Yang, Ping, K. N. Liou, Klaus Wyser, David Mitchell, 2000: Parameterization of the scattering and absorption properties of individual ice crystals. J. Geophys. Res., 105 (D4), 4699-4718.The scattering properties are tabulated for 56 wavelength bands from 0.20 to 5.0 microns and 24 particle lengths from 3 to 3500 microns. The eight ice crystal shapes are 1=hollow column, 2=solid column, 3=plate, 4=dendrite, 5=rough aggregate, 6=smooth aggregate, 7=4-bullet rosette, and 8=6-bullet rosette (see the article for pictures of these shapes).
The phase functions have been modified for this distribution by convolving the portions with scattering angles less than 10 degrees by a gaussian with 0.25 degree rms width and by adjusting the forward peak height to normalize each phase function. The reasons for doing this is that the original phase functions with the largest size parameters would require a huge number of Legendre series terms to be represented for SHDOM and also were not properly normalized. The number of Legendre terms required for the smoothed forward peak phase functions is 2500. The smoothing of the forward peak will not affect the radiative transfer results significantly for nearly all applications (one application where it could be an issue is sun photometry, but the TMS approximation in SHDOM is already poor for that application). These phase functions do not contain the "delta transmission", which is the direct transmission of rays through parallel faces of ice crystals. The extinction efficiency, single scattering albedo, and asymmetry parameter have thus been delta rescaled to be consistent. This reduces the extinction efficiency, single scattering albedo, and asymmetry parameter from the values in Ping Yang's original data. The extinction efficiency is well below 2 for crystals with parallel faces, such as plates and solid columns. The modified Ping Yang ice scattering data is stored in the file "sw_ice_scatter.db". This ascii file contains a header with useful information, followed by the data with one line per particle shape, wavelength, and particle size. Each line contains the following columns:
Heading | Explanation |
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S | shape index (1 to 8) |
Wave1 | starting wavelength of band (microns) |
Wave2 | ending wavelength of band (microns) |
Wavcen | center wavelength of band (microns) |
IndexRe | real part of index of refraction |
IndexIm | imaginary part of index of refraction |
SolarWt | fraction of solar flux in wavelength band |
ParLength | particle length (maximum extent) (microns) |
ParDarea | equivalent area spherical diameter (microns) |
ParDvol | equivalent volume spherical diameter (microns) |
Qext | extinction efficiency |
SSalb | single-scattering albedo |
Asym | asymmetry factor |
Phasefunc | phase function at 288 angles stored in a compressed format |
The log of the phase function values are stored in three digit base 95 (there are 95 printable characters in ascii). If the three characters of the base 95 number are represented by Cn (i.e. C1,C2,C3) then the base 95 digits are Dn=ICHAR(Cn)-32, and the phase function value are 10**(10*(D1/95+D2/95**2+D3/95**3)-4). This helps to compress the original 152 million bytes of ice scattering data down to only 10 millions bytes.
Make_ice_table reads the "sw_ice_scatter.db" database file to produce a scattering table file for gamma size distributions with a sequence of effective radii for one particle shape (i.e. it does not allow particle mixtures). The single scattering properties are averaged over the specified wavelength range using a solar temperature (5800 K) Planck function weighting. The program prints out the database bands and weightings that are used. The gamma distributions are in terms of the equivalent volume spherical diameter (Dv), not the particle length. The "b" parameter of the gamma distribution [n(D) = a Dv^alpha exp(-b*Dv)] is adjusted iteratively to achieve the correct effective radius. The effective radius is defined as one half the ratio of the third moment of Dv to the second moment of Da (the equivalent area spherical diameter). The user specified effective radius may not be achievable for a particular particle shape and size distribution width, in which case a different range of effective radius or a narrower distribution (larger alpha) will have to be chosen. The extinction in the output scattering table is normalized for distributions with an ice water content of 1 g/m^3 assuming an ice density of 0.916 g/cm^3.
Parameter | Description |
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ICESCATDB | filename of the ice scattering database (i.e. sw_ice_scatter.db) |
WAVELEN1 | wavelength range (microns) for this band |
WAVELEN2 | for monochromatic choose WAVELEN1=WAVELEN2 |
SHAPEIND | index of ice crystal shape (1=hollow column, 2=solid column, 3=plate, 4=dendrite, 5=rough aggregate, 6=smooth aggregate, 7=4-bullet rosette, 8=6-bullet rosette) |
NRETANB | number of effective radii entries in scattering table |
SRETAB | starting effective radius (micron) in scattering table |
ERETAB | ending effective radius (micron) in scattering table |
ALPHA | gamma distribution shape parameter |
ICETABFILE | output scattering table file name |