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(6.1)
∫ ( )
Here n(r)dr is the fraction of particles with equivalent-sphere radii between r and r +
dr, and r1 and r2 are the minimum and the maximum equivalent-sphere radii in the
size distribution [Mishchenko & Travis, 1998].
6.2.1 Modified gamma distribution (both codes):
(
( )
(
)⁄
( )
)
( )
(
( ) )
(6.2)
where Γis the gamma function, αand γare constants, and rc is the radius value
approximately corresponding to the peak of the distribution.
6.2.2 Log normal distribution (both codes)
( )
(
(
(
)
)
(
)
)
(6.3)
where rg and σg are the mean and standard deviations of r.
6.2.3 Power law distribution (both codes)
( )
{
(6.4)
For this distribution, the codes automatically calculate the minimum and the
maximum radii r1 and r2 on the basis of supplied effective radius reff and effective
variance veff which are analytically defined as:
(6.5)
∫ ( )
( )(
∫
)
(6.6)
where
∫
( )
(6.7)
6.2.4 Gamma distribution (both codes)
(
( )
(
)
( )
)⁄
(
)
(6.8)
where Γis the gamma function, and a and b are constants.
6.2.5 Modified power law distribution (both codes)
( )
( )
{
6.2.6 Bimodal volume log normal distribution (SPHER only)
This distribution will be implemented in the near future.
97
(6.9)