Numerical computations of facetted pattern formation in snow crystal growth

Facetted growth of snow crystals leads to a rich diversity of forms, and exhibits a remarkable sixfold symmetry. Snow crystal structures result from diffusion limited crystal growth in the presence of anisotropic surface energy and anisotropic attachment kinetics. It is by now well understood that the morphological stability of ice crystals strongly depends on supersaturation, crystal size and temperature. Until very recently it was very difficult to perform numerical simulations of this highly anisotropic crystal growth. In particular, obtaining facet growth in combination with dendritic branching is a challenging task. We present numerical simulations of snow crystal growth in two and three space dimensions using a new computational method recently introduced by the authors. We present both qualitative and quantitative computations. In particular, a linear relationship between tip velocity and supersaturation is observed. The computations also suggest that surface energy effects, although small, have a larger effect on crystal growth than previously expected. We compute solid plates, solid prisms, hollow columns, needles, dendrites, capped columns and scrolls on plates. Although all these forms appear in nature, most of these forms are computed here for the first time in numerical simulations for a continuum model.Comment: 12 pages, 28 figure

An accurate and computationally cheap microwave scattering method for ice aggregates: the Independent Monomer Approximation

The Discrete Dipole Approximation (DDA) is widely used to simulate scattering of microwaves by snowflakes, by discretising the snowflake into small “dipoles” which oscillate in response to (i) the incident wave and (ii) scattered waves from all the other dipoles in the particle. It is this coupling between all dipole pairs which makes solving the DDA system computationally expensive, and that cost grows non‐linearly as the number of crystals n within an aggregate is increased. Motivated by this, many studies have ignored the dipole coupling (the Rayleigh‐Gans Approximation, RGA). However, use of RGA leads to systematic underestimation of both scattering and absorption, and an inability to predict polarimetric properties. To address this, we present a new approach (the Independent Monomer Approximation, IMA) which solves the DDA system for each crystal “monomer” separately, then combines them to construct the full solution. By including intra‐monomer coupling, but neglecting inter‐monomer coupling, we save a factor of n in computation time over DDA. Benchmarking IMA against DDA solutions indicates that its accuracy is greatly superior to RGA, and provides ensemble scattering cross sections which closely agree with their more expensive DDA counterparts, particularly at size parameters smaller than ∼5. Addition of rime to the aggregates does not significantly degrade the results, despite the increased density. The use of IMA for radar remote sensing is evaluated, and we show that multi‐wavelength and multi‐polarisation parameters are successfully captured to within a few tenths of a dB for aggregates probed with frequencies between 3 and 200GHz, in contrast to RGA where errors of up to 2.5dB are observed. Finally we explore the realism of the IMA solutions in greater detail by analysing internal electric fields, and discuss some broader insights that IMA provides into the physical features of aggregates that are important for microwave scattering

Measurements of tropospheric ice clouds with a ground-based CMB polarization experiment, POLARBEAR

The polarization of the atmosphere has been a long-standing concern for ground-based experiments targeting cosmic microwave background (CMB) polarization. Ice crystals in upper tropospheric clouds scatter thermal radiation from the ground and produce a horizontally polarized signal. We report a detailed analysis of the cloud signal using a ground-based CMB experiment, Polarbear, located at the Atacama desert in Chile and observing at 150 GHz. We observe horizontally polarized temporal increases of low-frequency fluctuations ("polarized bursts," hereafter) of 720.1 K when clouds appear in a webcam monitoring the telescope and the sky. The hypothesis of no correlation between polarized bursts and clouds is rejected with >24\u3c3 statistical significance using three years of data. We consider many other possibilities including instrumental and environmental effects, and find no reasons other than clouds that can explain the data better. We also discuss the impact of the cloud polarization on future ground-based CMB polarization experiments

Classification of Snow Flakes and their Structures

Many snow flakes were photographed between 1951 and 1954 in Japan, and they were classified, according to the purposes by three methods, their metamorphic stages, shapes in falling state, and crystal habits. It was observed that the snow flakes change their crystal states in the process similar to that of the fallen snow. Considering aerodynamically the shape and velocity of snow flakes in falling state, a clue for presuming the uniformity of crystal habit in snow flakes was acquired. In the photographs of snow flakes obtained hitherto, it was found that in all types of snow crystals is formed one snow flake with the same type only, while another with almost all combinations between the different types is formed. All the ways of contact geometrically possible, namely, point, line, intertwined, and irregular contact were found in the snow flakes. The top of branch of dendritic crystals plays a leading role in the adhesion mechanism between the crystals. From those results, it was presumed that the large snow flakes might be composed of snow crystals of dendritic type