Chen, J.-P., and T.-C. Tsai, 2016: Triple-moment modal parameterization for the adaptive growth habit of pristine ice crystals. J. Atmos. Sci., 73, 2105–2122.  doi:10.1175/JAS-D-15-0220.1



A three-moment modal parameterization scheme was developed for describing variations in the shape of cloud ice crystals during growth by vapor deposition. The shape of ice crystals is represented using the volume-weighted aspect ratio, while the size spectrum of the crystal population is described using a three-parameter gamma function. Verified with binned spectral calculations, the proposed modal scheme performed quite accurately in the evolution of mass and shape of cloud ice crystals growing under idealized conditions. The associated error is within 1% in mass after 1000-s growth under water-saturation. When the ventilation effect is taken into account, the error remained within 5%. Error with regard to the bulk aspect ratio is generally about 3%. A failure to take into account the ice crystal shape led to a 45% underestimation in mass growth. Using only two moments to describe the gamma distribution led to a 37% underestimation in mass and 28% underestimation in the bulk aspect ratio of the ice crystals. The proposed scheme is able to capture the shape memory effect and the gradual adaptation of ice crystal aspect ratios to a new growth-habit regime.



Results for diffusional growth of ice crystals comparing modal parameterizations with binned calculation (black curve).  (a) The third moment M3; (b) bulk aspect ratio  .  

The three parameterizations compared include Shape3M (red curve), Shape2M (red dotted curve), and Sphere3M (blue curve) methods.  In (a), the Shape3M results nearly overlap the ShapeBin results.