Field (2000) analyzed the number and size of ice crystals in aggregates (snow) and found that they were dependent on the altitude (depth below cloud top, and therefore temperature). Zhang et al. (2013) found that with dcs=250 the simulated ice crystal effective radius agrees well with those calculated from observed ice size distribution. Consistently, Eidhammer et al. (2014) showed with dcs=250um the CAM5 modeled moments of the ice crystal size distribution agree best with in-situ measurements, if a constant value needs to be used. On the other hand, Cotton et al. (2013) found that the diameter D, which separates the ice crystals and aggregates in the size distribution, is centered around 100um and is not temperature dependent. However, they mentioned that "incorrectly sizing particles due to diffraction and out-of-focus images and residual shattering may still influence the shape of the PSD below ≈ 150 μm", so their estimates might be biased low.
A simple parameterization based on Field (2000) and Eidhammer et al. (2014).
References:
Masahiro Kajikawa and Andrew J. Heymsfield, 1989: Aggregation of Ice Crystals in Cirrus. J. Atmos. Sci., 46, 3108–3121.doi: http://dx.doi.org/10.1175/1520-0469(1989)046<3108:AOICIC>2.0.CO;2
David L. Mitchell, 1991: Evolution of Snow-Size Spectra in Cyclonic Storms. Part II: Deviations from the Exponential Form. J. Atmos. Sci., 48, 1885–1899.doi: http://dx.doi.org/10.1175/1520-0469(1991)048<1885:EOSSSI>2.0.CO;2
Field, P. R. (2000), Bimodal ice spectra in frontal clouds. Q.J.R. Meteorol. Soc., 126: 379–392. doi: 10.1002/qj.49712656302
Cardwell JR, Choularton TW, Wilson D, Kershar R. 2002. Use of anexplicit model of the microphysics of precipitating stratiform cloud totest a bulk microphysics scheme. Q. J. R. Meteorol. Soc. 128: 573 – 592.
Paul R. Field and Andrew J. Heymsfield, 2003: Aggregation and Scaling of Ice Crystal Size Distributions. J. Atmos. Sci., 60, 544–560.doi: http://dx.doi.org/10.1175/1520-0469(2003)060<0544:AASOIC>2.0.CO;2
Paul R. Field, Andrew J. Heymsfield, and Aaron Bansemer, 2007: Snow Size Distribution Parameterization for Midlatitude and Tropical Ice Clouds. J. Atmos. Sci., 64, 4346–4365.doi: http://dx.doi.org/10.1175/2007JAS2344.1
Cotton, R. J., Field, P. R., Ulanowski, Z., Kaye, P. H., Hirst, E., Greenaway, R. S., Crawford, I., Crosier, J. and Dorsey, J. (2013), The effective density of small ice particles obtained from in situ aircraft observations of mid-latitude cirrus. Q.J.R. Meteorol. Soc., 139: 1923–1934. doi: 10.1002/qj.2058
Zhang, K., Liu, X., Wang, M., Comstock, J. M., Mitchell, D. L., Mishra, S., and Mace, G. G.: Evaluating and constraining ice cloud parameterizations in CAM5 using aircraft measurements from the SPARTICUS campaign, Atmos. Chem. Phys., 13, 4963-4982, doi:10.5194/acp-13-4963-2013, 2013.
Eidhammer, T., Morrison, H., Bansemer, A., Gettelman, A., and Heymsfield, A. J.: Comparison of ice cloud properties simulated by the Community Atmosphere Model (CAM5) with in-situ observations, Atmos. Chem. Phys., 14, 10103-10118, doi:10.5194/acp-14-10103-2014, 2014.