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\begin{document}
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% !!! IMAGES START HERE !!!

\stepcounter{section}
\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay995}%
$\displaystyle \frac{d \zeta}{d t}
=  \frac{1}{a \cos \varphi}
\frac{\partial}{\partial \lambda}
\{ - (\zeta + f) u - \dot{\sigma} \DP{u}{\sigma}
- \frac{RT'}{a \cos \varphi} \DP{\pi}{\lambda} \}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay996}%
$\displaystyle \qquad    - \frac{1}{a \cos \varphi}
\DP{}{\varphi}
[ \{ (\zeta + f) v - \dot{\sigma} \DP{u}{\sigma}
-  \frac{RT'}{a} \DP{\pi}{\varphi} \} \cos \varphi]
- F^{diff}_{\zeta},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay997}%
$\displaystyle \DD{D}{t}
=   \frac{1}{a \cos \varphi}  \DP{}{\lambda}
\{ (\zeta + f) v - \dot{\sigma} \DP{u}{\sigma}
- x\frac{RT'}{a} \DP{\pi}{\varphi} \}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay998}%
$\displaystyle \qquad +  \frac{1}{a \cos \varphi}  \DP{}{\varphi}
[  \{ (\zeta + f) v - \dot{\sigma} \DP{u}{\sigma}
- \frac{RT'}{a} \DP{\pi}{\varphi} \} \cos \varphi]$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay999}%
$\displaystyle \qquad - \nabla^2 (\Phi  + R \overline{T} \pi + E )
- F^{diff}_{D},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1000}%
$\displaystyle \DD{\pi}{t}
=  - \frac{1}{a \cos \varphi} \DP{u}{\lambda}
- \frac{1}{a \cos \varphi} \DP{}{\varphi} ( v \cos \varphi)
- \frac{\partial \dot{\sigma}}{\partial \sigma},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1001}%
$\displaystyle \frac{\partial \Phi}{\partial \sigma} = - \frac{RT}{\sigma},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1002}%
$\displaystyle \DD{q}{t}
=  \frac{g}{p_s} \DP{F^{vdf}_q}{\sigma}
+ F^{diff}_q
+ S^{cond}_q,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1003}%
$\displaystyle \DD{T}{t}
=   \frac{R T}{c_p}
\left\{   \DP{\pi}{t}
+ \frac{u}{a \cos \varphi} \DP{\pi}{\lambda}
+ \frac{v}{a} \DP{\pi}{\varphi}
+ \frac{\dot{\sigma}}{\sigma} \right\}$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1004}%
$\displaystyle \qquad \qquad \mbox{}   + \frac{1}{c_p} \left(
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+ \frac{g}{p_s} \DP{F^{rad}_{T}}{\sigma} \right)
+  F^{diff}_{T} + L S^{cond}_q.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1006}%
$\displaystyle \DD{}{t}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1007}%
$\textstyle \equiv$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1008}%
$\displaystyle \DP{}{t}
+ \frac{u}{a \cos \varphi} \DP{}{\lambda}
+ \frac{v}{a} \DP{}{\varphi}
+ \dot{\sigma} \DP{}{\sigma},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1009}%
$\displaystyle \zeta$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1011}%
$\displaystyle \frac{1}{a \cos \varphi} \DP{v}{\lambda}
- \frac{1}{a \cos \varphi}
\DP{}{\varphi} (u \cos \varphi),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1012}%
$\displaystyle D$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1014}%
$\displaystyle \frac{1}{a \cos \varphi} \DP{u}{\lambda}
+ \frac{1}{a \cos \varphi}
\DP{}{\varphi} (v \cos \varphi),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1015}%
$\displaystyle \Phi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1017}%
$\displaystyle gz,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1018}%
$\displaystyle \pi$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1020}%
$\displaystyle \ln p_s,$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline621}%
$(\lambda, \varphi)$%
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline623}%
$\sigma$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline625}%
$u$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline627}%
$v$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline629}%
$\dot{\sigma}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline633}%
$T$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline635}%
$q$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline637}%
$p_s$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline639}%
$T_g$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline641}%
$\Phi$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline643}%
$f$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline645}%
$a$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline647}%
$g$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline649}%
$R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline651}%
$c_p$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline653}%
$L$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline655}%
$F^{diff}_{\zeta}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline657}%
$F^{diff}_{D}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline659}%
$F^{diff}_{T}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline661}%
$F^{diff}_{q}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline663}%
$F^{vdf}_u$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline665}%
$F^{vdf}_v$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline667}%
$F^{vdf}_T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline669}%
$F^{vdf}_q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline671}%
$S^{cond}_q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath171}%
\begin{displaymath}
        F^{diff} = - (-1)^n K \nabla^{2n}
   \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline673}%
$n=8$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline675}%
$K$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline677}%
$128$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline679}%
$64$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline681}%
$k$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline683}%
$\sigma_k$%
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\stepcounter{subsection}
\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath192}%
\begin{displaymath}
        \Deqlab{ds ��¸}
        \sum^{k}_{l=k-1} (C_{p}       T_l + L       q_l) \Delta p_l = 
        \sum^{k}_{l=k-1} (C_{p} \hat{T}_l + L \hat{q}_l) \Delta p_l,
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\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline695}%
$\hat{T}, \hat{q}$%
\lthtmlinlinemathZ
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{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline697}%
$T, q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline699}%
$(k,k-1)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1160}%
$\displaystyle ST_{k-1/2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1162}%
$\displaystyle \hat{T}_k - \hat{T}_{k-1}
+  \frac{L}{C_p}
\left( q^*(\hat{T}_{k},p_{k}) - q^*(\hat{T}_{k-1},p_{k-1}) \right)
- \frac{R}{C_p}
\frac{\Delta p_{k-1/2}}{p_{k-1/2}}
\frac{\hat{T}_k + \hat{T}_{k-1}}{2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1163}%
$\textstyle >$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1164}%
$\displaystyle 0.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1166}%
$\displaystyle \hat{q}_{k-1} > q^*(\hat{T}_{k-1},p_{k-1}), \ \ 
\hat{q}_{k}   > q^*(\hat{T}_{k}  ,p_{k}).$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline701}%
$(T_k, q_k)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1169}%
$\displaystyle T_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1170}%
$\textstyle =$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1171}%
$\displaystyle \hat{T}_{k-1} + \Delta T_{k-1},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1172}%
$\displaystyle T_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1174}%
$\displaystyle \hat{T}_{k}   + \Delta T_{k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1175}%
$\displaystyle q_{k-1}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1177}%
$\displaystyle q^* (\hat{T}_{k-1},p_{k-1})
+ \left. \DP{q^*}{T} \right|_{k-1}
\Delta T_{k-1},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1178}%
$\displaystyle q_{k}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1180}%
$\displaystyle q^* (\hat{T}_{k},p_{k})
+ \left. \DP{q^*}{T} \right|_{k}
\Delta T_{k},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath265}%
\begin{displaymath}
            \Delta T_{k} 
          =  \frac{
                   (1 + \gamma_{k-1}) \Delta p_{k-1} S_{k-1/2}
                 + [   1 + \gamma_{k-1} 
                     - \kappa \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}]
                   \frac{L}{C_p} \Delta \hat{Q}
             }{     (1 + \gamma_{k-1}) (1 + \gamma_{k}) 
                  (\Delta p_{k-1} + \Delta p_{k})
                + \kappa \frac{\Delta p_{k-1/2}}{2 p_{k-1/2}}
                  [   (1 + \gamma_{k-1}) \Delta p_{k-1} 
                    - (1 + \gamma_{k}) \Delta p_{k}]
            } \raisebox{-5mm}{,}
   \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath289}%
\begin{displaymath}
            \Delta T_{k-1} 
         =  - \frac{ (1 + \gamma_{k}) \Delta p_{k} 
             }{
                  (1 + \gamma_{k-1}) \Delta p_{k-1}
             } \Delta T_{k} 
            + \frac{ 1 }{ (1 + \gamma_{k-1}) \Delta p_{k-1} }
              \frac{L}{C_p}
              \Delta T_{k},
   \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath303}%
\begin{displaymath}
          \gamma_{k}   = \frac{L}{C_p} \left. \DP{q^*}{T} \right|_{k}, 
          \ \ 
          \gamma_{k-1} = \frac{L}{C_p} \left. \DP{q^*}{T} \right|_{k-1}, 
       \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath317}%
\begin{displaymath}
            \Delta \hat{Q} 
          =    (\hat{q}_{k-1} - q^*(\hat{T}_{k-1},p_{k-1}) ) \Delta p_{k-1}
            +  (\hat{q}_{k} - q^*(\hat{T}_{k},p_{k}) ) \Delta p_{k}.
       \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath332}%
\begin{displaymath}
          P = \sum^{K}_{k=1} (\hat{q}_k - q_k) \frac{\Delta p_k}{g}.
       \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmldisplayA{displaymath340}%
\begin{displaymath}
       \hat{q} > q^*(\hat{T},p),
   \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline703}%
$\hat{T}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline705}%
$\hat{q}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath346}%
\begin{displaymath}
        q = q^*(T,p)
     \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath348}%
\begin{displaymath}
      C_p T + Lq = C_p \hat{T} + L \hat{q}.
     \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1193}%
$\displaystyle T$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1195}%
$\displaystyle \hat{T}
+ \frac{L}{C_p}
\frac{\hat{q} - q^* (\hat{T},p)}
{1 + \frac{L}{C_p} \DP{q^*}{T}},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1196}%
$\displaystyle q$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1198}%
$\displaystyle \hat{q}
- \frac{L}{C_p} \DP{q^*}{T}
\frac{\hat{q} - q^* (\hat{T},p)}
{1 + \frac{L}{C_p} \DP{q^*}{T}}.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath374}%
\begin{displaymath}
         P = \frac{\Delta p}{g} (\hat{q} - q).
      \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline707}%
$F_{R,i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath381}%
\begin{displaymath}
          F_R(z) =   \left( \pi B(T_g) - \pi B(T_s) \right) {\cal T}^f(z,0)
                   +        \pi B(T(z_T))                  {\cal T}^f(z,z_T)
                   - \int_0^{z_T} \DD{\pi B}{\xi} {\cal T}^f(z,\xi) d \xi, 
       \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline709}%
${\cal T}^f(z_1,z_2)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline711}%
$z=z_1,z_2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline713}%
$\pi B \equiv \sigma_{SB} T^4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath392}%
\begin{displaymath}
          {\cal T}^f(z_1,z_2) 
         = \sum_{i=1}^{N_R} b_i 
          \exp \left( - \delta_R | \tau_{R,i}(z_1) - \tau_{R,i}(z_2) | 
            \right).
       \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline717}%
$\tau_i(z)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath399}%
\begin{displaymath}
          \tau_{R,i}(z) = \int_z^\infty k_{R,i} \rho q dz 
              + \int_z^\infty \bar{k}_{R,i} \rho dz,
       \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline719}%
$k_{R,i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline721}%
$\bar{k}_{R,i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline723}%
$i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline725}%
$b_i$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline729}%
$\delta_R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline737}%
$N_R$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline741}%
$\overline{k}_{R,i}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline743}%
$5.0 \times 10^{-5}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline747}%
$K_M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline749}%
$K_T$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline751}%
$K_q$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1255}%
$\displaystyle K_M$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1257}%
$\displaystyle l^2 \frac{\Delta |\Dvect{v}|}{\Delta z} S_M,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1258}%
$\displaystyle K_T = K_q$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1260}%
$\displaystyle l^2 \frac{\Delta |\Dvect{v}|}{\Delta z} S_H.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline759}%
$l$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath433}%
\begin{displaymath}
         l = \frac{\kappa z}{1+\kappa z/l_0},
       \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline761}%
$l_0=300$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline763}%
$\kappa=0.4$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline765}%
$S_M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline767}%
$S_H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1268}%
$\displaystyle S_M$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1270}%
$\displaystyle B_1^{1/2} ( 1- R_f )^{1/2}
\widetilde{S_M}^{3/2},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1271}%
$\displaystyle S_H$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1273}%
$\displaystyle B_1^{1/2} ( 1- R_f )^{1/2}
\widetilde{S_M}^{1/2} \widetilde{S_H},$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath449}%
\begin{displaymath}
          \widetilde{S_H} = \frac{ \alpha_1-\alpha_2 R_f }{ 1-R_f },
       \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath454}%
\begin{displaymath}
          \widetilde{S_M} = \frac{ \beta_1-\beta_2 R_f }
                                 { \beta_3-\beta_4 R_f } 
                  \widetilde{S_H}. 
       \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline769}%
$R_f$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath460}%
\begin{displaymath}
           R_f = \frac{1}{2 \beta_2}
                 \left[ \beta_1 + \beta_4 R_{iB}
              - \sqrt{ ( \beta_1 + \beta_4 R_{iB} )^2 
                       - 4 \beta_2 \beta_3 R_{iB} }
              \right] ,
       \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline771}%
$R_{iB}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1280}%
$\displaystyle \alpha_1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1282}%
$\displaystyle 3 A_2 \gamma_1,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1283}%
$\displaystyle \alpha_2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1285}%
$\displaystyle 3 A_2 (\gamma_1+\gamma_2),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1286}%
$\displaystyle \beta_1$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1288}%
$\displaystyle A_1 B_1 ( \gamma_1 - C_1 ),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1289}%
$\displaystyle \beta_2$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1291}%
$\displaystyle A_1 [ B_1 ( \gamma_1 - C_1 ) + 6 A_1 + 3 A_2 ],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1292}%
$\displaystyle \beta_3$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1294}%
$\displaystyle A_2 B_1,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1295}%
$\displaystyle \beta_4$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1297}%
$\displaystyle A_2 [ B_1 ( \gamma_1 + \gamma_2 ) - 3 A_1 ],$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath470}%
\begin{displaymath}
          (A_1, B_1, A_2, B_2, C_1 ) = ( 0.92, 16.6, 0.74, 10.1, 0.08 ) ,
       \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath472}%
\begin{displaymath}
          \gamma_1 = \frac{1}{3} - \frac{2 A_1}{B_1}\, , \, \, \, 
          \gamma_2 = \frac{B_2}{B_1} + 6\frac{A_1}{B_1},
       \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath483}%
\begin{displaymath}
          R_{iB} = \frac{\displaystyle 
               \frac{q}{\theta_s} \frac{\Delta \theta}{\Delta z} }
              {\displaystyle
                  \left( \frac{\Delta u}{\Delta z} \right)^2 
                + \left( \frac{\Delta v}{\Delta z} \right)^2
               }. 
       \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline775}%
${k-1/2}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline777}%
$(\Delta \bullet)$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline779}%
$\bullet_{k}
        - \bullet_{k-1}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

\stepcounter{subsubsection}
{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1307}%
$\displaystyle (F_{\lambda})_{1/2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1309}%
$\displaystyle - \rho_s C_{M} | \Dvect{v}_1 | u_1,$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1310}%
$\displaystyle (F_{\varphi})_{1/2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1313}%
$\displaystyle (F_{T})_{1/2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1315}%
$\displaystyle \rho_s C_{p} C_{H} | \Dvect{v}_1 |
(T_g - (\frac{T}{\Pi}_1)),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1316}%
$\displaystyle (F_{q})_{1/2}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1318}%
$\displaystyle \rho_s \beta C_{E} | \Dvect{v}_1 |
(q^*(T_g, p_s) - q_1),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline781}%
$1/2$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline785}%
$C_M$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline787}%
$C_H$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline789}%
$C_E$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1325}%
$\displaystyle C_M = \left\{
\begin{array}{ll}
C_{M0} \left( 1 + 10 R_{iB}/\sqrt{1 + 5 R_{iB} } \right)^{-1}
& R_{iB} \geq 0, \\
C_{M0} \left[1 - 10 R_{iB}
\left( 1 + 75 C_{M0}
\sqrt{\frac{z_1}{z_{M0}} |R_{iB}| }
\right)^{-1}
\right]
& R_{iB} < 0,
\end{array} \right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1327}%
$\displaystyle C_H = C_E = \left\{
\begin{array}{ll}
C_{H0} \left( 1 + 15 R_{iB}/\sqrt{1 + 5 R_{iB} } \right)^{-1}
& R_{iB} \geq 0, \\
C_{H0} \left[1 - 15 R_{iB}
\left( 1 + 75 C_{H0}
\sqrt{\frac{z_1}{z_{M0}} |R_{iB}| }
\right)^{-1}
\right]
& R_{iB} < 0,
\end{array} \right.$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmldisplayA{displaymath557}%
\begin{displaymath}
          R_{iB} = \frac{\frac{g}{\theta_s} (\theta_1 - \theta_g)/g}
                        {(u_1/z_1)^2}
                 = \frac{g}{\theta_s}
                   \frac{T_1 (p_s/p_1)^{\kappa} - T_g}
                        {u^2_1/z_1}.
       \end{displaymath}%
\lthtmldisplayZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline793}%
$C_{M0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline795}%
$C_{H0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1333}%
$\displaystyle C_{M0}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1335}%
$\displaystyle \left(
\frac{\kappa}
{\ln \left( \frac{z_1}{z_{M0}} \right)}
\right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1336}%
$\displaystyle C_{H0}$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_indisplay1338}%
$\displaystyle \left(
\frac{\kappa}
{\ln \left( \frac{z_1}{z_{H0}} \right)}
\right),$%
\lthtmlindisplaymathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline797}%
$z_{M0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline799}%
$z_{H0}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}

{\newpage\clearpage
\lthtmlinlinemathA{tex2html_wrap_inline801}%
$10^{-4}$%
\lthtmlinlinemathZ
\lthtmlcheckvsize\clearpage}


\end{document}
