Article

Modeling snow crystal growth III: three-dimensional snowfakes

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Abstract

We introduce a three-dimensional, computationally feasible, mesoscopic model for snow crystal growth, based on diffusion of vapor, anisotropic attachment, and a semi-liquid boundary layer. Several case studies are presented that faithfully emulate a wide variety of physical snowflakes.

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... The physical simulation of ice crystal growth by deposition is complicated by the continuing lack of detailed knowledge of the physics involved, and its dependence on temperature, pressure and vapor density [63]. Mathematical or semi-physical models approximating the growth in 2D [93] and 3D [36] have been developed, but purely physical models have not yet been achieved, owing to the uncertainties in molecularscale physics of ice surfaces. The physics-based modeling of aggregation was formulated by [108,71] and later extended to riming by [59]. ...
... The results of these models are typically only semi-physical in practice because the complexity of the physics and the variability of environmental conditions require simplifying assumptions and approximations to be made. Many of the models also use empirical formulas for the dimensions of the original ice crystals, although [53] used the 3D-crystal growth algorithm of [36]. The shapes produced with the physical approach are qualitatively realistic, but may demand a lot of computer resources. ...
Chapter
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... Much progress has been made recently on modeling real- istically shaped solid hydrometeors, including pristine ice crystals, (Gravner and Griffeath, 2009;Liu, 2008), and aggregates and graupel (Petty and Huang, 2010;Kuo et al., 2013). We start with the modeled hydrometeors cre- ated by Kuo. ...
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... In Part I, the authors described the simulation (using the ''snowfake'' algorithm) of individual pristine crystals such as dendritic forms, needles, and ''sandwich'' plates, based upon a method pioneered by Gravner and Griffeath (2009). By prescribing different control parameters in snowfake, a pool of pristine crystals with different sizes and geometries was generated and their properties were cataloged. ...
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In this study, two different particle models describing the structure and electromagnetic properties of snow are developed and evaluated for potential use in satellite combined radar-radiometer precipitation estimation algorithms. In the first model, snow particles are assumed to be homogeneous ice-air spheres with single-scattering properties derived from Mie theory. In the second model, snow particles are created by simulating the self-collection of pristine ice crystals into aggregate particles of different sizes, using different numbers and habits of the collected component crystals. Single-scattering properties of the resulting nonspherical snow particles are determined using the discrete dipole approximation. The size-distribution-integrated scattering properties of the spherical and nonspherical snow particles are incorporated into a dual-wavelength radar profiling algorithm that is applied to 14- and 34-GHz observations of stratiform precipitation from the ER-2 aircraftborne High-Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) radar. The retrieved ice precipitation profiles are then input to a forward radiative transfer calculation in an attempt to simulate coincident radiance observations from the Conical Scanning Millimeter-Wave Imaging Radiometer (CoSMIR). Much greater consistency between the simulated and observed CoSMIR radiances is obtained using estimated profiles that are based upon the nonspherical crystal/aggregate snow particle model. Despite this greater consistency, there remain some discrepancies between the higher moments of the HIWRAP-retrieved precipitation size distributions and in situ distributions derived from microphysics probe observations obtained from Citation aircraft underflights of the ER-2. These discrepancies can only be eliminated if a subset of lower-density crystal/aggregate snow particles is assumed in the radar algorithm and in the interpretation of the in situ data.
Chapter
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Field Guide to Snowflakes
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K. Libbrecht, "Field Guide to Snowflakes," Voyageur Press, 2006.
Lattice models for solidification and aggregation, Institute for Advanced Study preprint
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N. H. Packard, Lattice models for solidification and aggregation, Institute for Advanced Study preprint, 1984. Reprinted in "Theory and Application of Cellular Automata," S. Wolfram, editor, World Scientific, 1986, pp. 305-310.