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\DonJ


\Dtitle[\DselJ{deepconv-mars: ¿ôÍý¥â¥Ç¥ë}
              {deepconv-mars}]
{\DselJ
 {2 ¼¡¸µÈóÃÆÀ­Î®ÂÎ¥â¥Ç¥ë deepconv-mars \\Âè 1 Éô: ¿ôÍý¥â¥Ç¥ë²òÀâ} 
 {Two dimensional anelastic model deepconv-mars: \\Part 1, Governing equations}
}


\Dauthor{\DselJ{¾®¹âÀµ»Ì}{Masatsugu Odaka}}
\Ddate{\DselJ{2001 Ç¯ 11 ·î 1 Æü}{2001/11/01}}




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\lthtmlinlinemathA{tex2html_wrap_inline782}%
$z_{0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline784}%
$\mbox{Ri}_{B}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath665}%
\begin{displaymath}
  \mbox{Ri}_{B} \equiv \frac{gz_{1}(\Theta _{sfc}-\Theta _
  {z=z1})}{\overline{\Theta }_{z=z1}u_{z=z1}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline792}%
$\Theta _{z=z1}, \overline{\Theta }_{z=z1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline794}%
$\Theta_{sfc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline796}%
$=T_{sfc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline940}%
$q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath846}%
\begin{displaymath}
 \DD{q}{t} + \frac{1}{\rho _{0}}\DP{}{z}(\rho _{0}Wq) = D(q).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline944}%
$W$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath858}%
\begin{displaymath}
 W = - \frac{4\rho _{d}gr^{2}}{18\eta}
       \left(1+2\frac{\lambda_{r}}{r}\frac{p_{r}}{P_{0}}\right).
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline948}%
$\rho _{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline950}%
$r$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline952}%
$\eta $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline954}%
$\lambda _{r}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline956}%
$p_{r}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline960}%
$r_{m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline974}%
$\tau _{m}\equiv|F_{u}|$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline976}%
$\tau _{mc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline978}%
$F_{q}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline984}%
${}^{-3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline988}%
$\times10^{-5}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline996}%
$\lambda_{r}(p_{r})$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline998}%
$\times 10^{-6}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline1010}%
$\tau_{m} \geq \tau _{mc}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmldisplayA{displaymath1055}%
\begin{displaymath}
  Q_{rad}= Q_{rad,IR} + Q_{rad,NIR} + Q_{rad,dust,SR} + Q_{rad,dust,IR}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2514}%
$Q_{rad,IR}, Q_{rad,NIR}, Q_{rad,dust,SR}, Q_{rad,dust,IR}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2518}%
$Q_{rad,IR}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2520}%
$Q_{rad,NIR}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2524}%
$Q_{rad,dust,SR}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2526}%
$Q_{rad,dust,IR}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2538}%
$F_{IR}^{\uparrow}, F_{IR}^{\downarrow}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4660}%
$\displaystyle F_{IR}^{\uparrow}(z)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4662}%
$\displaystyle \sum _{i}\Delta \nu _{i}\left\{
\pi B_{\nu _{i},T}(z=0){\cal T}_{i}(0,z) +
\int _{0}^{z}\pi B_{\nu _{i},T}(z')\DD{{\cal T }_{i}(z,z')}{z'}\Dd z'
\right\},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4663}%
$\displaystyle F_{IR}^{\downarrow}(z)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4665}%
$\displaystyle \sum _{i}\Delta \nu _{i}\left\{
\int _{z}^{\infty }\pi B_{\nu _{i},T}(z')\DD{{\cal T}_{i}(z,z')}{z'}\Dd z'
\right\},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4666}%
$\displaystyle Q_{rad,IR}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4668}%
$\displaystyle -\frac{1}{\rho _{0}c_{p}}\DP{}{z}(F_{IR}^{\uparrow}(z) -
F_{IR}^{\downarrow}(z) ).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2554}%
$\Delta \nu _{i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2556}%
$B_{\nu _{i},T}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2560}%
$i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1137}%
\begin{displaymath}
  B_{\nu _{i},T} = \frac{2hc^{2}\nu _{i}^{3}}{e^{hc\nu_{i}/kT}-1} 
               = \frac{1.19\times 10^{-8}\nu _{i}^{3}}{e^{1.4387\nu_{i}/T}-1},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2564}%
$h$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2566}%
$c$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2570}%
$T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2572}%
${\cal T}_{i}(z,z')$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2574}%
$\nu _{i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2488}%
\begin{displaymath}
  {\cal T}_{i}(z,z') = \exp ( - W_{i}/\Delta \nu _{i}),
  \quad
  W_{i} = \frac{s_{i} u(z,z')}
  {\sqrt{ 1 + s_{i}u(z,z')/\alpha ^{*}_{i}}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2489}%
\begin{displaymath}
  u(z,z') = \int _{z}^{z'}1.67\rho _{0}\Dd z,
  \quad
  \alpha ^{*}_{i}=\alpha _{i} \overline{p}/p_{0}, 
  \quad
  \overline{p} = \int _{z}^{z'}P_{0} \Dd u / u.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2592}%
$s_{i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2594}%
$\alpha ^{*}_{i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2596}%
$\alpha _{i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2598}%
$u$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2600}%
$p_{0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2624}%
$F_{NIR}^{\downarrow}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4716}%
$\displaystyle F_{NIR}^{\downarrow}(z)$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4718}%
$\displaystyle \sum _{i}\Delta \nu _{i}\left\{
S_{\nu _{i}}{\cal T}_{i}(\infty,z)\mu_{0}
\right\},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4719}%
$\displaystyle Q_{rad,NIR}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4721}%
$\displaystyle \frac{1}{\rho _{0}}\DP{F_{IR}^{\downarrow}(z)}{z},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2642}%
$\mu _{0}=\cos \zeta$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2644}%
$\zeta $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2646}%
$S_{\nu
_{i}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4729}%
$\displaystyle S_{\nu _{i}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4731}%
$\displaystyle B_{\nu _{i},T_{sol}}
\left(\frac{F_{s}}{\sigma T_{sol}^{4}}\right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4732}%
$\displaystyle F_{s}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay4734}%
$\displaystyle I_{0}\left(\frac{r_{0}}{r}\right)^{2}\mu_{0},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2654}%
$T_{sol}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2656}%
$\sigma $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2658}%
$\times 10{}^{-8}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2662}%
${}^{-4}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2664}%
$I_{0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2670}%
$r_{0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2672}%
$F_{s}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2678}%
$\cos \zeta $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2490}%
\begin{displaymath}
  u(z,z') = \int _{z}^{z'}1.67\rho _{0}\Dd z / \mu_{0},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2714}%
$T=$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2740}%
$\Delta
\nu =$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2794}%
$\Delta \nu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2822}%
$\times 10{}^{-2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2824}%
$\times 10{}^{-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2826}%
$\times 10{}^{3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2828}%
$\times 10{}^{1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2832}%
$\times 10{}^{0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2834}%
$\times 10{}^{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2870}%
$\times 10{}^{4}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2874}%
$\times 10{}^{-3}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline2914}%
$\times 10{}^{5}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3078}%
$F_{dif,\nu_{i}}^{\uparrow}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3080}%
$F_{dif,\nu _{i}}^{\downarrow}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5139}%
$\displaystyle \DD{F_{dif,\nu _{i}}^{\uparrow}}{\tau _{\nu _{i}}^{*}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5141}%
$\displaystyle \gamma _{1,\nu _{i}}F_{dif,\nu _{i}}^{\uparrow} -
\gamma _{2,\nu _{i}}F_{dif,\nu _{i}}^{\downarrow} - \gamma _{3,\nu _{i}}
\tilde{\omega}_{\nu _{i}}^{*}S_{\nu _{i}}e^{-\tau _{\nu _{i}}^{*}/\mu_{0}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5142}%
$\displaystyle \DD{F_{dif,\nu _{i}}^{\downarrow}}{\tau _{\nu _{i}}^{*}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5144}%
$\displaystyle \gamma _{2,\nu _{i}}F_{dif,\nu _{i}}^{\uparrow} -
\gamma _{1,\nu _{i}}F_{dif,\nu _{i}}^{\downarrow} + (1-\gamma _{3,\nu _{i}})
\tilde{\omega}_{\nu _{i}}^{*}S_{\nu _{i}}e^{-\tau _{\nu _{i}}^{*}/\mu_{0}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3090}%
$F_{dif,\nu}^{\downarrow}\times A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3092}%
$A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3094}%
$\gamma _{1,\nu _{i}},\gamma _{2,\nu _{i}},\gamma _{3,\nu _{i}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3096}%
$F_{dif,\nu_{i}}^{\downarrow}=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3098}%
$F_{dif,\nu_{i}}^{\uparrow}= 
   F_{dif,\nu}^{\downarrow}\times A$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2491}%
\begin{displaymath} 
 \gamma _{1,\nu _{i}} = 
 \frac{1}{4}[7-(4+3g_{\nu _{i}}^{*})\tilde{\omega}_{\nu _{i}}^{*}], \quad 
 \gamma _{2,\nu _{i}} = 
 -\frac{1}{4}[1-(4-3g_{\nu _{i}}^{*})\tilde{\omega}_{\nu _{i}}^{*}],
 \quad
 \gamma _{3,\nu _{i}} = \frac{1}{4}(2-3g_{\nu _{i}}^{*}\mu_{0}), 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3104}%
$\tau _{\nu _{i}}^{*}, \tilde{\omega}_{\nu _{i}}^{*},
g_{\nu _{i}}^{*}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2492}%
\begin{displaymath}
  \tau _{\nu _{i}}^{*}=(1-\tilde{\omega}_{\nu _{i}}g_{\nu _{i}}^{2})\tau_{\nu
  _{i}}, \quad  
  \tilde{\omega}_{\nu _{i}}^{*} =  \frac{(1-g_{\nu _{i}}^{2})
  \tilde{\omega}_{\nu _{i}}} {1-\tilde{\omega}_{\nu _{i}}g_{\nu
  _{i}}^{2}}, 
  \quad
  g_{\nu _{i}}^{*} = \frac{g_{\nu _{i}}}{1+g_{\nu _{i}}}, 
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3112}%
$\tau _{\nu _{i}}, \tilde{\omega}_{\nu _{i}}, g_{\nu _{i}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5163}%
$\displaystyle \DD{F_{IR,\nu _{i}}^{\uparrow}}{\tau _{\nu _{i}}^{*}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5165}%
$\displaystyle \gamma _{1,\nu _{i}}F_{IR,\nu _{i}}^{\uparrow} -
\gamma _{2,\nu _{i}}F_{IR,\nu _{i}}^{\downarrow}
-2\pi (1-\tilde{\omega}_{\nu _{i}}^{*})
B_{\nu _{i},T}(\tau _{\nu _{i}}^{*}),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5166}%
$\displaystyle \DD{F_{IR,\nu _{i}}^{\downarrow}}{\tau _{\nu _{i}}^{*}}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5168}%
$\displaystyle \gamma _{2,\nu _{i}}F_{IR,\nu _{i}}^{\uparrow} -
\gamma _{1,\nu _{i}}F_{IR,\nu _{i}}^{\downarrow}
+2\pi (1-\tilde{\omega}_{\nu _{i}}^{*})B_{\nu _{i},T}(\tau _{\nu _{i}}^{*}).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3116}%
$F_{IR,\nu_{i}}^{\downarrow}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3118}%
$F_{IR,\nu_{i}}^{\uparrow}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3120}%
$\pi B_{\nu,
T_{sfc}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3124}%
$F_{IR,\nu_{i}}^{\downarrow}=0$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2493}%
\begin{displaymath}
  B_{\nu_{i},T} = \frac{1}{\nu _{2}-\nu _{1}}
                            \int _{\nu _{1}}^{\nu _{2}} B_{\nu ,T}\Dd \nu.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3132}%
$\nu_{1},\nu_{2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5181}%
$\displaystyle Q_{rad,dust,SR}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5183}%
$\displaystyle - \frac{1}{\rho _{a}c_{p}}\DD{}{z}
\left[\sum _{\nu _{i} } \Delta \nu _{i}
\left(F_{dif,\nu _{i}}^{\uparrow}-F_{dif,\nu _{i}}^{\downarrow}-
F_{dir,\nu _{i}}^{\downarrow}\right)
\right],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5184}%
$\displaystyle Q_{rad,dust,IR}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5186}%
$\displaystyle -\frac{1}{\rho _{a}c_{p}}\DD{}{z}
\left[\sum _{\nu _{i} } \Delta \nu _{i}
\left(F_{IR,\nu _{i}}^{\uparrow}-F_{IR,\nu _{i}}^{\downarrow}\right)
\right].$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3136}%
$F_{dir,\nu _{i}}^{\downarrow}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1826}%
\begin{displaymath}
  F_{dir,\nu _{i}}^{\downarrow} = \mu _{0}S_{\nu _{i}}
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\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1838}%
\begin{displaymath}
\DD{n(r)}{r} = n_{0}r ^{\alpha} \exp 
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             \left(\frac{r}{r_{m}}\right)^{\gamma }\right].
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3142}%
$\nu$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3144}%
$\tau _{\nu}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3146}%
$\beta _{e,\nu}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1856}%
\begin{displaymath}
  \tau _{\nu}(z) = - \int _{z_{t}}^{z} \beta _{e,\nu}(r) \Dd z
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3152}%
$z_{t}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3154}%
$\beta _{\nu,e}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1867}%
\begin{displaymath}
  \beta _{e,\nu} = \int _{0}^{\infty} \sigma_{e,\nu}(r)\DD{n(r)}{r}\Dd r
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3160}%
$\sigma_{e,\nu}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3162}%
$dn(r)/dr$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3164}%
$k_{e}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1882}%
\begin{displaymath}
  \rho _{a}q_{s}k_{e,\nu} = 
  \int _{0}^{\infty} \sigma_{e,\nu}(r)\DD{n(r)}{r}\Dd r
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3172}%
$\rho _{a}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3174}%
$q_{s}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3176}%
$\sigma_{s,\nu}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3178}%
$\sigma_{a,\nu}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5220}%
$\displaystyle \beta _{s,\nu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5222}%
$\displaystyle \int _{0}^{\infty} \sigma_{s,\nu}(r)\DD{n(r)}{r}\Dd r,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5223}%
$\displaystyle \beta _{a,\nu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5225}%
$\displaystyle \int _{0}^{\infty} \sigma_{a,\nu}(r)\DD{n(r)}{r}\Dd r,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3188}%
$\tilde{\omega}_{\nu}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1920}%
\begin{displaymath}
  \tilde{\omega}_{\nu} = \frac{\beta _{s,\nu}}{\beta _{a,\nu}}
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3192}%
$Q_{e,\nu}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath1931}%
\begin{displaymath}
  Q_{e,\nu} = \frac{\sigma_{e,\nu}}{\pi r^{2}},
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3196}%
$Q_{s,\nu}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3198}%
$Q_{a,\nu}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5237}%
$\displaystyle Q_{s,\nu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5239}%
$\displaystyle \frac{\sigma _{s,\nu}}{\pi r^{2}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5240}%
$\displaystyle Q_{a,\nu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5242}%
$\displaystyle \frac{\sigma _{a,\nu}}{\pi r^{2}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3206}%
$\overline{Q}_{e,\nu}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3214}%
$r_{eff}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5261}%
$\displaystyle \overline{Q}_{e,\nu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5262}%
$\textstyle \equiv$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5263}%
$\displaystyle \frac{\int _{0}^{\infty}Q_{e,\nu}\pi r ^{2}\DD{n(r)}{r}\Dd r}
{\int _{0}^{\infty}\pi r ^{2}\DD{n(r)}{r} \Dd r},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5264}%
$\displaystyle r_{eff}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5266}%
$\displaystyle \frac{\int _{0}^{\infty}r ^{3}\DD{n(r)}{r}\Dd r}
{\int _{0}^{\infty}r ^{2}\DD{n(r)}{r} \Dd r},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5268}%
$\displaystyle \beta _{e,\nu}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5270}%
$\displaystyle \overline{Q}_{e,\nu}
\int _{0}^{\infty} \pi r^{2}\DD{n(r)}{r}\Dd r,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5272}%
$\displaystyle \frac{\overline{Q}_{e,\nu}}{r_{eff}}
\int _{0}^{\infty} \pi r^{3}\DD{n(r)}{r}\Dd r,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5274}%
$\displaystyle \frac{\overline{Q}_{e,\nu}}{r_{eff}}
\frac{3\rho _{a}q_{s}}{4\pi \rho _{d}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2027}%
\begin{displaymath}
 \tau _{\nu} = -\int _{z_{t}}^{z} \frac{\overline{Q}_{e,\nu}}{r_{eff}}
     \frac{3\rho _{a}q_{s}}{4\pi \rho _{s}} \Dd z,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3260}%
$\tau _{5-1.6 \mu m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3264}%
$Q_{e,0.67 \mu m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3266}%
$\tau
_{0.67 \mu m}/\tau _{9 \mu m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3270}%
$\tau _{5-11.6 \mu m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3272}%
$Q_{e,\nu_{i}}/Q_{e,0.67\mu m}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3292}%
$\tilde{\omega}_{\nu _{i}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3294}%
$g_{\nu_{i}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3298}%
${}^{5}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3334}%
$\phi $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3338}%
$t$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3342}%
$2\pi t/T -\pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3364}%
$= 2\pi t/T -\pi$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5388}%
$\displaystyle I_{0}\left(\frac{r_{0}}{r}\right)^{2}\cos \zeta,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5389}%
$\displaystyle \cos \zeta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay5391}%
$\displaystyle \sin \phi \sin \delta + \cos \phi \cos \delta \cos h,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{eqnarraystar2137}%
\begin{eqnarray*}
  r &=&  \frac{a(1-e^{2})}{1+e\cos \omega}, \\
  \sin \delta &=& \sin \alpha \sin (\omega - \omega _{0})
\end{eqnarray*}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3378}%
$\theta $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3380}%
$a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3382}%
$e$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3384}%
$\alpha $%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3386}%
$\omega$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3388}%
$\omega _{0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3390}%
$r_{0}=a$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3392}%
$L_{s}\equiv \omega - \omega _{0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath2150}%
\begin{displaymath}
  F_{s} = I_{0}\left(\frac{1+e\cos (L_{s}+\omega_{0})}{1+e^{2}}\right)^{2}
  \left[
  \sin \phi \sin \alpha \sin L_{s} + 
  \cos h \cos \phi \sqrt{1-\sin ^{2}\alpha \sin ^{2}L_{s}}
  \right]
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3412}%
${}^{\circ}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3414}%
$L_{s}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{section}
{\newpage\clearpage
\lthtmldisplayA{displaymath3575}%
\begin{displaymath}
 \rho _{g}c_{p,g}\DP{T_{g}}{t} = k_{g}\DP[2]{T_{g}}{z}.
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3728}%
$T_{g}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3730}%
$\rho _{g}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3734}%
$c_{p,g}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3740}%
$k_{g}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3748}%
$T_{sfc} = T_{g}|_{z=0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath3623}%
\begin{displaymath}
  - k\left.\DP{T}{z}\right|_{z=0} = - F_{SR}(1-A) + F_{IR,net} + H ,
\end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3772}%
$F_{SR}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3776}%
$F_{IR,net}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3778}%
$H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3802}%
$\times 10^{-2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3810}%
$I\equiv \sqrt{\rho
_{g}c_{p,g}k_{g}}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3814}%
${}^{1/2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3818}%
$t_{d}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline3820}%
$\delta
_{d}\equiv\sqrt{k_{g}t_{d}/(\rho_{g}c_{p,g})}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}


\end{document}
