% ɽ��  2 ����������ή�Υ�ǥ� deepconv-mars ����: ������ǥ���
%       �� 5 �� ���ͥ�ǥ�
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% ����  2001/11/01  ��������
%       2007/04/24  ��������: �Ѹ��Ǥκ���
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\section{\DselJ{���ͥ�ǥ�}{Radiation}} \Dseclab{���ͥ�ǥ�}

\DselJ{
\Deqref{Ǯ�ϳؤμ�}��������Ͳ�Ǯ(���)�� $Q_{rad}$ ��, ������ã��������
�򤤤����������ͥե�å����μ�«(ȯ��)�ˤ��׻������. ��θ�������Ͳ�
���ϲ����絤�μ���ʬ�Ǥ��� CO${}_{2}$ �ˤ���ֳ����ͤεۼ����ͽФȶ��ֳ���Ĺ��
�Ǥ��������͵ۼ�, �����Ȥˤ���������ͤ��ֳ����ͤεۼ�, ����, �ͽФǤ���.
CO${}_{2}$ �ˤ�뻶��Ϲ�θ���ʤ�.
}
{
$Q_{rad}$ in equation \Deqref{Ǯ�ϳؤμ�} is
   given by convergence of
   net radiative heat flux which is calculated by using radiative
   transfer equation.
We consider following radiation processes in this model; absorption of
   near infrared solar radiation (NIR), absorption and emission of
   infrared radiation associated with atmospheric
   CO${}_{2}$, absorption and scattering of solar
   radiation, and absorption and emission of infrared radiation
   associated with dust.
}

\DselJ{
���Ͳ�Ǯ�� $Q_{rad}$ �ϰʲ��Τ褦��ɽ�����.
}
{
$Q_{rad}$ is represented as follows.
}
\begin{equation}
  Q_{rad}= Q_{rad,IR} + Q_{rad,NIR} + Q_{rad,dust,SR} + Q_{rad,dust,IR}.
\end{equation}
\DselJ{
������ $Q_{rad,IR}, Q_{rad,NIR}, Q_{rad,dust,SR}, Q_{rad,dust,IR}$ �Ϥ�
�줾�� CO${}_{2}$ �ֳ����Ͳ�Ǯ, CO2 ���ֳ����Ͳ�Ǯ, �����Ȥ��������Ͳ�Ǯ, ����
�Ȥ��ֳ����Ͳ�Ǯ��ɽ��. �ʲ��ˤ��줾��ΰ����ȷ׻���ˡ�򼨤�.
}
{
$Q_{rad,IR}$ and $Q_{rad,NIR}$ are the infrared and near infrared
   radiative heating rate associated with CO${}_{2}$
$Q_{rad,dust,SR}$ and $Q_{rad,dust,IR}$ are the solar and
   infrared radiative heating rate associated with dust.
The governing equations to calculate these heating rate 
   are described in following sections.
}

\subsection{\DselJ{CO${}_{2}$ ������}{
            Radiative transfer of atmospheric CO${}_{2}$}}

\DselJ{
CO${}_{2}$ �����ͤ��ֳ�����, �������ͤȤ�� Goody �Х�ɥ�ǥ�˽��äƷ׻�����
(�㤨�� Goody and Young, 1989 �򻲾�). �ֳ����ͤ� CO${}_{2}$ 15 $\mu$m �Х�ɤ�
��Ϳ������׻�����. �絤��ˤ���������, ����Ӳ������ֳ����� 
$F_{IR}^{\uparrow}, F_{IR}^{\downarrow}$, ����ˤ�����Ͳ�Ǯ 
$Q_{rad,IR}$ �ϰʲ��μ�����׻������.}
{
Both infrared and near infrared radiative flux associated with
   CO${}_{2}$ are calculated by Goody narrow band
   model (c.f., Goody and Young, 1989).
In calculating infrared radiative flux, CO${}_{2}$
   15 $\mu$m band is only considered.
The upward and downward infrared radiative flux 
   $F_{IR}^{\uparrow}, F_{IR}^{\downarrow}$
   and the infrared radiative heating rate per unit mass 
   $Q_{rad,IR}$ are calculated as follows.
}
\begin{eqnarray}
  F_{IR}^{\uparrow}(z) &=& \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\}, \\
  F_{IR}^{\downarrow}(z) &=& \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\}, \\
  Q_{rad,IR} &=& -\frac{1}{\rho _{0}c_{p}}\DP{}{z}(F_{IR}^{\uparrow}(z) - 
     F_{IR}^{\downarrow}(z) ). \Deqlab{CO${}_{2}$�ֳ����Ͳ�Ǯ}
\end{eqnarray}
\DselJ
{
������ $\Delta \nu _{i}$ �ϥХ����, $B_{\nu _{i},T}$ �ϥץ�󥯴ؿ�,
}
{
$\Delta \nu _{i}$ is the $i$th narrow band width and
   $B_{\nu _{i},T}$ is the Plank function which is
   represented as follows.
}
\begin{equation}
  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},
  \Deqlab{�ץ�󥯴ؿ�}
\end{equation}
\DselJ{
�Ǥ���($h$ �ϥץ�����, $c$ �ϸ�®, $k$ �ϥܥ�ĥޥ����, $T$ �ϲ���
�Ǥ���). ${\cal T}_{i}(z,z')$ ���ȿ� $\nu _{i}$ �Τޤ����� $\Delta \nu _{i}
$ ��ʿ�Ѥ���Ʃ��ؿ���, �ʲ���ɽ�����Ѥ���. 
}
{
where $h$ is the Plank constant, $c$ is
   speed of light, $k$ is the Boltzmann constant, and
   $T$ is temperature.
${\cal T}_{i}(z,z')$  is the transmission function averaged over
   $\Delta \nu _{i}$ around $\nu _{i}$.
}

\[
  {\cal T}_{i}(z,z') = \exp ( - W_{i}/\Delta \nu _{i}),
  \quad
  W_{i} = \frac{s_{i} u(z,z')}
  {\sqrt{ 1 + s_{i}u(z,z')/\alpha ^{*}_{i}}},
\]
\[
  u(z,z') = \int _{z}^{z'}1.67\rho _{0}\Dd z,
  \quad
  \alpha ^{*}_{i}=\alpha _{i} \overline{p}/p_{0}, 
  \quad
  \overline{p} = \int _{z}^{z'}P_{0} \Dd u / u.
\]

\DselJ{
������ $s_{i}$ �ϵۼ�������, $\alpha ^{*}_{i}$ �ϵۼ����٤ȵۼ������Ȥ�
�Ѥ�ʿ����, $\alpha _{i}$ �Ϥ��δ����, $u$ ��ͭ����ϩĹ, $p_{0}$ �ϴ��
����(1013 hPa)�Ǥ���.}
{
$s_{i}$ is line strength, $\alpha ^{*}_{i}$ is
   square root of the product of line strength and line width and 
   $\alpha _{i}$ 
   is the reference value of $\alpha ^{*}_{i}$,
   $u$ is effective path length, and $p_{0}$ 
   is reference pressure (= 1013 hPa).
}

\DselJ{
���ֳ����۸��� CO${}_{2}$ �ˤ��ۼ���, CO${}_{2}$ �� 4.3 $\mu$m, 2.7
$\mu$m, 2.0$ \mu$m �Х�ɤ��θ����. �����Х���ΰ�β���������
$F_{NIR}^{\downarrow}$ �Ȥ��μ�«�ˤ�����Ͳ�Ǯ $Q_{rad,NIR}$ ��
}
{
In calculating near infrared solar radiative flux,
   CO${}_{2}$ 4.3 $\mu$m, 2.7 $\mu$m, and 2.0 $\mu$m band are considered.  
The near infrared solar radiative flux 
   $F_{NIR}^{\downarrow}$ and $Q_{rad,NIR}$ are calculated as follows.
}
\begin{eqnarray}
  F_{NIR}^{\downarrow}(z) &=& \sum _{i}\Delta \nu _{i}\left\{
      S_{\nu _{i}}{\cal T}_{i}(\infty,z)\mu_{0}
      \right\}, \\
  Q_{rad,NIR} &=& \frac{1}{\rho _{0}}\DP{F_{IR}^{\downarrow}(z)}{z}, 
      \Deqlab{CO${}_{2}$���ֳ����Ͳ�Ǯ}
\end{eqnarray}

\DselJ{
��ɽ�����. ������ $\mu _{0}=\cos \zeta$, $\zeta $ ������ŷĺ��, $S_{\nu
_{i}}$ ���絤��ü�Ǥ������������ͤ�,
}
{
where $\mu _{0}=\cos \zeta$, $\zeta$ is the solar
   zenith angle, and $S_{\nu_{i}}$ is the solar radiative flux
   per unit wave length at the top of atmosphere which is represented
   as follows.
}
\begin{eqnarray}
  S_{\nu _{i}} &=& B_{\nu _{i},T_{sol}}
                 \left(\frac{F_{s}}{\sigma T_{sol}^{4}}\right), \\
  F_{s} &=& I_{0}\left(\frac{r_{0}}{r}\right)^{2}\mu_{0},
\end{eqnarray}

\DselJ{
�Ǥ���. ������ $T_{sol}$ ������ɽ�̲���(5760 K), $\sigma $ �ϥ��ƥե���
�ܥ�ĥޥ����(5.67$\times 10{}^{-8}$ Wm${}^{-2}$K${}^{-4}$), 
$I_{0}$ �ϲ�����ƻ��
��ʿ���������(591 Wm${}^{-2}$), $r$ �ϲ��������ۤ�ʿ�ѵ�Υ, $r_{0}$ ��
����ʿ����, $F_{s}$ ������Ĺ����ʬ���줿�絤��ü�Ǥ������������ͤǤ�
��. $F_{s}$ �ϵ���, ����, ����ˤ�ä��Ѳ�����. $F_{s}$ �� $\cos \zeta $ 
�η׻���ˡ�ξܺ٤�\Dsecref{�������ͤ�ŷĺ��}�˼���.}
{
where $T_{sol}$  is the surface temperature of the sun (=
   5760 K), $\sigma$ is the Stefan-Boltzmann constant (=
   5.67$\times 10{}^{-8}$ Wm${}^{-2}$K${}^{-4}$),
   $I_{0}$ is solar constant on the mean radius of Mars orbit
   (= 591 Wm${}^{-2}$), $r$ and $r_{0}$
   is the radius of Mars orbit and its mean
   value, $F_{s}$ is solar
   radiative flux at the top of atmosphere.
$F_{s}$ is depend on season, latitude and local time.
Detail descriptions of $F_{s}$ and $\cos \zeta$ are
   shown in \Dsecref{�������ͤ�ŷĺ��}.
}

\DselJ{
�ȿ�ʿ�Ѥ��줿Ʃ��ؿ���, �ֳ����ͤξ���Ʊ�ͤ˷׻�����. ������ͭ����ϩ
Ĺ $u$ ��
}
{
The transmission function averaged over $\Delta \nu_{i}$ in near
   infrared wavelength region is similar to that in infrared
   wavelength region except for the effective path length $u$.
}
\[
  u(z,z') = \int _{z}^{z'}1.67\rho _{0}\Dd z / \mu_{0},
\]

\DselJ{�Ǥ���.}{}

\subsection*{\DselJ{�ѥ�᡼��}{Parameters}}\Dseclab{�Х�ɥѥ�᡼��}

\DselJ{
CO${}_{2}$ �����ͥ�ǥ�ˤ����Ƹ����ѥ�᡼����, �Х�ɤμ�����ȳƥ�
��ɤǤεۼ����٤ȵۼ��������ͤǤ���. �Х�ɤμ������ Savij\"arvi
(1991a) �˽स�Ƥ���. �ۼ����٤ȵۼ��������ͤ� Houghton (1986) �δ�����
Ͽ��ɽ�ˤ��� $T=$220 K ���ͤ���Ѥ���.  �ʲ��� Houghton (1986) �δ�����
Ͽ��ɽ�ˤ��� 220 K �Ǥ� $s_{i}$ (cm${}^{-1}$/(gcm${}^{-2}$)${}^{-1}$) �� 
$\alpha _{i}$(g${}^{-1}$) �Τ���, �ܸ���ǻ��Ѥ�����Τ�ƷǤ���. 15
$\mu$m �Х�ɤ� 500 cm${}^{-1}$ ���� 900 cm ${}^{-1}$ �ޤ�, 4.3 $\mu$m 
�Х�ɤ� 2200 cm${}^{-1}$ ���� 2450 cm ${}^{-1}$ �ޤǤ򤽤줾�� $\Delta
\nu =$ 25 cm${}^{-1}$ ��ʬ�䤹��.  2.7 $\mu$m �Х�ɤ� 3150 cm${}^{-1}$ 
���� 4100 cm ${}^{-1}$ �ޤ�, 2.0 $\mu$m �Х�ɤ� 4600 cm${}^{-1}$ ���� 
5400 cm ${}^{-1}$ �ޤǤ򤽤줾�� $\Delta \nu =$ 100 cm${}^{-1}$ ��ʬ�䤹
��.
}
{
The number of narrow band and its band width are similar to those of
   Savij\"arvi (1991a).
The line strength and the square root of the
   product of line strength and line width are quoted from
   those at 220 K listed by Houghton (1986).
These vaues are listed in Table 4 $\sim$ Table 7.

CO${}_{2}$ 15 $\mu$m band ranges from 500
   cm${}^{-1}$ to 900 cm${}^{-1}$ and 4.3 $\mu$m band ranges from
   2200 cm${}^{-1}$ to 2450 cm${}^{-1}$, where $\Delta \nu_{i}$
   is equal to 25 cm${}^{-1}$.
CO${}_{2}$ 2.7 $\mu$m band ranges from 3150
   cm${}^{-1}$ to 4100 cm${}^{-1}$  and 4.0 $\mu$m band ranges from
   4600 cm${}^{-1}$ to 5400 cm${}^{-1}$ , where 
   $\Delta \nu$ is equal to 100 cm${}^{-1}$.
}

\begin{table}[p]
\begin{center}
\caption{\DselJ{CO${}_{2}$ 15 $\mu$m �Х�ɥѥ�᡼��}{
         Parameters of CO${}_{2}$ 15 $\mu$m band}}
\begin{tabular}{||c|c|c||c|c|c||} \hline
$\nu _{i}$(cm${}^{-1}$) & $s_{i}$ & $\alpha _{i}$ &
$\nu _{i}$(cm${}^{-1}$) & $s_{i}$ & $\alpha _{i}$ \\ \hline
512.5 & 1.952$\times 10{}^{-2}$ & 2.870$\times 10{}^{-1}$ &
712.5 & 1.232$\times 10{}^{3}$  & 8.387$\times 10{}^{1}$ \\
537.5 & 2.785$\times 10{}^{-1}$ & 1.215$\times 10{}^{0}$ &
737.5 & 2.042$\times 10{}^{2}$  & 2.852$\times 10{}^{1}$ \\
562.5 & 5.495$\times 10{}^{-1}$ & 2.404$\times 10{}^{0}$ &
762.5 & 7.278$\times 10{}^{0}$  & 6.239$\times 10{}^{0}$ \\
587.5 & 5.331$\times 10{}^{0}$  & 1.958$\times 10{}^{1}$ &
787.5 & 1.337$\times 10{}^{0}$  & 2.765$\times 10{}^{0}$ \\
612.5 & 5.196$\times 10{}^{2}$  & 5.804$\times 10{}^{1}$ &
812.5 & 3.974$\times 10{}^{-1}$ & 8.897$\times 10{}^{-1}$ \\
637.5 & 7.778$\times 10{}^{3}$  & 2.084$\times 10{}^{2}$ &
837.5 & 1.280$\times 10{}^{-2}$ & 3.198$\times 10{}^{-1}$ \\
662.5 & 8.746$\times 10{}^{4}$  & 7.594$\times 10{}^{2}$ &
862.5 & 2.501$\times 10{}^{-3}$ & 1.506$\times 10{}^{-1}$ \\
687.5 & 2.600$\times 10{}^{4}$  & 2.635$\times 10{}^{2}$ &
887.5 & 3.937$\times 10{}^{-3}$ & 1.446$\times 10{}^{-1}$ \\ \hline
\end{tabular}
%\end{center}
%\end{table}
%
%\begin{table}[h]
%\begin{center}
\caption{\DselJ{CO${}_{2}$ 4.3 $\mu$m �Х�ɥѥ�᡼��}
         {Parameters of CO${}_{2}$ 4.3 $\mu$m band}}
\begin{tabular}{||c|c|c||c|c|c||} \hline
$\nu _{i}$(cm${}^{-1}$) & $s_{i}$ & $\alpha _{i}$ &
$\nu _{i}$(cm${}^{-1}$) & $s_{i}$ & $\alpha _{i}$ \\ \hline
2212.5 & 9.504$\times 10{}^{-1}$ & 2.866$\times 10{}^{0}$ &
2337.5 & 5.587$\times 10{}^{5}$  & 1.206$\times 10{}^{3}$ \\
2237.5 & 2.217$\times 10{}^{2}$  & 3.000$\times 10{}^{1}$ &
2362.5 & 6.819$\times 10{}^{5}$  & 1.182$\times 10{}^{3}$ \\
2262.5 & 4.566$\times 10{}^{3}$  & 1.134$\times 10{}^{2}$ &
2387.5 & 1.256$\times 10{}^{4}$  & 8.873$\times 10{}^{1}$ \\
2287.5 & 7.965$\times 10{}^{3}$  & 2.011$\times 10{}^{2}$ &
2412.5 & 7.065$\times 10{}^{-1}$ & 3.404$\times 10{}^{-1}$ \\
2312.5 & 1.055$\times 10{}^{5}$  & 5.880$\times 10{}^{2}$ &
2437.5 & 8.522$\times 10{}^{-2}$ & 4.236$\times 10{}^{-1}$ \\ \hline
\end{tabular}
%\end{center}
%\end{table}
%
%\begin{table}[tbh]
%\begin{center}
\caption{\DselJ{CO${}_{2}$ 2.7 $\mu$m �Х�ɥѥ�᡼��}
         {Parameters of CO${}_{2}$ 2.7 $\mu$m band}}
\begin{tabular}{||c|c|c||c|c|c||} \hline
$\nu _{i}$(cm${}^{-1}$) & $s_{i}$ & $\alpha _{i}$ &
$\nu _{i}$(cm${}^{-1}$) & $s_{i}$ & $\alpha _{i}$ \\ \hline
3150 & 1.324$\times 10{}^{-1}$ & 9.836$\times 10{}^{-1}$ &
3650 & 1.543$\times 10{}^{4}$  & 3.245$\times 10{}^{2}$ \\
3250 & 7.731$\times 10{}^{-2}$ & 4.900$\times 10{}^{-1}$ &
3750 & 1.649$\times 10{}^{4}$  & 2.722$\times 10{}^{2}$ \\
3350 & 1.232$\times 10{}^{0}$  & 2.952$\times 10{}^{0}$ &
3850 & 1.180$\times 10{}^{-1}$ & 9.535$\times 10{}^{-1}$ \\
3450 & 5.159$\times 10{}^{0}$  & 7.639$\times 10{}^{0}$ &
3950 & 1.464$\times 10{}^{-2}$ & 2.601$\times 10{}^{-1}$ \\
3550 & 4.299$\times 10{}^{3}$  & 1.914$\times 10{}^{2}$ &
4050 & 1.251$\times 10{}^{-2}$ & 2.021$\times 10{}^{-1}$ \\ \hline
\end{tabular}
%\end{center}
%\end{table}
%
%\begin{table}[h]
%\begin{center}
\caption{\DselJ{CO${}_{2}$ 2.0 $\mu$m �Х�ɥѥ�᡼��}
         {Parameters of CO${}_{2}$ 2.0 $\mu$m band}}
\begin{tabular}{||c|c|c||c|c|c||} \hline
$\nu _{i}$(cm${}^{-1}$) & $s_{i}$ & $\alpha _{i}$ &
$\nu _{i}$(cm${}^{-1}$) & $s_{i}$ & $\alpha _{i}$ \\ \hline
4650 & 2.185$\times 10{}^{-1}$ & 1.916$\times 10{}^{0}$ &
5050 & 8.778$\times 10{}^{1}$  & 2.012$\times 10{}^{1}$ \\
4750 & 2.040$\times 10{}^{0}$  & 6.475$\times 10{}^{0}$ &
5150 & 8.346$\times 10{}^{1}$  & 1.804$\times 10{}^{1}$ \\
4850 & 1.197$\times 10{}^{2}$  & 3.112$\times 10{}^{1}$ &
5250 & 8.518$\times 10{}^{-2}$ & 8.474$\times 10{}^{-1}$ \\
4950 & 4.829$\times 10{}^{2}$  & 5.759$\times 10{}^{1}$ &
5350 & 4.951$\times 10{}^{-1}$ & 1.597$\times 10{}^{0}$ \\ \hline
\end{tabular}
\end{center}
\end{table}

\subsection{\DselJ{�����Ȥ�����}{Radiative transfer of dust}}

\DselJ{
�����Ȥˤ����������, �ֳ����ͤεۼ�, ����, �ͽФϤȤ�� 
$\delta$-Eddington ���(�㤨�� Liou, 1980 �򻲾�)���Ѥ��Ʒ׻�����.
$\delta$-Eddington ������������ʻ���Τ����絤������ã��׻��������
�褯�Ѥ�������ˡ�Ǥ���. �Ļ��������ֳ������Ф�������Ȥ����оΰ��Ҥ�
�Ȥ�����������ɽ�� 0 ���� 1 ���ϰϤˤ���.
}
{
The solar and infrared radiative flux associated with dust are
   calculated by using the $\delta$-Eddington approximation 
   (c.f., Liou, 1980).
The $\delta$-Eddington approximation is well used in calculating
   radiative transfer with anisotropic scattering.
The asymmetry factor of dust for solar and infrared radiation 
   are between 0 and 1 which means forward scattering occurs. 
}

\DselJ{
�����Ȥˤ���������ͤλ�����
��������ͥե�å��� $F_{dif,\nu_{i}}^{\uparrow}$, 
���������ͥե�å���$F_{dif,\nu _{i}}^{\downarrow}$ 
�ϰʲ��μ��Ƿ׻������.
}
{
The upward and downward diffuse solar radiative flux per unit wave
   length associated with dust $F_{dif,\nu_{i}}^{\uparrow}$, 
   $F_{dif,\nu _{i}}^{\downarrow}$ 
   are obtained as solutions of following
   equations.
}
\begin{eqnarray}
  \DD{F_{dif,\nu _{i}}^{\uparrow}}{\tau _{\nu _{i}}^{*}} &=&
  \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}}, 
  \Deqlab{�����Ȥξ������������} \\
  \DD{F_{dif,\nu _{i}}^{\downarrow}}{\tau _{\nu _{i}}^{*}} &=&
  \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}}.
  \Deqlab{�����Ȥβ�������������}
\end{eqnarray}

\DselJ{
��������, �絤��ü�Ǥβ��������� $F_{dif,\nu_{i}}^{\downarrow}$ �� 0, 
�絤��ü�Ǥξ�������� $F_{dif,\nu_{i}}^{\uparrow}$ �� 
$F_{dif,\nu}^{\downarrow}\times A$ ($A$ ����ɽ�̥���٥�) �Ǥ�
��. $\gamma _{1,\nu _{i}},\gamma _{2,\nu _{i}},\gamma _{3,\nu _{i}}$ ��
���줾��
}
{
The boundary condition of 
   \Deqref{�����Ȥξ������������} and 
   \Deqref{�����Ȥβ�������������}
   are that $F_{dif,\nu_{i}}^{\downarrow}=0$
   at the top
   of atmosphere and $F_{dif,\nu_{i}}^{\uparrow}= 
   F_{dif,\nu}^{\downarrow}\times A$ 
   at the surface, where $A$ is the surface albedo.
$\gamma _{1,\nu _{i}},\gamma _{2,\nu _{i}},\gamma _{3,\nu _{i}}$
   are expressed as follows.
}
\[ 
 \gamma _{1,\nu _{i}} = 
 \frac{1}{4}[7-(4+3g_{\nu _{i}}^{*})\tilde{\omega}_{\nu _{i}}^{*}], \quad 
 \gamma _{2,\nu _{i}} = 
 -\frac{1}{4}[1-(4-3g_{\nu _{i}}^{*})\tilde{\omega}_{\nu _{i}}^{*}],
 \quad
 \gamma _{3,\nu _{i}} = \frac{1}{4}(2-3g_{\nu _{i}}^{*}\mu_{0}), 
\] 

\DselJ{
��ɽ�����.  $\tau _{\nu _{i}}^{*}, \tilde{\omega}_{\nu _{i}}^{*},
g_{\nu _{i}}^{*}$ �� $\delta$-Eddington �����ȼ���������줿����Ū����, 
�켡���𥢥�٥�, ���оΰ��Ҥ�, ���줾��
}
{
where $\tau _{\nu _{i}}^{*}, \tilde{\omega}_{\nu _{i}}^{*},
  g_{\nu _{i}}^{*}$ are optical depth, single scattering
   albedo and asymmetry factor scaled by $\delta$-Eddington
   approximation, which are given as follows.
}
\[
  \tau _{\nu _{i}}^{*}=(1-\tilde{\omega}_{\nu _{i}}g_{\nu _{i}}^{2})\tau_{\nu
  _{i}}, \quad  
  \tilde{\omega}_{\nu _{i}}^{*} =  \frac{(1-g_{\nu _{i}}^{2})
  \tilde{\omega}_{\nu _{i}}} {1-\tilde{\omega}_{\nu _{i}}g_{\nu
  _{i}}^{2}}, 
  \quad
  g_{\nu _{i}}^{*} = \frac{g_{\nu _{i}}}{1+g_{\nu _{i}}}, 
\] 

\DselJ{
�Ǥ���. $\tau _{\nu _{i}}, \tilde{\omega}_{\nu _{i}}, g_{\nu _{i}}$ �Ϥ�
�Ȥ�Ȥθ���Ū����, �켡���𥢥�٥�, ���оΰ��ҤǤ���.
}
{
where $\tau _{\nu _{i}}, \tilde{\omega}_{\nu _{i}}, g_{\nu _{i}}$ 
   are optical depth, single scattering
   albedo and asymmetry factor, respectively.
}

\DselJ{
�����Ȥˤ���ֳ����ͤεۼ��Ȼ���, �ͽФ�Ʊ�ͤ˷׻�����. ����������ľã��
�ΰ켡�����ɽ����������Ǯ�ռ͹ब�դ�.}
{
The upward and downward infrared radiative flux per unit wave length
   associated with dust are obtained as solutions of similar equations
   used for calculation of diffuse solar flux 
   (\Deqref{�����Ȥξ������������}, \Deqref{�����Ȥβ�������������})
   except for the
   last term in right hand side of each equation.
}
\begin{eqnarray}
  \DD{F_{IR,\nu _{i}}^{\uparrow}}{\tau _{\nu _{i}}^{*}} &=&
   \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}}^{*}), 
  \Deqlab{�����Ȥξ�����ֳ�����} \\
  \DD{F_{IR,\nu _{i}}^{\downarrow}}{\tau _{\nu _{i}}^{*}} &=&
   \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}}^{*}).
  \Deqlab{�����Ȥβ������ֳ�����}
\end{eqnarray}

\DselJ{
��������, �絤��ü�Ǥβ��������� $F_{IR,\nu_{i}}^{\downarrow}$ �� 0, 
�絤��ü�Ǥξ�������� $F_{IR,\nu_{i}}^{\uparrow}$ �� $\pi B_{\nu,
T_{sfc}}$ �Ǥ���. \Deqref{�����Ȥξ�����ֳ�����}, \Deqref{�����Ȥβ���
���ֳ�����}����Υץ�󥯴ؿ� $B_{\nu_{i} ,T}$ ��, �Х����Ǥ�ʿ���ͤ�
�Ѥ���.
}
{
The boundary condition of 
  \Deqref{�����Ȥξ�����ֳ�����}
   and \Deqref{�����Ȥβ������ֳ�����}
   is that $F_{IR,\nu_{i}}^{\downarrow}=0$ at the top
   of atmosphere and $F_{IR,\nu_{i}}^{\uparrow}$ is equal to 
   $\pi B_{\nu,T_{sfc}}$ at the surface.
The Plank function $B_{\nu_{i} ,T}$  in 
   \Deqref{�����Ȥξ�����ֳ�����}
   and \Deqref{�����Ȥβ������ֳ�����} is averaged over the band width.
}
\[
  B_{\nu_{i},T} = \frac{1}{\nu _{2}-\nu _{1}}
                            \int _{\nu _{1}}^{\nu _{2}} B_{\nu ,T}\Dd \nu.
\]

\DselJ{
������ $\nu_{1},\nu_{2}$ �ϳƥХ�ɤξ�ü�Ȳ�ü����Ĺ�Ǥ���.
}
{
$\nu_{1},\nu_{2}$ are the lower and upper wave length of the
   band.
}

\DselJ{
���������ͤˤ�����Ͳ�ǮΨ�ϰʲ��μ��Ƿ׻������. 
}
{
The radiative heating rate associated with dust is calculated as follows.
}
\begin{eqnarray}
  Q_{rad,dust,SR} &=& - \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], \Deqlab{�����Ȥ��������Ͳ�Ǯ}\\
  Q_{rad,dust,IR} &=& -\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]. \Deqlab{�����Ȥ��ֳ����Ͳ�Ǯ}
\end{eqnarray}

\DselJ{
������ $F_{dir,\nu _{i}}^{\downarrow}$ ��ľã�������ͥե�å�����,
}
{
$F_{dir,\nu _{i}}^{\downarrow}$
    is the direct solar radiative flux per unit wave length, 
}
\begin{equation}
  F_{dir,\nu _{i}}^{\downarrow} = \mu _{0}S_{\nu _{i}}
  e^{-\tau_{\nu _{i}}/\mu _{0}}
\end{equation}

\DselJ{
�Ǥ���.
}

\DselJ{
�����Ȥμ��̺����椫�����Ū��������뤿��ˤ�, �����Ȥ�ͭ��Ⱦ�� 
$r_{m}$ ��ɬ�פȤʤ�. 
�ܥ�ǥ�Ǥϥ����Ȥ�γ��ʬ�ۤȤ��� Toon {\it et al.} (1977) 
���Ѥ���줿�ѷ�����޴ؿ�ʬ�ۤ��ꤹ��.
}
{
The dust opacity is calculated by using the mass mixing ratio
   and effective radius of dust.
In this model, we suppose that the size distribution of dust particle
   is the modified gamma distribution (Toon {\it et al.}, 1977).
}
\begin{equation}
\DD{n(r)}{r} = n_{0}r ^{\alpha} \exp 
    \left[ - \left(\frac{\alpha}{\gamma }\right)
             \left(\frac{r}{r_{m}}\right)^{\gamma }\right].
  \Deqlab{�����Ȥ�γ��ʬ��}
\end{equation}


\subsection*{\DselJ{�����Ȥθ���Ū����}{Dust opacity}}

\DselJ{
�ȿ� $\nu$ �θ����Ф������Ū���� $\tau _{\nu}$ ��, ñ�����Ѥ�����ξû�
���� $\beta _{e,\nu}$ ���Ѥ���
}
{
The monoclomatic optical depth $\tau _{\nu}$ is represented
   by using the extinction coefficient per unit volume 
   $\beta _{e,\nu}$ as follows.
}
\begin{equation}
  \tau _{\nu}(z) = - \int _{z_{t}}^{z} \beta _{e,\nu}(r) \Dd z
  \Deqlab{����Ū����}
\end{equation}
\DselJ{
��ɽ�����. ������ $z_{t}$ ���絤��ü���٤Ǥ���.  $\beta _{\nu,e}$ ��
}
{
where $z_{t}$ is altitude at the top of atmosphere.
$\beta _{\nu,e}$ is given as follows.
}
\begin{equation}
  \beta _{e,\nu} = \int _{0}^{\infty} \sigma_{e,\nu}(r)\DD{n(r)}{r}\Dd r
  \Deqlab{�û������Ⱦû������Ѥδط�}
\end{equation}
\DselJ{
��ɽ�����. ������ $\sigma_{e,\nu}$ ��{\bf �û�������}(extinction cross
section), $dn(r)/dr$ �ϻ���ʪ����γ��ʬ�۴ؿ��Ǥ���(cf. Liou, 1980; ����,
1999). ���̾û����� $k_{e}$ �Ȥδط���, 
}
{
where $\sigma_{e,\nu}$ is the extinction cross section,
   $dn(r)/dr$ is the size distribution of scattering particle
   (cf. Liou, 1980; Shibata, 1999).
By using extinction coefficient per unit mass $k_{e}$,
   \Deqref{�û������Ⱦû������Ѥδط�} is rewritten as follows. 
}
\begin{equation}
  \rho _{a}q_{s}k_{e,\nu} = 
  \int _{0}^{\infty} \sigma_{e,\nu}(r)\DD{n(r)}{r}\Dd r
\end{equation}
\DselJ{
�Ȥʤ�. ������ $\rho _{a}$ ���絤��̩��, $q_{s}$ �ϻ���ʪ���μ��̺�����
�Ǥ���. Ʊ�ͤ�ñ�����Ѥ�����λ��𷸿�, �ۼ�������, {\bf ����������}
(scattering cross section) $\sigma_{s,\nu}$, {\bf �ۼ�������}(absorption
cross section) $\sigma_{a,\nu}$ ���Ѥ���}
{
where $\rho _{a}$ is atmospheric density, and $q_{s}$ is
   mass mixing ratio of scattering particle.
Similarly, the scattering and absorption coefficient per unit volume
   are represented by using the scattering cross section 
   $\sigma_{s,\nu}$ and the absorption cross section 
  $\sigma_{a,\nu}$ as follows.
}
\begin{eqnarray}
  \beta _{s,\nu} &=& \int _{0}^{\infty} \sigma_{s,\nu}(r)\DD{n(r)}{r}\Dd r, \\
  \beta _{a,\nu} &=& \int _{0}^{\infty} \sigma_{a,\nu}(r)\DD{n(r)}{r}\Dd r, 
\end{eqnarray}
\DselJ{
��ɽ�����. ���ξ��켡���𥢥�٥� $\tilde{\omega}_{\nu}$ ��
}
{
and the single scattering albedo $\tilde{\omega}_{\nu}$ is given as follows.
}
\begin{equation}
  \tilde{\omega}_{\nu} = \frac{\beta _{s,\nu}}{\beta _{a,\nu}}
\end{equation}
\DselJ{
�Ȥʤ�. 
}{}

\DselJ{
�û������Ѥ������Ū�����Ѥǳ�ä��ͤ�{\bf �û���Ψ}(extinction
efficiency )�ȸƤ�, ����� $Q_{e,\nu}$ ��ɽ��.}
{
The extinction efficiency $Q_{e,\nu}$ is defined as
   the ration of extinction cross section to geometric cross section.
}
\begin{equation}
  Q_{e,\nu} = \frac{\sigma_{e,\nu}}{\pi r^{2}},
\end{equation}

\DselJ{
Ʊ�ͤ�{\bf �����Ψ}(scattering efficiency) $Q_{s,\nu}$, {\bf �ۼ���Ψ}
(absorption efficiency) $Q_{a,\nu}$ ����������.
}
{
Similarly, 
the scattering efficiency $Q_{s,\nu}$ and 
   absorption efficiency $Q_{a,\nu}$ is defined as follows.
}
\begin{eqnarray}
 Q_{s,\nu}&=& \frac{\sigma _{s,\nu}}{\pi r^{2}}, \\
 Q_{a,\nu}&=& \frac{\sigma _{a,\nu}}{\pi r^{2}}.
\end{eqnarray}

\DselJ{
�ܥ�ǥ�ˤ����Ƥ�, �����Ȥμ��̺����� $q$ ����Τ�ʪ���̤Ȥ��ƥ����Ȥ�
����Ū���������. Ϳ������ѥ�᡼����γ��ʬ�ۤ�ʿ�Ѥ��줿�û���Ψ�� 
$\overline{Q}_{e,\nu}$, �켡���𥢥�٥� $\tilde{\omega}_{\nu}$, γ��ʬ
�۴ؿ� $dn(r)/dr$, ���Υ⡼��Ⱦ�� $r_{m}$ ��{\bf ͭ��Ⱦ��}(�����Ѳý�ʿ
��Ⱦ��(cross section weighted mean radius) �Ȥ⤤��) $r_{eff}$, �����ƥ�
���Ȥ�̩�� $\rho _{d}$ �Ǥ���.  $\overline{Q}_{e,\nu}$, $r_{eff}$ �Ϥ���
����}
{
In this model, the dust opacity is derived from the
   mass mixing ratio of atmospheric dust. 
Given parameters are the cross section weighted mean extinction
   efficiency $\overline{Q}_{e,\nu}$, the single scattering albedo 
   $\tilde{\omega}_{\nu}$, the size distribution function of dust
   $dn(r)/dr$, the mode radius $r_{m}$, the effective (or, cross section
   weighted mean) radius $r_{eff}$, and the density of dust
   particle $\rho _{d}$.
$\overline{Q}_{e,\nu}$ and $r_{eff}$ are defined as
   follows, respectively. 
}
\begin{eqnarray}
  \overline{Q}_{e,\nu} &\equiv&
           \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},\\
  r_{eff} &\equiv& \frac{\int _{0}^{\infty}r ^{3}\DD{n(r)}{r}\Dd r}
                      {\int _{0}^{\infty}r ^{2}\DD{n(r)}{r} \Dd r},
\end{eqnarray}
\DselJ{
��Ϳ������. 
}

\DselJ{
����ʪ���η��������Ȳ��ꤹ���ñ�̼��̤�����ξû�������, }
{
Supposing that the shape of scattering particle is sphere, 
   the extinction coefficient per unit mass is given as follows.
}
\begin{eqnarray}
 \beta _{e,\nu} &=& \overline{Q}_{e,\nu} 
                \int _{0}^{\infty} \pi r^{2}\DD{n(r)}{r}\Dd r, \nonumber \\
 &=& \frac{\overline{Q}_{e,\nu}}{r_{eff}}
     \int _{0}^{\infty} \pi r^{3}\DD{n(r)}{r}\Dd r, \nonumber \\
 &=& \frac{\overline{Q}_{e,\nu}}{r_{eff}}
     \frac{3\rho _{a}q_{s}}{4\pi \rho _{d}},
\end{eqnarray}
\DselJ{
�Ȥʤ�. ������ $\rho _{a}$ ���絤��̩�٤Ǥ���. �������äƸ���Ū������ 
$\tau _{\nu}$ ��
}
{
where $\rho _{a}$ is the atmospheric density.
Therefore, the optical depth can be represented by using the mass
   mixing ratio as follows.
}
\begin{equation}
 \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,
 \Deqlab{������ˤ�����Ū����}
\end{equation}
\DselJ{
�Ȥʤ�. 
}{}

\subsection*{\DselJ{�ѥ�᡼��}{Parameters}}

\DselJ{
���������ͤι�θ������Ĺ�ΰ�ȸ��إѥ�᡼���� Forget {\it et al.}
(1999)�Τ���˽स�Ƥ���. ������ CO${}_{2}$ �� 15 $\mu$m �Х�ɤȽŤʤ� 
11.6--20 $\mu$m �Х�ɤϹ�θ���ʤ�. �ۼ������Ťʤ����������ã�ΰ�����
¿��ʣ���ˤʤ뤫��Ǥ���. �Ļ����Ĺ�ΰ�Х�ɤ� CO${}_{2}$ ���ֳ��ۼ���
�Ȥεۼ����νŤʤ��̵�뤹��. CO${}_{2}$ �ˤ�äƵۼ���������������̤�
�����������̤� 1\% ���٤ʤΤ�, �ۼ����νŤʤ��̵�뤷�Ƥ����ͷ׻��η��
���Ѥ��ʤ���Ƚ�Ǥ���.}
{
The values of band width and optical parameters of dust (extinction
   efficiency, single scattering albedo, asymmetry factor) considered
   in this model are following to those of Forget {\it et al.} (1999)
   except for 11.6--20 $\mu$m band of dust. 
The overlap between visible band of dust and CO${}_{2}$ near infrared band 
   is omitted.
}

\DselJ{
5--11.6 $\mu$m �ֳ��ۼ��Х�ɤθ���Ū���� $\tau _{5-1.6 \mu m}$ �� 0.67
$\mu$m �ˤ�����û����� $Q_{e,0.67 \mu m}$ ���Ѥ��Ʒ׻����줿�Ļ������
�������Ū������, ��¬���������Ƥ���Ļ���ֳ��θ���Ū�������� $\tau
_{0.67 \mu m}/\tau _{9 \mu m}$ �����Ѥ��Ʒ׻�����.  20--200 $\mu$m �Х�
�ɤθ���Ū������, $\tau _{5-11.6 \mu m}$ ��\Dtabref{�����Ȥθ��إѥ�᡼
��}�˼����� $Q_{e,\nu_{i}}/Q_{e,0.67\mu m}$ ���椫��׻�����.
}
{
The 5-11.6 $\mu$m infrared dust opacity $\tau _{5-1.6 \mu m}$ is
   obtained by dividing the visible dust opacity by the visible to
   infrared opacity ratio $\tau_{0.67 \mu m}/\tau _{9 \mu m}$, 
   which is set to be 2. (Forget, 1998).
The 20-200 $\mu$m infrared dust opacity is calculated by using 
   $\tau _{5-11.6 \mu m}$
    and the value of $Q_{e,\nu_{i}}/Q_{e,0.67\mu m}$
   shown in \Dtabref{�����Ȥθ��إѥ�᡼��}.
}


\begin{table}[h]
\begin{center}
\caption{\DselJ{�����ȤΥХ�ɤȸ��إѥ�᡼��}{Band width and optical parameters of dust}}
\begin{tabular}{||c|c|c|c|c||} \hline
\DselJ{�Х��}{Band}($\mu$m) & \DselJ{�Х��}{Band}(cm${}^{-2}$) & $Q_{e,\nu _{i}}/Q_{e,0.67\mu m}$ 
& $\tilde{\omega}_{\nu _{i}}$ & $g_{\nu_{i}}$ \\ \hline
0.1--5 $\mu$m & 2000--10${}^{5}$ & 1.0 & 0.920 & 0.55  \\  
5--11.6 $\mu$m & 870--2000 & 0.253 & 0.470 & 0.528 \\ 
20--200 $\mu$m & 50--500 & 0.166 & 0.370 & 0.362 \\ \hline
\end{tabular}
\Dtablab{�����Ȥθ��إѥ�᡼��}

\caption{\DselJ{����¾�Υ����Ȥ˴ؤ���ѥ�᡼��}{Other parameters}}
\begin{tabular}{||c|c|c||} \hline
\DselJ{�ѥ�᡼��}{Parameters} & \DselJ{ɸ����}{Standard values} & \DselJ{����}{Note} \\ \hline
$Q_{e,0.67\mu m}$ & 3.04 &  Ockert-Bell, {\it et al.} (1997)  \\
$\tau _{0.67 \mu m}/\tau _{9\mu m}$ & 2 & Forget (1998)  \\ 
$r_{eff}$ & 2.5 $\mu$m & Pollack {\it et al.} (1979)   \\ 
$r_{m}$ & 0.4 $\mu$m & Pollack {\it et al.} (1979)   \\ \hline
\end{tabular}
\Dtablab{����¾�Υ����Ȥ˴ؤ���ѥ�᡼��}
\end{center}
\end{table}

\subsection{\DselJ{�������ͥե�å�����ŷĺ�ѥѥ�᡼��}{Solar flux and zenith angle}}\Dseclab{�������ͤ�ŷĺ��}

\DselJ{
����Ĺ����ʬ���줿�絤��ü�ˤ������������ͥե�å��� $F_{s}$ ��, ����, 
����, ����ˤ�ä��Ѳ�����. �����Ǥϵ���, ���٤���ꤷ�����γƻ���ˤ�
���� $F_{s}$ �η׻���ˡ�򼨤�. 
}
{
The solar flux at the top of atmosphere $F_{s}$ is depend on
   season, latitude and local time.
In this section, we show $F_{s}$ as a function of local time
   at a specified season and latitude.
}

\DselJ{
ʿ�ѵ�ƻ��Υ��Ǥ���������� $I_{0}$ (Wm${}^{-2}$), ���ۤ���ε�Υ�� $r$, 
����ʿ�ѵ�Υ�� $r_{0}$, ����ŷĺ�Ѥ� $\zeta $, ���٤� $\phi $, ���ۤ���
�ޤ� $\delta $ , ����(������ $t$ ���� $\pi$ ���줿���, $2\pi t/T -\pi$)
�� $h$ �Ȥ���. �������� $F_{s}$ ��
}
{
Suppose that $I_{0}$ (Wm${}^{-2}$) is solar constant on the mean orbital radius
   of Planet, $r$ and $r_{0}$ is the radius of
   orbit and its mean value, $\zeta$ is solar zenith
   angle, $\phi$ is latitude, $\delta$ is the solar
   inclination, $h$ is the hour angle
   ($= 2\pi t/T -\pi$, $T$ is length of day ). 
$F_{s}$ is represented by using these variables as follows.
}
\begin{eqnarray}
  F_{s} &=& I_{0}\left(\frac{r_{0}}{r}\right)^{2}\cos \zeta, \\
  \cos \zeta &=& \sin \phi \sin \delta + \cos \phi \cos \delta \cos h,
\end{eqnarray}
\DselJ{
��Ϳ������(�㤨�о���, 1999 �򻲾�). ���ۤ���ε�Υ $r$ ���ְ� $\delta
$ ��,
}
{
(c.f., Ogura, 1999).
$r$ and $\delta$ are given as follows.
}
\begin{eqnarray*}
  r &=&  \frac{a(1-e^{2})}{1+e\cos \omega}, \\
  \sin \delta &=& \sin \alpha \sin (\omega - \omega _{0})
\end{eqnarray*}
\DselJ{
��ɽ�����. ������ $\theta $ �϶�������������ۤγ��ٰ���, $a$ �ϵ�ƻĹ
Ⱦ��, $e$ �ϵ�ƻΥ��Ψ, $\alpha $ �ϼ�ž���η���, $\omega$ ��
��������, $\omega _{0}$ �϶�����
����ν�ʬ�����ٰ��֤Ǥ���. �ʾ�μ��� $r_{0}=a$, �����濴���� 
$L_{s}\equiv \omega - \omega _{0}$ ���Ѥ��ƤޤȤ���,}
{
where $\theta$ is the longitude relative to the
   perihelion, $a$ is the semimajor axis of orbit, $e$
   is the eccentricity, $\alpha$ is
   the declination, $\omega$; is the true anomaly, 
   and $\omega_{0}$ is the longitude of vernal
   equinox relative to the perihelion.
By introducing the areocentric longitude of the sun 
   $L_{s}\equiv \omega - \omega _{0}$,
   $F_{s}$ is rewritten as follows.   
}
\begin{equation}
  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{equation}
\DselJ{
�Ȥʤ�.}{} 

\subsection*{\DselJ{�ѥ�᡼��}{Parameters}}

\DselJ{
�絤��ü���������ͥե�å����׻��˸����ѥ�᡼����ɸ������ϰʲ��Τ褦
�ˤʤäƤ���.
}{}

\begin{table}[h]
\begin{center}
\caption{\DselJ{�������ͥե�å����׻��Υѥ�᡼��}{Parameters for solar flux and zenith angle}}
\begin{tabular}{||c|c|c||}  \hline 
\DselJ{�ѥ�᡼��}{Parameters} & \DselJ{ɸ����}{Standard values} & \DselJ{����}{Note} \\  \hline 
$\phi$ & 20${}^{\circ}$N & Pollack {\it et al.} (1979)  \\
$L_{s}$ & 100 ${}^{\circ}$ & ��\\
$e$ & 0.093 & \DselJ{����ǯɽ 2000 ǯ��}{} \\ 
$\alpha$ & 25.2${}^{\circ}$ & \DselJ{��}{} \\ 
$\omega _{0}$ & 110${}^{\circ}$ & \DselJ{Carr (1996) ��1-1}{Carr (1996), Fig. 1} \\ 
$I_{0}$ & 591 Wm${}^{-2}$  & \DselJ{����ǯɽ 2000 ǯ��}{} \\ \hline
\end{tabular}
\end{center}
\end{table}



 