MAKE_MIE_TABLE

Make_mie_table calculates the single scattering properties of gamma or lognormal distributions of spherical particles and outputs the results in a scattering table. If the particle type is water or ice then an integration across the specified wavelength band may be performed. If an aerosol particle type is chosen then the index of refraction of the aerosol is specified.

For water or ice particles an integration across the wavelength range may be done. In this case a series of Mie calculations are performed at a specified wavelength spacing using the correct index of refraction for each wavelength. The alternative is to use the Planck function averaged index of refraction and central wavelength, which takes less computation but may be less accurate (depending on the spectral band width). For solar wavelengths (< 3 um) the Planck function is for a solar temperature (5800 K), for longwave wavelengths (> 5 um) the Planck function is for an atmospheric temperature (270 K), while between 3 and 5 um a straight average is used.

If an aerosol particle type is chosen then the particle bulk density of the aerosol is specified. The density is needed because the output scattering table extinction is normalized for a mass content of 1 g/m^3.

The gamma distribution of cloud droplet sizes is n(r) = a r^alpha exp(-b*r) where r is the droplet radius, and a, b, alpha specify the gamma distribution. The number concentration of droplets is N = a Gamma(alpha+1)/ b^(alpha+1), where Gamma is the gamma function. The effective radius of the distribution is r_eff = (alpha+3)/b, while the effective variance is v_eff = 1/(alpha+3). A typical value for water clouds is v_eff=0.1 or alpha=7. For ice clouds a typical value is alpha=1 or 2. An exponential distribution is obtained with alpha=0. A large value of alpha gives close to a monodisperse distribution.

The lognormal distribution of cloud droplet sizes is n(r) = a/r exp( -[ln(r/r0)]^2 / (2*sigma^2) ) where r0 is the logarithmic mode of the distribution and sigma is the standard deviation of the log. The number concentration of droplets is N = sqrt(2*pi)*sigma*a. The effective radius of the distribution is r_eff = r0*exp(2.5*sigma^2) and the effective variance of the distribution is v_eff = exp(sigma^2)-1. A common value for water clouds is sigma=.35, or v_eff=0.130, and a common value for aerosol distributions is sigma=0.7.

The maximum radius of the distribution is specified by the user because it is the critical determinant of the Mie calculation computer time. There are often microphysical reasons for truncating the theoretical size distribution; for example, one might say that the cloud droplet mode ends at a radius of 50 microns. For a narrow gamma distribution (alpha=7) of cloud droplets, a maximum radius of only twice the largest effective radius gives virtually the same optical properties as the untruncated gamma distribution. For a wide lognormal distribution, as might be used for an aerosol distribution, a much larger maximum radius relative to the largest effective radius would be required if no truncation was desired. If there is truncation make_mie_table uses an iterative procedure to adjust the size distribution modal radius to achieve the desired effective radius. Thus one can be assured that the size distributions have the effective radii reported in the output scattering table even if there is truncation of the theoretical distribution. The number and spacing of the integration steps over the size distribution is controlled by the GET_NSIZE and GET_SIZES subroutines. The default formula is DELX = max(0.01,0.03*X**0.5), where X is the size parameter (2*pi*r/lambda, lambda=wavelength) and DELX is the integration step. This integration spacing is adequate for most purposes, but can be easily changed if higher accuracy is sought.

Input Parameters

Parameter Description
WAVELEN1 wavelength range (microns) for this band
WAVELEN2 for monochromatic choose WAVELEN1=WAVELEN2
PARTYPE particle type: W=water, I=ice, A=aerosol if PARTTYPE='A' then the index of refraction is input, otherwise tables for water and ice index are used.
AVGFLAG 'A' for spectral average over the wavelength range (for PARTYPE='W' or 'I'), 'C' to use the central wavelength.
DELTAWAVE wavelength interval for averaging (micron)
RINDEX aerosol complex index of refraction (negative imaginary part)
PARDENS aerosol particle bulk density (g/cm^3)
DISTFLAG 'G' for gamma distribution or 'L' for lognormal distribution
ALPHA distribution shape parameter (either alpha in gamma distribution or sigma in lognormal distribution). Effective variance = 1/(alpha+3) for gamma, exp(alpha^2)-1 for lognormal.
NRETANB number of effective radii entries in Mie table
SRETAB starting effective radius (micron) in Mie table
ERETAB ending effective radius (micron) in Mie table
MAXRADIUS maxium particle radius in size distribution (micron)
MIEFILE output Mie scattering table file name