% ɽ��   dcpam5 ��1�� ʪ������ ���� AGCM5 ���ͥ�ǥ� Υ����ǥ�
%
% ���� 
%\Drireki{93/03/18 �¸��ء��ݺ�����}
%\Drireki{2010/04/14 �ⶶ˧��}
%\Drireki{2010/11/04 ��������}
%\Drireki{2011/07/01 �ⶶ˧��}


\section{Υ��ɽ��: AGCM5 ���ͥ�ǥ�}


\subsection{Ĺ������}

Ĺ�Ȥˤ����� $\pi B(\tau)$ ��Ʃ��Ψ�ϲ��Τ褦��Υ���������. 
%
\begin{eqnarray}
  \pi B_{k} &=& \sigma_{SB} T_{k}^4
\\
  \pi B_s   &=& \sigma_{SB} T_{s}^4
\\
  {\cal T}_{k+\frac{1}{2},k'+\frac{1}{2}}
    &=& \sum_{l=1}^{l_{max,S}} \Delta g_{L,l}
          \exp( - \alpha (   | \tau_{L,wv,k+\frac{1}{2},l} - \tau_{L,wv,k'+\frac{1}{2},l} |    \nonumber
\\
    & & \hspace{30mm}
                           + | \tau_{L,da,k+\frac{1}{2},l} - \tau_{L,da,k'+\frac{1}{2},l} | ) )
\\
  \tau_{L,wv,k-\frac{1}{2},l}
    &=& k_{L,wv,l} M_{wv,k-\frac{1}{2}}
\\
  \tau_{L,da,k-\frac{1}{2},l}
    &=& k_{L,da,l} M_{da,k-\frac{1}{2}}
\\
  M_{wv,k-\frac{1}{2}}
    &=& \sum_{k'=k}^{k_{max}} q_{wv,k'} \frac{ p_{k'-\frac{1}{2}} - p_{k'+\frac{1}{2}} }{g}
\\
  M_{da,k-\frac{1}{2}}
    &=& \frac{p_{k-\frac{1}{2}}}{g}
\end{eqnarray}
%
\begin{eqnarray}
  {\cal T}_{k+\frac{1}{2},k'+\frac{1}{2}}
    &=& \sum_{l=1}^{l_{max,S}} \Delta g_{L,l}
          \exp( - \alpha (   k_{L,wv,l} | M_{wv,k+\frac{1}{2}} - M_{wv,k'+\frac{1}{2}} |    \nonumber
\\
    & & \hspace{30mm}
                           + k_{L,da,l} | M_{da,k+\frac{1}{2}} - M_{da,k'+\frac{1}{2}} | ) )
\\
  M_{wv,k-\frac{1}{2}}
    &=& \sum_{k'=k}^{k_{max}} q_{wv,k'} \frac{ p_{k'-\frac{1}{2}} - p_{k'+\frac{1}{2}} }{g}
\\
  M_{da,k-\frac{1}{2}}
    &=& \frac{p_{k-\frac{1}{2}}}{g}
\end{eqnarray}
%
������, $l_{max,L}$ ��, Ĺ�����ͤˤ�����, �ѻ���Ψ�ؿ����Ф�����ʬ��ʬ���ο� (�ΰ�ο�) �Ǥ���, 
$\Delta g_{L,l}$ ���ѻ���Ψ�ؿ��� $l$ ���ܤ��ΰ�����Ǥ���. 




\subsection{û������}

û�����ͥե�å����ϲ��Τ褦��Υ���������. 
%
\begin{eqnarray}
  F_{k+\frac{1}{2}}
    &=& - ( 1 - A_a ) F_{0}(\chi) {\cal T}_{dir,k+\frac{1}{2}}(\chi) \nonumber
\\  
    & & \hspace{10mm}
        + ( 1 - A_a ) F_{0}(\chi) A_s {\cal T}_{dif,k+\frac{1}{2}}(\chi)
\\
  {\cal T}_{dir,k+\frac{1}{2}}(\chi)
    &=& \sum_{l=1}^{l_{max,S}}
          \exp[ - \sec \chi \{ \tau_{S,wv,k+\frac{1}{2},l}
                             + \tau_{S,da,k+\frac{1}{2},l} \} ] \Delta g_{S,l}
\\
  {\cal T}_{dif,k+\frac{1}{2}}(\chi)
    &=& \sum_{l=1}^{l_{max,S}}
          \exp[ - \sec \chi \{ \tau_{S,wv,\frac{1}{2},l}
                             + \tau_{S,da,\frac{1}{2},l} \} ] \nonumber
\\
    & & \hspace{10mm}
          \cdot 
          \exp[ - \alpha    \{ \tau_{S,wv,\frac{1}{2},l} - \tau_{S,wv,k+\frac{1}{2},l}   \nonumber
\\
    & & \hspace{35mm}
                             + \tau_{S,da,\frac{1}{2},l} - \tau_{S,da,k+\frac{1}{2},l} \} ] \Delta g_{S,l}
\\
  \tau_{S,wv,k-\frac{1}{2},l}
    &=& k_{S,wv,l} M_{wv,k-\frac{1}{2}}
\\
  \tau_{S,da,k-\frac{1}{2},l}
    &=& k_{S,da,l} M_{da,k-\frac{1}{2}}
\end{eqnarray}


% �����ȥ����� (yot, 2011/07/01).
\iffalse

�������鲼�Ͼä�ͽ��.
%
\begin{eqnarray}
  {\cal T}_{dir,k+\frac{1}{2}}(\chi)
    &=& \sum_{l=1}^{l_{max,S}} \Delta g_{S,l}
          \exp[ - \sec \chi \{ k_{S,wv,l} M_{wv,k+\frac{1}{2}}   \nonumber
\\
    & & \hspace{30mm}
                             + k_{S,da,l} M_{da,k+\frac{1}{2}} \} ] \Delta g_l
\\
  {\cal T}_{dif,k+\frac{1}{2}}(\chi)
    &=& \sum_{l=1}^{l_{max,S}}
          \exp[ - \sec \chi \{ k_{S,wv,l} M_{wv,\frac{1}{2}}
                             + k_{S,da,l} M_{da,\frac{1}{2}} \} ] \nonumber
\\
    & & \hspace{20mm}
          \exp[ - \alpha    \{   k_{S,wv,l} | M_{wv,\frac{1}{2}} - M_{wv,k+\frac{1}{2}} |   \nonumber
\\
    & & \hspace{35mm}
                               + k_{S,da,l} | M_{da,\frac{1}{2}} - M_{da,k+\frac{1}{2}} | \} ] \Delta g_{S,l}
\end{eqnarray}
%
������, $l_{max,S}$ ��, û�����ͤˤ������ѻ���Ψ�ؿ����Ф�����ʬ��ʬ����
�� (�ΰ�ο�) �Ǥ���, 
$\Delta g_{S,l}$ ���ѻ���Ψ�ؿ��� $l$ ���ܤ��ΰ�����Ǥ���. 

\fi
