}, ...)^{T}$">|; 

$key = q/displaystyleleft.left.left.rho_{0,j-frac{1}{2}}K_{i+frac{1}{2},j-frac{1}{2}}^{n}2},j-1}^{n}right)rightslashDeltaz_{j-frac{1}{2}}right]right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="379" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$\displaystyle \left.
\left.
\left. \rho _{0,j-\frac{1}{2}}
K_{i+\frac{1}{2},j-\...
...{i+\frac{1}{2},j-1}^{n}\right)
\right/\Delta z_{j-\frac{1}{2}}
\right]\right\},$">|; 

$key = q/{displaymath}Dvect{V}Dvect{D_{x}H}+Dvect{VLambdaH}=Dvect{S}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="\begin{displaymath}
\Dvect{V}\Dvect{D_{x}H} + \Dvect{V\Lambda H} = \Dvect{S}.
\end{displaymath}">|; 

$key = q/displaystyleFtheta_{z(i,j+frac{1}{2})}^{n}=rho_{0,j+frac{1}{2}}w_{i,j+frac{1}{2}rac{9}{16}theta_{i,j}^{n}-frac{1}{16}theta_{i,j-1}^{n}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="557" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$\displaystyle F\theta _{z(i,j+\frac{1}{2})}^{n}
=
\rho _{0,j+\frac{1}{2}}w_{i,j...
...^{n}
+ \frac{9}{16}\theta _{i,j}^{n}
- \frac{1}{16}\theta _{i,j-1}^{n} \right).$">|; 

$key = q/[mbox{DKADV}]_{i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="$[\mbox{DKADV}]_{i,j}^{n}$">|; 

$key = q/[mbox{DTDIF}]_{i,j}^{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$[\mbox{DTDIF}]_{i,j}^{N}$">|; 

$key = q/displaystyleF_{IR,i,j+frac{1}{2}}^{uparrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="$\displaystyle F_{IR,i,j+\frac{1}{2}}^{\uparrow}$">|; 

$key = q/mbox{D[UVW]ADV};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\mbox{D[UVW]ADV}$">|; 

$key = q/lambda_{i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$\lambda_{i}$">|; 

$key = q/displaystylefrac{1}{(Deltax)^{2}}left{left[K_{i+frac{1}{2},j+frac{1}{2}}^{n}left,j+frac{1}{2}}^{n}-w_{i-1,j+frac{1}{2}}^{n}right)right]right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="568" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$\displaystyle \frac{1}{(\Delta x)^{2}}\left\{
\left[ K_{i+\frac{1}{2},j+\frac{1...
...
\left(w_{i,j+\frac{1}{2}}^{n}-w_{i-1,j+\frac{1}{2}}^{n}\right)
\right]
\right.$">|; 

$key = q/displaystylefrac{1}{(Deltax)^{2}}left{left[K_{i+1,j}^{n}left(u_{i+frac{3}{2},j}^{i+frac{1}{2},j}^{n}-u_{i-frac{1}{2},j}^{n}right)right]right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="466" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$\displaystyle \frac{1}{(\Delta x)^{2}}\left\{
\left[ K_{i+1,j}^{n}
\left(u_{i+\...
...n}
\left(u_{i+\frac{1}{2},j}^{n}-u_{i-\frac{1}{2},j}^{n}\right)
\right]
\right.$">|; 

$key = q/V_{i}(z);MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$V_{i}(z)$">|; 

$key = q/J'timesJ';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img245.png"
 ALT="$J'\times J'$">|; 

$key = q/displaystylew_{i,j+frac{1}{2}}^{n+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$\displaystyle w_{i,j+\frac{1}{2}}^{n+1}$">|; 

$key = q/i,j;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$i, j$">|; 

$key = q/displaystyleF_{IR,nu_{m},i,j-frac{1}{2}}^{uparrow}-Deltatau_{nu_{m},j}left[gamma}}^{uparrow}+F_{IR,nu_{m},i,j-frac{1}{2}}^{uparrow}}{2}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="432" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="$\displaystyle F_{IR,\nu_{m},i,j-\frac{1}{2}}^{\uparrow} -
\Delta \tau _{\nu_{m}...
...\frac{1}{2}}^{\uparrow} +
F_{IR,\nu_{m},i,j-\frac{1}{2}}^{\uparrow}}{2}
\right.$">|; 

$key = q/displaystyleF_{IR,nu_{m},i,j-frac{1}{2}}^{downarrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img216.png"
 ALT="$\displaystyle F_{IR,\nu_{m},i,j-\frac{1}{2}}^{\downarrow}$">|; 

$key = q/Deltax;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\Delta
x$">|; 

$key = q/Dvect{Lambda};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$\Dvect{\Lambda }$">|; 

$key = q/displaystyleleft.+[mbox{BUOY}]_{i,j'-frac{1}{2}}^{n}right)Deltaz_{j'-frac{1}{2}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$\displaystyle \left.
+ [\mbox{BUOY}]_{i,j'-\frac{1}{2}}^{n}
\right)\Delta z_{j'-\frac{1}{2}}$">|; 

$key = q/displaystylerho_{0,j}=frac{P_{0,j}}{RT_{0,j}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="61" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$\displaystyle \rho _{0,j} = \frac{P_{0,j}}{RT_{0,j}}.$">|; 

$key = q/[mbox{DQNLD}]_{i,j}^{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="$[\mbox{DQNLD}]_{i,j}^{N}$">|; 

$key = q/displaystyle-frac{4rho_{d}gr_{mod}^{2}}{18eta}left(1+2frac{lambda_{r}}{r_{mod}}frac{p_{r}}{P_{0,j}}right)rho_{0,j}q_{i,j}^{n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="$\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},$">|; 

$key = q/displaystyleA_{i,i+2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$\displaystyle A_{i,i+2}$">|; 

$key = q/[mbox{DQDIF}]_{i,j}^{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="$[\mbox{DQDIF}]_{i,j}^{N}$">|; 

$key = q/{displaymath}q_{i,j}^{n+1}=q_{i,j}^{N}+dtleft{[mbox{DQADV}]_{i,j}^{n}+[mbox{DQDIDQFALL}]_{i,j}^{N}+[mbox{DQNLD}]_{i,j}^{N}right}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="587" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="\begin{displaymath}
q_{i,j}^{n+1}
= q_{i,j}^{N} + dt \left\{
[\mbox{DQADV}]_...
... [\mbox{DQFALL}]_{i,j}^{N}+
[\mbox{DQNLD}]_{i,j}^{N} \right\}
\end{displaymath}">|; 

$key = q/displaystyle+frac{2}{3}varepsilon_{i,j}^{n}left[frac{u_{i,j+frac{1}{2}}^{n}-u_{i{w_{i+frac{1}{2},j}^{n}-w_{i-frac{1}{2},j}^{n}}{Deltax}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="348" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="$\displaystyle + \frac{2}{3}\varepsilon _{i,j}^{n} \left[
\frac{u_{i,j+\frac{1}{...
..._{j}} +
\frac{w_{i+\frac{1}{2},j}^{n}-w_{i-\frac{1}{2},j}^{n}}{\Delta x}\right]$">|; 

$key = q/{displaymath}N=left{array{{lcl}n-1&mbox{for}&mbox{leapfrog},n&mbox{for}&mbox{forrog},Deltat&mbox{for}&mbox{forward}.array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="491" HEIGHT="59" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="\begin{displaymath}
N = \left\{
\begin{array}{lcl}
n-1 &amp; \mbox{for} &amp; \mbox{l...
... \Delta t &amp; \mbox{for} &amp; \mbox{forward}.
\end{array} \right.
\end{displaymath}">|; 

$key = q/{displaymath}Q_{dis,i,j}^{N}=frac{C_{epsilon}}{lc_{p}}(varepsilon_{i,j}^{N})^{frac{3}{2}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="50" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="\begin{displaymath}
Q_{dis,i,j}^{N} = \frac{C_{\epsilon}}{lc_{p}}
(\varepsilon _{i,j}^{N})^{\frac{3}{2}},
\end{displaymath}">|; 

$key = q/[mbox{D[UVW]VIS}]_{i+frac{1}{2},j}^{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="154" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$[\mbox{D[UVW]VIS}]_{i+\frac{1}{2},j}^{N}$">|; 

$key = q/Dvect{P}=Dvect{V}cdotDvect{H};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$\Dvect{P} = \Dvect{V}\cdot
\Dvect{H}$">|; 

$key = q/displaystyleF_{theta,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="$\displaystyle F_{\theta,i}$">|; 

$key = q/displaystylelnP_{0,j}=lnP_{00}-sum_{j=1}^{j}frac{g}{RT_{0,j}}Deltaz_{j},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$\displaystyle \ln P_{0,j} = \ln P_{00}
- \sum _{j=1}^{j}\frac{g}{RT_{0,j}}\Delta z_{j},$">|; 

$key = q/displaystyleA_{i+1,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$\displaystyle A_{i+1,i}$">|; 

$key = q/displaystyle(16.0cdot10^{3}cdotrho_{0,j+frac{1}{2}}Deltaz_{j+frac{1}{2}}slashDeltax),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$\displaystyle (16.0 \cdot 10^{3} \cdot \rho _{0,j+\frac{1}{2}}
\Delta z_{j+\frac{1}{2}}/\Delta x ),$">|; 

$key = q/displaystyleF_{IR,nu_{m},i,j+frac{1}{2}}^{downarrow}+Deltatau_{nu_{m},j}left[gam}}^{uparrow}+F_{IR,nu_{m},i,j-frac{1}{2}}^{uparrow}}{2}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="432" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img217.png"
 ALT="$\displaystyle F_{IR,\nu_{m},i,j+\frac{1}{2}}^{\downarrow} +
\Delta \tau _{\nu_{...
...\frac{1}{2}}^{\uparrow} +
F_{IR,\nu_{m},i,j-\frac{1}{2}}^{\uparrow}}{2}
\right.$">|; 

$key = q/displaystylembox{DKNLD}_{i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="$\displaystyle \mbox{DKNLD}_{i,j}^{n}$">|; 

$key = q/{displaymath}u(z_{j+frac{1}{2}},z_{J+frac{3}{2}})=frac{1.67g|P_{0,j+frac{1}{2}}-_{0,J+frac{3}{2}}|}{mbox{MAX}(coszeta,epsilon)}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="56" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="\begin{displaymath}
u(z_{j+\frac{1}{2}},z_{J+\frac{3}{2}}) =
\frac{1.67 g \ve...
...{0,J+\frac{3}{2}} \vert}
{\mbox{MAX}(\cos \zeta, \epsilon )}.
\end{displaymath}">|; 

$key = q/Dvect{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img249.png"
 ALT="$\Dvect{S}$">|; 

$key = q/{eqnarraystar}DP{u}{t}&=&-DP{hat{P}}{x}+alpha,DP{v}{t}&=&beta,DP{w}{t}&=&-DP{hat{P}}{z}{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="147" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="\begin{eqnarray*}
\DP{u}{t} &amp;=&amp; -\DP{\hat{P}}{x} + \alpha , \\\\
\DP{v}{t} &amp;=&amp; \beta , \\\\
\DP{w}{t} &amp;=&amp; -\DP{\hat{P}}{z}
\end{eqnarray*}">|; 

$key = q/displaystyleF_{dif,nu_{m},i,j+frac{1}{2}}^{downarrow}+Deltatau_{nu_{m},j}left[ga}^{uparrow}+F_{dif,nu_{m},i,j-frac{1}{2}}^{uparrow}}{2}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="437" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="$\displaystyle F_{dif,\nu_{m},i,j+\frac{1}{2}}^{\downarrow} +
\Delta \tau _{\nu_...
...frac{1}{2}}^{\uparrow} +
F_{dif,\nu_{m},i,j-\frac{1}{2}}^{\uparrow}}{2}
\right.$">|; 

$key = q/displaystyleleft.-w_{i,j+frac{1}{2}}^{n}left(Ddivrho_{0}Dvect{v}slashrho_{0,j}right)_{i,j+frac{1}{2}}^{n}right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$\displaystyle \left.
- w_{i,j+\frac{1}{2}}^{n}
\left(\Ddiv \rho _{0}\Dvect{v}/\rho _{0,j}\right)
_{i,j+\frac{1}{2}}^{n}
\right\},$">|; 

$key = q/{}_{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="${}_{2}$">|; 

$key = q/displaystyleDvect{H};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$\displaystyle \Dvect{H}$">|; 

$key = q/displaystylev_{i+frac{1}{2},j}^{N}+dtbeta_{i+frac{1}{2},j}^{n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$\displaystyle v_{i+\frac{1}{2},j}^{N}
+ dt \beta _{i+\frac{1}{2},j}^{n},$">|; 

$key = q/z;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$z$">|; 

$key = q/displaystylembox{DUNLV}_{i+frac{1}{2},j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$\displaystyle \mbox{DUNLV}_{i+\frac{1}{2},j}^{n}$">|; 

$key = q/displaystylefrac{1.19times10^{-8}nu_{m}^{3}}{e^{1.4387nu_{i}slashT_{i,j}}-1},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="$\displaystyle \frac{1.19\times 10^{-8}\nu _{m}^{3}}
{e^{1.4387\nu_{i}/T_{i,j}}-1},$">|; 

$key = q/displaystyleDvect{F}_{IR,nu_{m}}^{uparrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img220.png"
 ALT="$\displaystyle \Dvect{F}_{IR,\nu_{m}}^{\uparrow}$">|; 

$key = q/displaystyle+frac{kappaDeltat}{Deltaz_{j}}frac{T_{i,j-1}^{n}}{overline{Deltaz}_{z_{j}}frac{T_{i,j+1}^{n+1}}{overline{Deltaz}_{j+frac{1}{2}}}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="543" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img237.png"
 ALT="$\displaystyle + \frac{\kappa \Delta t}{\Delta z_{j}}
\frac{T_{i,j-1}^{n}}
{\ove...
... t}{\Delta z_{j}}
\frac{T_{i,j+1}^{n+1}}
{\overline{\Delta z}_{j+\frac{1}{2}}}.$">|; 

$key = q/{displaymath}S_{j}=left{array{{ll}frac{Deltat}{rho_{g}c_{p,g}Deltaz_{J'}}[-F_{s}(1-A)+F_{IR,net}+H],&j=J'0,&jneqJ'array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="428" HEIGHT="64" BORDER="0"
 SRC="|."$dir".q|img250.png"
 ALT="\begin{displaymath}
S_{j} = \left\{
\begin{array}{ll}
\frac{\Delta t}{\rho _{...
...F_{IR,net} + H], &amp; j=J' \\\\
0, &amp; j\neq J'
\end{array}\right.
\end{displaymath}">|; 

$key = q/m;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$m$">|; 

$key = q/Theta_{0,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$\Theta _{0,j}$">|; 

$key = q/displaystyleF_{u,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="$\displaystyle F_{u,i}$">|; 

$key = q/displaystyleleft.left.-v_{i+frac{1}{2},j}^{n}left(Ddivrho_{0}Dvect{v}slashrho_{0}right)_{i+frac{1}{2},j}^{n}right}rightslashDeltax,;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$\displaystyle \left.
\left.
- v_{i+\frac{1}{2},j}^{n}
\left(\Ddiv \rho _{0}\Dvect{v}/\rho _{0}\right)_{i+\frac{1}{2},j}^{n}
\right\}
\right/ \Delta x,$">|; 

$key = q/{eqnarraystar}K_{NLD,i+frac{1}{2},j}^{n}&=&mbox{MIN}left[K_{NLD,max},quad0.01fraLD,max}&=&0.2frac{(Deltax)^{2}}{Deltat}.{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="594" HEIGHT="191" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="\begin{eqnarray*}
K_{NLD,i+\frac{1}{2},j}^{n}
&amp;=&amp;
\mbox{MIN}
\left[ K_{NLD...
... /2000, \\\\
K_{NLD,max} &amp;=&amp; 0.2\frac{(\Delta x)^{2}}{\Delta t}.
\end{eqnarray*}">|; 

$key = q/displaystyle+left.left(rho_{0,j+frac{1}{2}}u_{i+frac{1}{2},j+frac{1}{2}}^{n}w_{i,j-frac{1}{2}}^{n}right)Deltaxrightslash(rho_{0,j}Deltaz_{j});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="551" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$\displaystyle +
\left.
\left(
\rho _{0,j+\frac{1}{2}}
u_{i+\frac{1}{2},j+\frac{...
...\frac{1}{2},j-\frac{1}{2}}^{n}
\right)
\Delta x\right/(\rho _{0,j}\Delta z_{j})$">|; 

$key = q/J;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$J$">|; 

$key = q/displaystylefrac{1}{rho_{0}Deltaz_{i}}left(frac{1}{24Deltaz_{i-frac{3}{2}}}frac{Deltaz_{i-frac{1}{2}}}frac{(rho_{0,i}+rho_{0,i-1})}{2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="490" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$\displaystyle \frac{1}{\rho _{0}\Delta z_{i}}\left(
\frac{1}{24\Delta z_{i-\fra...
...rac{9}{8\Delta z_{i-\frac{1}{2}}}\frac{(\rho _
{0,i}+\rho _{0,i-1})}{2}\right),$">|; 

$key = q/displaystylembox{DKBP}_{i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$\displaystyle \mbox{DKBP}_{i,j}^{n}$">|; 

$key = q/displaystyle-left{left(v_{i+1,j}^{n}u_{i+1,j}^{n}-v_{i-1,j}^{n}u_{i-1,j}^{n}right)right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$\displaystyle - \left\{
\left(v_{i+1,j}^{n}u_{i+1,j}^{n} - v_{i-1,j}^{n}u_{i-1,j}^{n}\right)
\right.$">|; 

$key = q/displaystylefrac{1}{rho_{0,j}Deltaz_{j}}left[rho_{0,j+frac{1}{2}}tilde{K}_{i,j+fa_{i,j}^{n}-theta_{i,j-1}^{n})}{Deltaz_{j-frac{1}{2}}}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="535" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$\displaystyle \frac{1}{\rho _{0,j}\Delta z_{j}}
\left[ \rho _{0,j+\frac{1}{2}}
...
...c{
(\theta _{i,j}^{n} -\theta _{i,j-1}^{n})}{\Delta z_{j-\frac{1}{2}}}
\right],$">|; 

$key = q/displaystyle+left.frac{1}{rho_{0,j}Deltaz_{j}}left[-frac{1}{24}Ftheta_{z(i,j+fra)}^{n}+frac{1}{24}Ftheta_{z(i,j-frac{3}{2})}^{n}right]right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="586" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$\displaystyle + \left.
\frac{1}{\rho _{0,j}\Delta z_{j}}\left[
- \frac{1}{24}F\...
...c{1}{2})}^{n}
+ \frac{1}{24}F\theta _{z(i,j-\frac{3}{2})}^{n} \right] \right\},$">|; 

$key = q/Dvect{F}_{dif,nu_{m}}^{uparrow}=(F_{dif,nu_{m},i,frac{1}{2}}^{uparrow},F_{dif,nu}}^{uparrow},...,F_{dif,nu_{m},i,J+frac{1}{2}}^{uparrow})^{T};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="397" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="$\Dvect{F}_{dif,\nu_{m}}^{\uparrow}=(
F_{dif,\nu_{m},i,\frac{1}{2}}^{\uparrow},
...
...,i,\frac{3}{2}}^{\uparrow},...,
F_{dif,\nu_{m},i,J+\frac{1}{2}}^{\uparrow})^{T}$">|; 

$key = q/sim;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="18" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$\sim$">|; 

$key = q/{displaymath}Dvect{T}^{n+1}=Dvect{A}^{-1}cdot(Dvect{B}cdotDvect{T}^{n}+Dvect{S}),{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img247.png"
 ALT="\begin{displaymath}
\Dvect{T}^{n+1} = \Dvect{A}^{-1} \cdot
(\Dvect{B}\cdot \Dvect{T}^{n} + \Dvect{S}),
\end{displaymath}">|; 

$key = q/[mbox{DQFALL}]_{i,j}^{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="$[\mbox{DQFALL}]_{i,j}^{N}$">|; 

$key = q/T_{j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$T_{j}$">|; 

$key = q/{displaymath}Dvect{D_{x}P}+Dvect{D_{z}P}=Dvect{S}{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="\begin{displaymath}
\Dvect{D_{x}P} + \Dvect{D_{z}P} = \Dvect{S}
\end{displaymath}">|; 

$key = q/[mbox{DTDI0}]_{i,j}^{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$[\mbox{DTDI0}]_{i,j}^{N}$">|; 

$key = q/displaystylesum_{k_{x}=1}^{NXslash2-1}left[Dvect{D_{x}}+Dvect{Lambda}right]_{k_{x}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$\displaystyle \sum_{k_{x}=1}^{NX/2-1}
\left[\Dvect{D_{x}} + \Dvect{\Lambda }\right]_{k_{x}}$">|; 

$key = q/displaystyleF_{IR,nu_{m},i,j+frac{1}{2}}^{uparrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="$\displaystyle F_{IR,\nu_{m},i,j+\frac{1}{2}}^{\uparrow}$">|; 

$key = q/{displaymath}tilde{K}_{i+frac{1}{2},j}^{n}=0.5(tilde{K}_{i+1,j}^{n}+tilde{K}_{i,n}=0.5(tilde{K}_{i,j+1}^{n}+tilde{K}_{i,j}^{n}).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="466" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="\begin{displaymath}
\tilde{K}_{i+\frac{1}{2},j}^{n}
= 0.5(\tilde{K}_{i+1,j}^{...
...{2}}^{n}
= 0.5(\tilde{K}_{i,j+1}^{n} +\tilde{K}_{i,j}^{n} ).
\end{displaymath}">|; 

$key = q/displaystylembox{DTAD0}_{i,j}^{n}=-left{frac{1}{rho_{0,j}Deltax}Theta_{0,j}left[}{2},j)}^{n}+frac{1}{24}F_{x(i-frac{3}{2},j)}^{n}right]right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="662" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$\displaystyle \mbox{DTAD0}_{i,j}^{n}
= - \left\{
\frac{1}{\rho _{0,j}\Delta x}\...
...(i-\frac{1}{2},j)}^{n}
+ \frac{1}{24}F_{x(i-\frac{3}{2},j)}^{n} \right]
\right.$">|; 

$key = q/{displaymath}P_{0,j+frac{1}{2}}=0.5(P_{0,j}+P_{0,j+1}),quadoverline{p}_{jj'}=sum1}{2}}|}{u(z_{j+frac{1}{2}},z_{j'+frac{1}{2}})},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="63" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="\begin{displaymath}
P_{0,j+\frac{1}{2}} = 0.5(P_{0,j}+P_{0,j+1}),
\quad
\over...
...\frac{1}{2}}\vert}
{u(z_{j+\frac{1}{2}},z_{j'+\frac{1}{2}})},
\end{displaymath}">|; 

$key = q/Dvect{V};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$\Dvect{V}$">|; 

$key = q/displaystylefrac{1}{(Deltax)^{2}}left[K_{NLD,i+frac{1}{2},j}^{n}(varepsilon_{i+1n}-varepsilon_{i-1,j}^{n})right]+frac{1}{rho_{0,j}Deltaz_{j}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="563" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="$\displaystyle \frac{1}{(\Delta x)^{2}}
\left[
K_{NLD,i+\frac{1}{2},j}^{n}(\vare...
...{i,j}^{n} -\varepsilon_{i-1,j}^{n})
\right] + \frac{1}{\rho _{0,j}\Delta z_{j}}$">|; 

$key = q/displaystyleQ_{rad,i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="$\displaystyle Q_{rad,i,j}^{n}$">|; 

$key = q/Pi_{0,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$\Pi_{0,j}$">|; 

$key = q/displaystyle+frac{(Deltax)^{2}}{rho_{0,j}Deltaz_{j}}left[left.rho_{0,j+1}K_{i,j+(w_{i,j+1}^{n}-w_{i,j}^{n}right)rightslashDeltaz_{j+1}-right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="389" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$\displaystyle + \frac{(\Delta x)^{2}}{\rho _{0,j}\Delta z_{j}}
\left[ \left.
\r...
...j+1}^{n}
\left(w_{i,j+1}^{n}-w_{i,j}^{n}\right)
\right/\Delta z_{j+1} -
\right.$">|; 

$key = q/displaystylevarepsilon_{i,j}^{N}+dtleft{[mbox{DKADV}]_{i,j}^{n}+[mbox{DKDIF}]_{i,j}^{N}+[mbox{DKNLD}]_{i,j}^{N}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="409" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="$\displaystyle \varepsilon _{i,j}^{N} + dt \left\{
[\mbox{DKADV}]_{i,j}^{n} +
[\mbox{DKDIF}]_{i,j}^{N} +
[\mbox{DKNLD}]_{i,j}^{N} \right.$">|; 

$key = q/Dvect{P},Dvect{D_{x}},Dvect{D_{z}},Dvect{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$\Dvect{P}, \Dvect{D_{x}}, \Dvect{D_{z}},
\Dvect{S}$">|; 

$key = q/displaystyleleft.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)rightslashDeltaz_{j-1}right]right}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="303" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$\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\}.$">|; 

$key = q/{displaymath}Deltatau_{nu_{m},j}=frac{overline{Q}_{e,nu_{m}}}{r_{eff}}frac{3rho_c{1}{2}}=sum_{j'=j+1}^{J+1}Deltatau_{nu_{m},j'}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="437" HEIGHT="61" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="\begin{displaymath}
\Delta \tau _{\nu_{m}, j}= \frac{\overline{Q}_{e,\nu_{m}}}{...
...+\frac{1}{2}} = \sum _{j'=j+1}^{J+1}\Delta \tau _{\nu_{m},j'}.
\end{displaymath}">|; 

$key = q/displaystyle-frac{1}{Deltax}left{left(w_{i+frac{1}{2},j+frac{1}{2}}^{n}u_{i+frac+frac{1}{2}}^{n}u_{i-frac{1}{2},j+frac{1}{2}}^{n}right)right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="378" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$\displaystyle - \frac{1}{\Delta x}\left\{
\left(w_{i+\frac{1}{2},j+\frac{1}{2}}...
...ac{1}{2},j+\frac{1}{2}}^{n}
u_{i-\frac{1}{2},j+\frac{1}{2}}^{n}
\right)
\right.$">|; 

$key = q/{displaymath}hat{P},quadDP[2]{}{x},quadfrac{1}{rho_{0}}DP{}{z}left(rho_0DP{}{z}rfrac{1}{rho_{0}}DdivDvect{v}right)+DP{}{x}alpha,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="417" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="\begin{displaymath}
\hat{P}, \quad
\DP[2]{}{x}, \quad
\frac{1}{\rho _{0}}\DP{...
...frac{1}{\rho _{0}}\Ddiv \Dvect{v}\right)
+ \DP{}{x}\alpha ,
\end{displaymath}">|; 

$key = q/displaystylembox{DVVIS}_{i+frac{1}{2},j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$\displaystyle \mbox{DVVIS}_{i+\frac{1}{2},j}^{n}$">|; 

$key = q/displaystyleFQf_{z(i,j-frac{1}{2})}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="$\displaystyle FQf_{z(i,j-\frac{1}{2})}^{n}$">|; 

$key = q/displaystylevarepsilon_{i,j}^{n+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="$\displaystyle \varepsilon _{i,j}^{n+1}$">|; 

$key = q/{displaymath}mbox{Ri}_{B,i}equivfrac{gz_{1}(Theta_{sfc,i}-Theta_{i,1})}{overline{Theta}_{0,1}u_{i,frac{1}{2}}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="57" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="\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}">|; 

$key = q/displaystyle[mbox{DVADV}]_{i+frac{1}{2},j}^{n}+[mbox{DVCOLI}]_{i+frac{1}{2},j}^{IS}]_{i+frac{1}{2},j}^{N}+[mbox{DVNLV}]_{i+frac{1}{2},j}^{N},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="528" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$\displaystyle [\mbox{DVADV}]_{i+\frac{1}{2},j}^{n}
+ [\mbox{DVCOLI}]_{i+\frac{1...
...
+ [\mbox{DVVIS}]_{i+\frac{1}{2},j}^{N}
+ [\mbox{DVNLV}]_{i+\frac{1}{2},j}^{N},$">|; 

$key = q/0leqjleqJ;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$0\leq j \leq J$">|; 

$key = q/displaystyle-frac{1}{rho_{0}Deltaz_{i}}left(frac{1}{24Deltaz_{i+frac{3}{2}}}frac{(rho_{0,i+2}+rho_{0,i+1})}{2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="309" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$\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),$">|; 

$key = q/displaystyleDvect{C}Dvect{F}_{dif,nu_{m}}^{uparrow}+Dvect{D}Dvect{F}_{dif,nu_{m}}^{downarrow}+Dvect{S}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="220" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="$\displaystyle \Dvect{C}\Dvect{F}_{dif,\nu_{m}}^{\uparrow} +
\Dvect{D}\Dvect{F}_{dif,\nu_{m}}^{\downarrow} + \Dvect{S}.$">|; 

$key = q/displaystyleDvect{F}_{dif,nu_{m}}^{downarrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="$\displaystyle \Dvect{F}_{dif,\nu_{m}}^{\downarrow}$">|; 

$key = q/displaystyleFtheta_{x(i+frac{1}{2},j)}^{n}=rho_{0,j}u_{i+frac{1}{2},j}^{n}left(-rac{9}{16}theta_{i,j}^{n}-frac{1}{16}theta_{i-1,j}^{n}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="538" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$\displaystyle F\theta _{x(i+\frac{1}{2},j)}^{n}
=
\rho _{0,j}u_{i+\frac{1}{2},j...
...^{n}
+ \frac{9}{16}\theta _{i,j}^{n}
- \frac{1}{16}\theta _{i-1,j}^{n} \right),$">|; 

$key = q/displaystylegamma_{i,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$\displaystyle \gamma _{i,j}$">|; 

$key = q/{eqnarraystar}&&A_{11}=4+frac{kappaDeltat}{Deltaz_{1}}left(frac{1}{overline{Deltoverline{Deltaz}_{J'-frac{1}{2}}}right),{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="485" HEIGHT="128" BORDER="0"
 SRC="|."$dir".q|img248.png"
 ALT="\begin{eqnarray*}
&amp;&amp;
A_{11}=4 + \frac{\kappa \Delta t}{\Delta z_{1}}
\left( \f...
...
\left( \frac{1}{\overline{\Delta z}_{J'-\frac{1}{2}}} \right),
\end{eqnarray*}">|; 

$key = q/displaystylembox{DWADV}_{i,j+frac{1}{2}}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$\displaystyle \mbox{DWADV}_{i,j+\frac{1}{2}}^{n}$">|; 

$key = q/pi;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\pi $">|; 

$key = q/{displaymath}mbox{DTDI0}_{i,j}^{n}=frac{1}{rho_{0,j}Deltaz_{j}}left[rho_{0,j+fraheta_{0,j-1}^{n})}{Deltaz_{j-frac{1}{2}}}right],{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="660" HEIGHT="64" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="\begin{displaymath}
\mbox{DTDI0}_{i,j}^{n}
=
\frac{1}{\rho _{0,j}\Delta z_{j}...
...{n} -\Theta _{0,j-1}^{n})}{\Delta z_{j-\frac{1}{2}}}
\right],
\end{displaymath}">|; 

$key = q/displaystyleF_{dif,nu_{m},i,j+frac{1}{2}}^{uparrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="$\displaystyle F_{dif,\nu_{m},i,j+\frac{1}{2}}^{\uparrow}$">|; 

$key = q/Q_{rad,i,j}^{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$Q_{rad,i,j}^{N}$">|; 

$key = q/displaystylev_{i+frac{1}{2},j}^{n+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$\displaystyle v_{i+\frac{1}{2},j}^{n+1}$">|; 

$key = q/displaystyleDvect{F}_{dif,nu_{m}}^{uparrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="$\displaystyle \Dvect{F}_{dif,\nu_{m}}^{\uparrow}$">|; 

$key = q/hat{P};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="21" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$\hat{P}$">|; 

$key = q/displaystyleF_{dif,nu_{m},i,j-frac{1}{2}}^{uparrow}-Deltatau_{nu_{m},j}left[gamm}^{uparrow}+F_{dif,nu_{m},i,j-frac{1}{2}}^{uparrow}}{2}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="437" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="$\displaystyle F_{dif,\nu_{m},i,j-\frac{1}{2}}^{\uparrow} -
\Delta \tau _{\nu_{m...
...frac{1}{2}}^{\uparrow} +
F_{dif,\nu_{m},i,j-\frac{1}{2}}^{\uparrow}}{2}
\right.$">|; 

$key = q/J';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img225.png"
 ALT="$J'$">|; 

$key = q/displaystyle-frac{1}{rho_{0}Deltaz_{i}}left(frac{1}{24Deltaz_{i-frac{3}{2}}}frac{(rho_{0,i-1}+rho_{0,i-2})}{2}right).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="309" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$\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).$">|; 

$key = q/Dvect{D_{z}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$\Dvect{D_{z}}$">|; 

$key = q/{displaymath}left(DP[2]{}{x}+frac{1}{rho_{0}}DP{}{z}rho_{0}DP{}{z}right)P=DP{}{t{rho_{0}}Ddivrho_{0}Dvect{v}right)+DP{}{x}alpha,{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="395" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="\begin{displaymath}
\left(\DP[2]{}{x} +\frac{1}{\rho _{0}}\DP{}{z}\rho _{0}\DP{...
...\rho _{0}}\Ddiv \rho _{0}\Dvect{v}\right)
+ \DP{}{x}\alpha ,
\end{displaymath}">|; 

$key = q/displaystyleF_{dif,nu_{m},i,j-frac{1}{2}}^{downarrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="$\displaystyle F_{dif,\nu_{m},i,j-\frac{1}{2}}^{\downarrow}$">|; 

$key = q/Dvect{F}_{IR,nu_{m}}^{uparrow}=(F_{IR,nu_{m},i,frac{1}{2}}^{uparrow},F_{IR,nu_{m2}}^{uparrow},...,F_{IR,nu_{m},i,J+frac{1}{2}}^{uparrow})^{T};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="391" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img219.png"
 ALT="$\Dvect{F}_{IR,\nu_{m}}^{\uparrow}=(F_{IR,\nu_{m},i,\frac{1}{2}}^{\uparrow},
F_{...
...},i,\frac{3}{2}}^{\uparrow},...,
F_{IR,\nu_{m},i,J+\frac{1}{2}}^{\uparrow})^{T}$">|; 

$key = q/{displaymath}frac{1}{rho_{0}}DP{}{z}rho_{0}DP{}{z}pi{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="\begin{displaymath}
\frac{1}{\rho _{0}}\DP{}{z}\rho _{0}\DP{}{z} \pi
\end{displaymath}">|; 

$key = q/displaystyle-fv_{i+frac{1}{2},j}^{n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$\displaystyle - f v_{i+\frac{1}{2},j}^{n},$">|; 

$key = q/epsilon;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="$\epsilon $">|; 

$key = q/A_{i,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$A_{i,j}$">|; 

$key = q/displaystylesum_{m}Deltanu_{m}left{piB_{nu_{i},T_{sfc,i}}{calT}_{i}(0,z_{j+frac{1}{2}})right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="244" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="$\displaystyle \sum _{m}\Delta \nu _{m}\left\{
\pi B_{\nu _{i},T_{sfc,i}}{\cal T}_{i}(0,z_{j+\frac{1}{2}})
\right.$">|; 

$key = q/displaystyleF_{IR,i,j+frac{1}{2}}^{downarrow};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="$\displaystyle F_{IR,i,j+\frac{1}{2}}^{\downarrow}$">|; 

$key = q/{displaymath}F_{NIR,i,j+frac{1}{2}}^{downarrow}=sum_{m}Deltanu_{m}left{S_{nu_{m}z_{j+frac{1}{2}},z_{J+frac{3}{2}})coszetaright}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="384" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="\begin{displaymath}
F_{NIR,i,j+\frac{1}{2}}^{\downarrow} = \sum _{m}\Delta \nu ...
...{i}(z_{j+\frac{1}{2}},z_{J+\frac{3}{2}})\cos \zeta
\right\}.
\end{displaymath}">|; 

$key = q/displaystylealpha_{i+frac{1}{2},j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$\displaystyle \alpha _{i+\frac{1}{2},j}$">|; 

$key = q/displaystylefrac{1}{(Deltax)^{2}}left[tilde{K}_{i+frac{1}{2},j}^{n}(theta_{i+1,ji-frac{1}{2},j}^{n}(theta_{i,j}^{n}-theta_{i-1,j}^{n})right]+;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="426" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="$\displaystyle \frac{1}{(\Delta x)^{2}}
\left[
\tilde{K}_{i+\frac{1}{2},j}^{n}(\...
...ilde{K}_{i-\frac{1}{2},j}^{n}(\theta _{i,j}^{n} -\theta _{i-1,j}^{n})
\right] +$">|; 

$key = q/displaystyle+fu_{i+frac{1}{2},j}^{n}.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$\displaystyle + f u_{i+\frac{1}{2},j}^{n}.$">|; 

$key = q/[mbox{D[UVW]NLV}]_{i+frac{1}{2},j}^{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$[\mbox{D[UVW]NLV}]_{i+\frac{1}{2},j}^{N}$">|; 

$key = q/displaystylembox{BUOY}_{i,j+frac{1}{2}}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$\displaystyle \mbox{BUOY}_{i,j+\frac{1}{2}}^{n}$">|; 

$key = q/displaystylesum_{j'=0}^{j}left([mbox{DWADV}]_{i,j'-frac{1}{2}}^{n}+[mbox{DWVIS}],j'-frac{1}{2}}^{N}+[mbox{DWNLV}]_{i,j'-frac{1}{2}}^{N}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="451" HEIGHT="72" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\displaystyle \sum _{j'=0}^{j}
\left(
[\mbox{DWADV}]_{i,j'-\frac{1}{2}}^{n}
+ [...
...{DWVIS}]_{i,j'-\frac{1}{2}}^{N}
+ [\mbox{DWNLV}]_{i,j'-\frac{1}{2}}^{N}
\right.$">|; 

$key = q/displaystyleu_{i+frac{1}{2},j}^{n+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$\displaystyle u_{i+\frac{1}{2},j}^{n+1}$">|; 

$key = q/displaystyle-left.gamma_{1,nu_{m}}frac{F_{IR,nu_{m},i,j+frac{1}{2}}^{downarrow}+{2}+2pi(1-tilde{omega}_{nu_{m}}^{*})B_{nu_{m},T_{i,j}}right].;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="469" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img218.png"
 ALT="$\displaystyle - \left.
\gamma _{1,\nu_{m}}\frac{F_{IR,\nu_{m},i,j+\frac{1}{2}}^...
...wnarrow}}{2}
+2\pi (1-\tilde{\omega}_{\nu_{m}}^{*})B_{\nu_{m},T_{i,j}}
\right].$">|; 

$key = q/j=1;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img229.png"
 ALT="$j = 1$">|; 

$key = q/overline{Deltaz}_{j+frac{1}{2}}=(Deltaz_{j+1}+Deltaz_{j})slash2;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img238.png"
 ALT="$\overline{\Delta z}_{j+\frac{1}{2}}=(\Delta z_{j+1}+\Delta
z_{j})/2$">|; 

$key = q/{eqnarraystar}hat{P}&equiv&c_{p}Theta_{0}pi-gamma,alpha&equiv&-uDP{u}{x}-wDP{u}{z}+gfrac{theta}{Theta_{0}}+D(w)right)Ddz{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="385" HEIGHT="182" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="\begin{eqnarray*}
\hat{P} &amp;\equiv&amp; c_{p}\Theta _{0}\pi - \gamma , \\\\
\alpha &amp;...
... - w\DP{w}{z} + g\frac{\theta}{\Theta _{0}}
+ D(w)\right) \Dd z
\end{eqnarray*}">|; 

$key = q/(n+1)Deltat;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img234.png"
 ALT="$(n+1)\Delta t$">|; 

$key = q/displaystyle-frac{1}{Deltax}left{left(u_{i+1,j}^{n}u_{i+1,j}^{n}-u_{i-1,j}^{n}u_{i-1,j}^{n}right)right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$\displaystyle - \frac{1}{\Delta x}\left\{
\left(u_{i+1,j}^{n}u_{i+1,j}^{n} - u_{i-1,j}^{n}u_{i-1,j}^{n}\right)
\right.$">|; 

$key = q/displaystyletheta_{i,j}^{N}+dtleft{frac{Theta_{0,j}}{T_{0,j}}(Q_{rad,i,j}^{N}+Q_{dis,i,j}^{N})right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="266" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$\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.$">|; 

$key = q/Deltaz_{j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$\Delta z_{j}$">|; 

$key = q/{eqnarraystar}&&A_{jj}=4+frac{kappaDeltat}{Deltaz_{j}}left(frac{1}{overline{Deltrac{1}{overline{Deltaz}_{i-frac{1}{2}}},{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="669" HEIGHT="128" BORDER="0"
 SRC="|."$dir".q|img244.png"
 ALT="\begin{eqnarray*}
&amp;&amp;
A_{jj}=4 + \frac{\kappa \Delta t}{\Delta z_{j}}
\left( \f...
...t}{\Delta z_{i}}
\frac{1}{\overline{\Delta z}_{i-\frac{1}{2}}},
\end{eqnarray*}">|; 

$key = q/{displaymath}left(Dvect{D_{x}}+Dvect{Lambda}right)Dvect{H}=Dvect{V}^{-1}Dvect{S},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="\begin{displaymath}
\left(\Dvect{D_{x}} + \Dvect{\Lambda }\right) \Dvect{H}
= \Dvect{V}^{-1}\Dvect{S},
\end{displaymath}">|; 

$key = q/displaystyle+left.frac{1}{rho_{0,j}Deltaz_{j}}left[-frac{1}{24}FTheta_{0,z(j+fra)}^{n}+frac{1}{24}FTheta_{0,z(j-frac{3}{2})}^{n}right]right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="618" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="$\displaystyle + \left.
\frac{1}{\rho _{0,j}\Delta z_{j}}\left[
- \frac{1}{24}F\...
...c{1}{2})}^{n}
+ \frac{1}{24}F\Theta _{0,z(j-\frac{3}{2})}^{n} \right] \right\},$">|; 

$key = q/displaystyle2K_{i,j}^{n}left[left(frac{u_{i+frac{1}{2},j}^{n}-u_{i-frac{1}{2},j}}{2}}^{n}-w_{i,j-frac{1}{2}}^{n}}{Deltaz_{j}}right)^{2}right];MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="408" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$\displaystyle 2K_{i,j}^{n}\left[
\left(
\frac{u_{i+\frac{1}{2},j}^{n}-u_{i-\fra...
...i,j+\frac{1}{2}}^{n}-w_{i,j-\frac{1}{2}}^{n}}{\Delta z_{j}}
\right)^{2}
\right]$">|; 

$key = q/displaystyleA_{i+2,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$\displaystyle A_{i+2,i}$">|; 

$key = q/displaystyleleft.-u_{i+frac{1}{2},j}^{n}left(Ddivrho_{0}Dvect{v}slashrho_{0}right)_{i+frac{1}{2},j}^{n}right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="216" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$\displaystyle \left.
- u_{i+\frac{1}{2},j}^{n}
\left(\Ddiv \rho _{0}\Dvect{v}/\rho _{0}\right)
_{i+\frac{1}{2},j}^{n}
\right\},$">|; 

$key = q/{displaymath}u_{i,j+frac{1}{2}}^{n}=0.5left(u_{i+frac{1}{2},j+frac{1}{2}}^{n}+u_2}}^{n}+w_{i+frac{1}{2},j-frac{1}{2}}^{n}right).{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="592" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="\begin{displaymath}
u_{i,j+\frac{1}{2}}^{n} =
0.5\left(u_{i+\frac{1}{2},j+\fra...
...rac{1}{2}}^{n} +
w_{i+\frac{1}{2},j-\frac{1}{2}}^{n}\right).
\end{displaymath}">|; 

$key = q/P_{0,j},rho_{0,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$P_{0,j}, \rho _{0,j}$">|; 

$key = q/displaystyleleft{left[left(v_{i+frac{3}{2},j}^{n}-v_{i+frac{1}{2},j}^{n}right)^{c{1}{2},j+1}^{n}-v_{i+frac{1}{2},j}^{n}right)^{3}right.right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$\displaystyle \left\{
\left[
\left(v_{i+\frac{3}{2},j}^{n}-v_{i+\frac{1}{2},j}^...
...t(v_{i+\frac{1}{2},j+1}^{n}-v_{i+\frac{1}{2},j}^{n}
\right)^{3} \right.
\right.$">|; 

$key = q/{displaymath}F_{*,net,i,j+frac{1}{2}}=F_{IR,i,j+frac{1}{2}}^{uparrow}-F_{IR,i,j+taP_{0,j}=P_{0,j+frac{1}{2}}-P_{0,j-frac{1}{2}}.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="490" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="\begin{displaymath}
F_{*,net,i,j+\frac{1}{2}} =
F_{IR,i,j+\frac{1}{2}}^{\uparr...
...d
\Delta P_{0,j} = P_{0,j+\frac{1}{2}} - P_{0,j-\frac{1}{2}}.
\end{displaymath}">|; 

$key = q/displaystyle+left.[mbox{DTADV}]_{i,j}^{n}+[mbox{DTAD0}]_{i,j}^{n}+[mbox{DTDIF}]_{i,j}^{N}+[mbox{DTDI0}]_{i,j}^{N}right};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="458" HEIGHT="47" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="$\displaystyle + \left.
[\mbox{DTADV}]_{i,j}^{n} +
[\mbox{DTAD0}]_{i,j}^{n} +
[\mbox{DTDIF}]_{i,j}^{N} +
[\mbox{DTDI0}]_{i,j}^{N} \right\}$">|; 

$key = q/Dvect{D_{z}V}=Dvect{VLambda};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$\Dvect{D_{z}V} = \Dvect{V\Lambda }$">|; 

$key = q/displaystyleT_{i,j};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="$\displaystyle T_{i,j}$">|; 

$key = q/displaystylefrac{g}{Theta_{0,j+frac{1}{2}}}theta_{i,j+frac{1}{2}}^{n},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="55" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\displaystyle \frac{g}{\Theta _{0,j+\frac{1}{2}}}
\theta _{i,j+\frac{1}{2}}^{n},$">|; 

$key = q/displaystylembox{DKSP}_{i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$\displaystyle \mbox{DKSP}_{i,j}^{n}$">|; 

$key = q/displaystylembox{DTDIF}_{i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$\displaystyle \mbox{DTDIF}_{i,j}^{n}$">|; 

$key = q/displaystyle-left.gamma_{2,nu_{m}}frac{F_{IR,nu_{m},i,j+frac{1}{2}}^{downarrow}+{2}-2pi(1-tilde{omega}_{nu_{m}}^{*})B_{nu_{m},T_{i,j}}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="470" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="$\displaystyle - \left.
\gamma _{2,\nu_{m}}\frac{F_{IR,\nu_{m},i,j+\frac{1}{2}}^...
...wnarrow}}{2}
-2\pi (1-\tilde{\omega}_{\nu_{m}}^{*})B_{\nu_{m},T_{i,j}}
\right],$">|; 

$key = q/displaystylembox{DQFALL}_{i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="$\displaystyle \mbox{DQFALL}_{i,j}^{n}$">|; 

$key = q/displaystyleleft{left[left(w_{i+1,j+frac{1}{2}}^{n}-w_{i,j+frac{1}{2}}^{n}right)rac{1}{2}}^{n}-w_{i-1,j+frac{1}{2}}^{n}right)^{3}right]right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="389" HEIGHT="57" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\displaystyle \left\{
\left[
\left(w_{i+1,j+\frac{1}{2}}^{n}-w_{i,j+\frac{1}{2}...
...ft(w_{i,j+\frac{1}{2}}^{n}-w_{i-1,j+\frac{1}{2}}^{n}\right)^{3}
\right]
\right.$">|; 

$key = q/{eqnarraystar}&&u_{i+frac{1}{2},j+frac{1}{2}}^{n}=0.5left(u_{i+frac{1}{2},j+1}^{_{0,j+frac{1}{2}}Deltaz_{j+frac{1}{2}}}.{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="537" HEIGHT="397" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="\begin{eqnarray*}
&amp;&amp; u_{i+\frac{1}{2},j+\frac{1}{2}}^{n} =
0.5\left(u_{i+\frac...
...w_{i,j}^{n}}
{\rho _{0,j+\frac{1}{2}}\Delta z_{j+\frac{1}{2}}}.
\end{eqnarray*}">|; 

$key = q/kappa=k_{g}slashrho_{g}c_{p,g};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img233.png"
 ALT="$\kappa = k_{g}/\rho _{g}c_{p,g}$">|; 

$key = q/Deltat;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$\Delta t$">|; 

$key = q/displaystylembox{DWNLV}_{i,j+frac{1}{2}}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$\displaystyle \mbox{DWNLV}_{i,j+\frac{1}{2}}^{n}$">|; 

$key = q/displaystylesum_{k=1}^{NXslash2-1}left[Dvect{V}^{-1}Dvect{S}right]_{k_{x}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$\displaystyle \sum_{k=1}^{NX/2-1}
\left[\Dvect{V}^{-1}\Dvect{S}\right]_{k_{x}},$">|; 

$key = q/displaystylembox{DTADV}_{i,j}^{n}=-left{frac{1}{rho_{0,j}Deltax}left[-frac{1}{24j)}^{n}+frac{1}{24}Ftheta_{x(i-frac{3}{2},j)}^{n}right]right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="679" HEIGHT="66" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$\displaystyle \mbox{DTADV}_{i,j}^{n}
= - \left\{
\frac{1}{\rho _{0,j}\Delta x}\...
...c{1}{2},j)}^{n}
+ \frac{1}{24}F\theta _{x(i-\frac{3}{2},j)}^{n} \right]
\right.$">|; 

$key = q/displaystyleDvect{A}Dvect{F}_{dif,nu_{m}}^{uparrow}+Dvect{B}Dvect{F}_{dif,nu_{m}}^{downarrow}+Dvect{R},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="45" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="$\displaystyle \Dvect{A}\Dvect{F}_{dif,\nu_{m}}^{\uparrow} +
\Dvect{B}\Dvect{F}_{dif,\nu_{m}}^{\downarrow} + \Dvect{R},$">|; 

$key = q/{displaymath}C_{D,i}=left{array{{lcl}C_{Dn}left(1-frac{ambox{Ri}_{B,i}}{1+c|mbox_{B,i})^{2}}&for&mbox{Ri}_{B,i}geq0,array{right.{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="402" HEIGHT="77" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="\begin{displaymath}
C_{D,i} = \left\{
\begin{array}{lcl}
C_{Dn}\left( 1 -
\f...
...B,i})^{2}}&amp; for &amp; \mbox{Ri}_{B,i} \geq 0,
\end{array}\right.
\end{displaymath}">|; 

$key = q/displaystyle-frac{1}{rho_{0}Deltaz_{i}}left(frac{9}{8Deltazm_{i+frac{1}{2}}}fracDeltaz_{i-frac{1}{2}}}frac{(rho_{0,i}+rho_{0,i-1})}{2}right),;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="495" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$\displaystyle - \frac{1}{\rho _{0}\Delta z_{i}}\left(
\frac{9}{8\Delta zm_{i+\f...
...rac{9}{8\Delta z_{i-\frac{1}{2}}}\frac{(\rho _
{0,i}+\rho _{0,i-1})}{2}\right),$">|; 

$key = q/[mbox{DKDIF}]_{i,j}^{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$[\mbox{DKDIF}]_{i,j}^{N}$">|; 

$key = q/[mbox{DQADV}]_{i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="$[\mbox{DQADV}]_{i,j}^{n}$">|; 

$key = q/displaystylefrac{kappa}{4Deltaz_{j}}left(frac{T_{i,j+1}^{n+1}-T_{i,j}^{n+1}}{DelT_{i,j}^{n+1}-T_{i,j-1}^{n+1}}{Deltaz_{j}+Deltaz_{j-1}}right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="311" HEIGHT="69" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img231.png"
 ALT="$\displaystyle \frac{\kappa}{4\Delta z_{j}}
\left( \frac{T_{i,j+1}^{n+1} - T_{i,...
... -
\frac{T_{i,j}^{n+1} - T_{i,j-1}^{n+1}}
{\Delta z_{j}+\Delta z_{j-1}}
\right.$">|; 

$key = q/displaystylembox{DUADV}_{i+frac{1}{2},j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$\displaystyle \mbox{DUADV}_{i+\frac{1}{2},j}^{n}$">|; 

$key = q/[mbox{DKNLD}]_{i,j}^{N};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="$[\mbox{DKNLD}]_{i,j}^{N}$">|; 

$key = q/x;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$x$">|; 

$key = q/displaystyle+[mbox{DUVIS}]_{i+frac{1}{2},j}^{N}+[mbox{DUNLV}]_{i+frac{1}{2},j}^{N},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$\displaystyle + [\mbox{DUVIS}]_{i+\frac{1}{2},j}^{N}
+ [\mbox{DUNLV}]_{i+\frac{1}{2},j}^{N} ,$">|; 

$key = q/displaystyleA_{i,i+1};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$\displaystyle A_{i,i+1}$">|; 

$key = q/displaystyleA_{i,i};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$\displaystyle A_{i,i}$">|; 

$key = q/displaystyleleft[rho_{0,j+frac{1}{2}}K_{NLD,i,j+frac{1}{2}}^{n}frac{(varepsilon_}^{n}-varepsilon_{*i,j-1}^{n})}{Deltaz_{j-frac{1}{2}}}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="549" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="$\displaystyle \left[ \rho _{0,j+\frac{1}{2}}
K_{NLD,i,j+\frac{1}{2}}^{n}
\frac{...
...epsilon_{i,j}^{n}-\varepsilon_{*i,j-1}^{n})}{\Delta z_{j-\frac{1}{2}}}
\right],$">|; 

$key = q/Q_{rad,i,j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="$Q_{rad,i,j}^{n}$">|; 

$key = q/displaystylerho_{0}C_{D,i}|u_{i,frac{1}{2}}|(T_{sfc,i}-T_{i,1}).;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="206" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="$\displaystyle \rho _{0}C_{D,i}\vert u_{i,\frac{1}{2}}\vert(T_{sfc,i}-T_{i,1}).$">|; 

$key = q/{displaymath}{calT}_{m}(z_{j+frac{1}{2}},z_{j'+frac{1}{2}})=exp(-W_{m,j,j'}slashc{1}{2}},z_{j'+frac{1}{2}})slashalpha^{*}_{m}}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="643" HEIGHT="65" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="\begin{displaymath}
{\cal T}_{m}(z_{j+\frac{1}{2}},z_{j'+\frac{1}{2}}) =
\exp...
...{*}(z_{j+\frac{1}{2}},z_{j'+\frac{1}{2}})/
\alpha ^{*}_{m}}},
\end{displaymath}">|; 

$key = q/displaystyle-rho_{0}C_{D,i}|u_{i,frac{1}{2}}|u_{i,frac{1}{2}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="$\displaystyle - \rho _{0}C_{D,i}\vert u_{i,\frac{1}{2}}\vert u_{i,\frac{1}{2}},$">|; 

$key = q/displaystylebeta_{i+frac{1}{2},j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$\displaystyle \beta _{i+\frac{1}{2},j}^{n}$">|; 

$key = q/displaystyle+frac{(Deltax)^{2}}{rho_{0,j}Deltaz_{j}}left[left.rho_{0,j+frac{1}{2frac{1}{2},j}^{n}right)rightslashDeltaz_{j+frac{1}{2}}-right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="452" HEIGHT="65" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\displaystyle + \frac{(\Delta x)^{2}}{\rho _{0,j}\Delta z_{j}}
\left[ \left.
\r...
...1}^{n}-u_{i+\frac{1}{2},j}^{n}\right)
\right/\Delta z_{j+\frac{1}{2}} -
\right.$">|; 

$key = q/displaystyle-frac{1}{rho_{0,j}Deltaz_{j}}left{FQf_{z(i,j+frac{1}{2})}^{n}-FQf_{z(i,j-frac{1}{2})}^{n}right},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="321" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="$\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\},$">|; 

$key = q/{displaymath}u(z_{j+frac{1}{2}},z_{j'+frac{1}{2}})=1.67g|P_{0,j+frac{1}{2}}-P_{0{*}_{m}=alpha_{m}frac{overline{p}_{jj'}}{p_{0}},{displaymath};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="452" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="\begin{displaymath}
u(z_{j+\frac{1}{2}},z_{j'+\frac{1}{2}}) = 1.67
g \vert P_...
...\alpha ^{*}_{m}=\alpha _{m} \frac{\overline{p}_{jj'}}{p_{0}},
\end{displaymath}">|; 

$key = q/displaystyle+K_{i,j}^{n}left[frac{u_{i,j+frac{1}{2}}^{n}-u_{i,j-frac{1}{2}}^{n}}i+frac{1}{2},j}^{n}-w_{i-frac{1}{2},j}^{n}}{Deltax}right]^{2};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="350" HEIGHT="82" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="$\displaystyle + K_{i,j}^{n}
\left[
\frac{u_{i,j+\frac{1}{2}}^{n}-u_{i,j-\frac{1...
...} +
\frac{w_{i+\frac{1}{2},j}^{n}-w_{i-\frac{1}{2},j}^{n}}{\Delta x}\right]^{2}$">|; 

$key = q/displaystylePi_{0,j}(theta_{i,j}+Theta_{0,j});MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="$\displaystyle \Pi _{0,j}(\theta _{i,j}+\Theta _{0,j})$">|; 

$key = q/j=1,2,...J';MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img226.png"
 ALT="$j=1,2,...J'$">|; 

$key = q/DP{}{z}=0;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="42" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="$\DP{}{z}=0$">|; 

$key = q/displaystyleDvect{V}^{-1}Dvect{S};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$\displaystyle \Dvect{V}^{-1}\Dvect{S}$">|; 

$key = q/displaystylefrac{1}{(Deltax)^{2}}left{left[K_{i+1,j}^{n}left(v_{i+frac{3}{2},j}^{i+frac{1}{2},j}^{n}-v_{i-frac{1}{2},j}^{n}right)right]right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="460" HEIGHT="59" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\displaystyle \frac{1}{(\Delta x)^{2}}
\left\{
\left[ K_{i+1,j}^{n}
\left(v_{i+...
...n}
\left(v_{i+\frac{1}{2},j}^{n}-v_{i-\frac{1}{2},j}^{n}\right)
\right]
\right.$">|; 

$key = q/displaystylembox{DVADV}_{i+frac{1}{2},j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$\displaystyle \mbox{DVADV}_{i+\frac{1}{2},j}^{n}$">|; 

$key = q/displaystyle-frac{kappaDeltat}{Deltaz_{j}}frac{T_{i,j-1}^{n+1}}{overline{Deltaz}az_{j}}frac{T_{i,j+1}^{n+1}}{overline{Deltaz}_{j+frac{1}{2}}};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="550" HEIGHT="76" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img236.png"
 ALT="$\displaystyle - \frac{\kappa \Delta t}{\Delta z_{j}}
\frac{T_{i,j-1}^{n+1}}
{\o...
...a t}{\Delta z_{j}}
\frac{T_{i,j+1}^{n+1}}
{\overline{\Delta z}_{j+\frac{1}{2}}}$">|; 

$key = q/displaystyleleft{left[left(u_{i+frac{3}{2},j}^{n}-u_{i+frac{1}{2},j}^{n}right)^{c{1}{2},j+1}^{n}-u_{i+frac{1}{2},j}^{n}right)^{3}right.right.;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="556" HEIGHT="56" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$\displaystyle \left\{
\left[
\left(u_{i+\frac{3}{2},j}^{n}-u_{i+\frac{1}{2},j}^...
...t(u_{i+\frac{1}{2},j+1}^{n}-u_{i+\frac{1}{2},j}^{n}
\right)^{3} \right. \right.$">|; 

$key = q/displaystylembox{DVNLV}_{i+frac{1}{2},j}^{n};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$\displaystyle \mbox{DVNLV}_{i+\frac{1}{2},j}^{n}$">|; 

$key = q/displaystyle-left.gamma_{1,nu_{m}}frac{F_{dif,nu_{m},i,j+frac{1}{2}}^{downarrow}^{*}S_{0}e^{-tau_{nu_{m},j+frac{1}{2}}^{*}slashmu_{0}}right],;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="544" HEIGHT="85" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="$\displaystyle - \left.
\gamma _{1,\nu_{m}}\frac{F_{dif,\nu_{m},i,j+\frac{1}{2}}...
...ga}_{\nu_{m}}^{*}
S_{0}e^{-\tau _{\nu_{m},j+\frac{1}{2}} ^{*}/\mu_{0}}
\right],$">|; 

$key = q/displaystyle-frac{g}{c_{p}}frac{F_{*,net,i,j+frac{1}{2}}-F_{*,net,i,j-frac{1}{2}}}{DeltaP_{0,j}},;MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="68" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="$\displaystyle - \frac{g}{c_{p}}
\frac{F_{*,net,i,j+\frac{1}{2}} -
F_{*,net,i,j-\frac{1}{2}}}
{\Delta P _{0,j}},$">|; 

$key = q/{eqnarraystar}A_{jk}&=&left{array{{cl}-frac{1}{2}Deltatau_{nu_{m},j}gamma_{1,nu_{*}slashmu_{0}}&jleqJ-10&j=Jarray{right.{eqnarraystar};MSF=1.6;LFS=12;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="489" HEIGHT="453" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="\begin{eqnarray*}
A_{jk} &amp;=&amp; \left\{
\begin{array}{cl}
- \frac{1}{2}\Delta \t...
...}}^{*}
/\mu_{0}} &amp;
j\leq J-1 \\\\
0 &amp; j=J
\end{array} \right.
\end{eqnarray*}">|; 

$key = q/displaystylefrac{T_{i,j}^{n+1}-T_{i,j}^{n}}{Deltat};MSF=1.6;LFS=12;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="69" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img230.png"
 ALT="$\displaystyle \frac{T_{i,j}^{n+1}-T_{i,j}^{n}}{\Delta t}$">|; 

1;