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A.d.iii. Radiative transfer of dust
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The absorption, scattering and emission of solar and infrared
radiation associated with dust are
calculated by using the δ-Eddington approximation (c.f., Liou, 1980).
The δ-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.
The upward and downward diffuse solar radiative flux per unit wave
length associated with dust ( ,  ) are obtained as solutions of following
equations.
The boundary condition of (A.31) and (A.32) is that = 0 at the top
of atmosphere and = ×
A at the surface, where A is the surface albedo.
 are expressed as follows.
where  are optical depth, single scattering
albedo and asymmetry factor modified by δ-Eddington
approximation, which are given as follows.
where  are optical depth, single scattering
albedo and asymmetry factor, respectively.
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 ((A.31), (A.32)) except that
the single scattering of direct Solar radiation term is replaced by
the thermal emission term.
The boundary condition of (A.33) and (A.34) is that  = 0 at the top
of atmosphere and  is equal to  at
the surface.
The Plank function  in (A.33) and (A.34) is averaged over the band width.
 are the lower and upper wave length of the
band.
The radiative heating rate associated with dust is calculated as follows.
 is the direct solar radiative flux per
unit wave length,
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(A.37) |
The band width and optical parameters of dust
(extinction efficiency, single scattering albedo, asymmetry
factor) in each band are same as those of Forget et al. (1999)
except in 11.6 - 20 μm band which is not considered in our
model for computational simplicity.
The overlapping between dust solar band and the
CO2 near infrared band is not considered.
The effect of this simplification can be negligible because the total
radiative flux absorbed by CO2 in the
near infrared band are 1 % of incident solar radiative flux at the
top of atmosphere.
The value of extinction efficiency for solar radiation  is
3.04 which is the value for 0.67 μm solar radiation presented
by Ockert-Bell, et al.
(1997) .
The visible to infrared opacity ratio is set to be 2 (Forget, 1998).
Detail descriptions of band width and optical parameters of dust
are shown in appendix A.d.v .
The dust opacity is calculated by using the mass mixing ratio
and effective radius of dust.
The effective radius is calculated by using the size distribution
function of dust particle (see appendix A.d.iv).
In this model, we suppose that the size distribution of dust particle
is the modified gamma distribution (Toon et al., 1977).
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(A.38) |
where   m.
By using these parameters, we obtain the effective radius is equal to
2.5 μm (Pollack et al.,
1979).
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