Snow Crystal Growth Research Articles

X-Band Radar and Surface-Based Observations of Cold-Season Precipitation in Western Colorado’s Complex Terrain

Abstract Hydrologic processes associated with intermountain cold-season precipitation in the Upper Colorado River basin have important impacts on avalanche forecasting and water resource management. However, traditional weather radar networks struggle with observations in this complex terrain. Data collected during the Study of Precipitation, the Lower Atmosphere, and the Surface for Hydrometeorology (SPLASH) and its sister campaign, Surface Atmosphere Integrated Field Laboratory (SAIL) in the East River watershed of western Colorado, are used to examine a multistorm period from 23 December 2021 to 1 January 2022 that contributed 35% of the total winter precipitation in this watershed. Dual-polarization X-band radar and disdrometer measurements show ∼30-mm differences in precipitation amount at two sites in proximity over four distinct storm events within the period. Wind patterns, synoptic forcings, microphysical characteristics of precipitation, and surface meteorology are analyzed to explain the observed spatial variability of cold-season precipitation in complex mountainous terrain. Analysis shows that differences over time within this event are mainly accounted for by synoptic forcings, such as frontal passages; differences between sites are accounted for by the impact of variations in local wind patterns on precipitation microphysics. Patterns of surface precipitation intensity are compared and found to be correlated with X-band radar signatures; a relationship between a strong dendritic growth stage and intense low-density surface precipitation is reinforced by this study. This relationship demonstrates the importance of particle growth mechanisms on surface snowfall patterns in high-altitude complex terrain, underscoring the importance of realistic microphysical parameterizations. Significance Statement The amount and density of snowpack from western Colorado winter storms have significant impacts on water resources in the Upper Colorado River basin. Snowpack characteristics are affected by small-scale differences in how snow forms in the atmosphere. These differences are hard to study in the complex terrain of the Rockies, but data from the SPLASH and SAIL field campaigns allows us to investigate how snow crystal formation and mountain-driven wind patterns affect snow near the surface. Our study finds that snow crystal growth varies over small space and time scales and is likely controlled by the terrain beneath a given location and resultant local wind patterns. These results imply that predicting snowpack in the Rockies requires properly representing local wind patterns and crystal growth processes in models.

Snowpack and avalanche characterization over the 2021–2022 winter season in Sisimiut, West Greenland

In Greenland, snow avalanches have been recognized as a significant hazard and a risk to communities for decades. However, prior to this study, no formal avalanche database nor avalanche forecasting service existed in Greenland. This study was conducted over the 2021–2022 snow season to advance snow science research in Greenland and provide the town of Sisimiut with an avalanche bulletin service based on snowpack stability, weather conditions, and avalanche activity monitoring data within the Sisimiut backcountry. Snowpack stratigraphies were assessed and stability tests were performed periodically using standardized methods, and the results were linked with daily weather monitoring and avalanche event characterization. The observed avalanche activity was dominated by slab avalanches, accounting for 96% of the registered events. Instabilities were mainly driven by specific temperature patterns, strong winds, and rain episodes. During cold and calm periods, slow kinetic growth of snow crystals in low-density layers was observed. Abrupt thermal increases were recurrent, resulting in softening of superficial slabs with consequent reactivation of buried weak layers, thus reducing snowpack stability. On the other hand, prolonged warmer temperatures lowered the thermal gradient within the snowpack, leading to rounding and bonding of weak layer grains, thus recovering the snowpack stability. As observed on three occasions, rain events caused the formation of persistent weak layers and should be considered a warning for future snowpack instability. As a result of this study, we retroactively linked local weather patterns with snowpack instability and provided the first periodical avalanche bulletin service for Sisimiut.

Nonisothermal cellular automata simulation of two-dimensional snow crystal growth.

Natural snowflakes exhibit remarkable diversity with a fascinating sixfold symmetry and fractal structure. Efforts to discover the snow crystal growth pattern and mechanism behind it have been made in the past 50 years. Among those, cellular automata (CA) have made certain progress. To investigate the influence of latent heat release in snow crystal growth and have a deeper understanding of crystal growth characteristics, an improved CA model combined with vapor diffusion and heat diffusion is proposed to investigate the snowflake growth process in a two-dimensional and nonisothermal field in this paper. Simulation results show that obtained snow crystal growth behavior is consistent with previous experimental observations and satisfies the crystal growth dynamic theory. Latent heat release impacts the small structure of snow crystals, and it could have a more significant influence on snowflake morphology when vapor diffusion is slow and heat diffusion is dominating.

Three-dimensional aspects of sidebranch formation during the growth of snow crystals

The nature of sidebranching in the facetted regions of snow crystals is investigated. It is shown that during the growth of a snow crystal, an initial sidebranch-pair forms after step bunching occurs on the leading prism planes, followed by step bunching on the adjacent flat basal face, producing a macrostep between the main branch and sidebranch feature. A Michelson interferometer–reflecting microscope setup was used to in-situ observe the three-dimensional morphology of a growing snow-crystal branch in a diffusion chamber. The macrostep on the basal plane was found to occur in the cases of simple facet growth, repetitive facet growth, and rounded tip growth, with the rounded tips forming at higher supersaturations. Thus, snow-crystal sidebranching involves a separation of the supply route of diffusing molecules on basal plane from the tip of the main-branch. Moreover, the sidebranches would fully sprout when the supersaturation increased, at which time the facetted branch tip abruptly narrowed and became rounded. These results indicate important roles of both the surface diffusion of water molecules and step migration for dendritic morphological instability on snow crystals.

Surface phase transitions and crystal habits of ice in the atmosphere.

With climate modeling predicting a raise of at least 2°C by year 2100, the fate of ice has become a serious concern, but we still do not understand how ice grows (or melts). In the atmosphere, crystal growth rates of basal and prism facets exhibit an enigmatic temperature dependence and crossover up to three times in a range between 0° and -40°. Here, we use large-scale computer simulations to characterize the ice surface and identify a sequence of previously unidentified phase transitions on the main facets of ice crystallites. Unexpectedly, we find that as temperature is increased, the crystal surface transforms from a disordered phase with proliferation of steps to a smooth phase with small step density. This causes the anomalous increase of step free energies and provides the long sought explanation for the enigmatic crossover of snow crystal growth rates found in the atmosphere.

A phase field model for snow crystal growth in three dimensions

Snowflake growth provides a fascinating example of spontaneous pattern formation in nature. Attempts to understand this phenomenon have led to important insights in non-equilibrium dynamics observed in various active scientific fields, ranging from pattern formation in physical and chemical systems, to self-assembly problems in biology. Yet, very few models currently succeed in reproducing the diversity of snowflake forms in three dimensions, and the link between model parameters and thermodynamic quantities is not established. Here, we report a modified phase field model that describes the subtlety of the ice vapour phase transition, through anisotropic water molecules attachment and condensation, surface diffusion, and strong anisotropic surface tension, that guarantee the anisotropy, faceting and dendritic growth of snowflakes. We demonstrate that this model reproduces the growth dynamics of the most challenging morphologies of snowflakes from the Nakaya diagram. We find that the growth dynamics of snow crystals matches the selection theory, consistently with previous experimental observations.

隣接面過程（AFP）と雪の結晶成長

隣接面過程（AFP）と雪の結晶成長

Lattice Boltzmann simulation of water isotope fractionation during ice crystal growth in clouds

We describe a lattice Boltzmann (LB) method for simulating water isotope fractionation during diffusion-limited ice crystal growth by vapor deposition from water-oversaturated air. These conditions apply to the growth of snow crystals in clouds where the vapor composition is controlled by the presence of both ice crystals and water droplets. Modeling of water condensation with the LB method has the advantage of allowing concentration fields to evolve based on local conditions so that the controls on grain shapes of the condensed phase can be studied simultaneously with the controls on isotopic composition and growth rate. Water isotope fractionation during snow crystal growth involves kinetic effects due to diffusion of water vapor in air, which requires careful consideration of the boundary conditions at the ice-vapor interface. The boundary condition is relatively simple for water isotopes because the molecular exchange rate for water at the interface is large compared to the crystal growth rate. Our results for the bulk crystal isotopic composition are consistent with simpler models using analytical solutions for radial geometry. However, the model results are sufficiently different for oxygen isotopes that they could affect the interpretation of D-excess values of snow and ice. The extent of vapor oversaturation plays a major role in determining the water isotope fractionation as well as the degree of dendritic growth. Departures from isotopic equilibrium increase at colder temperatures as diffusivity decreases. Dendritic crystals are isotopically heterogeneous. Isotopic variations within individual snow crystals could yield information on the microphysics of ice condensation as well as on the accommodation or sticking coefficient of water associated with vapor deposition. Our results are ultimately a first step in implementing LB models for kinetically controlled condensation or precipitation reactions, but needs to be extended also to cases where the molecular exchange rate is comparable to the crystal growth rate. This approach could also be applicable to aerosol chemical evolution.

Interface control and snow crystal growth.

The growth of snow crystals is dependent on the temperature and saturation of the environment. In the case of dendrites, Reiter's local two-dimensional model provides a realistic approach to the study of dendrite growth. In this paper we obtain a new geometric rule that incorporates interface control, a basic mechanism of crystallization that is not taken into account in the original Reiter model. By defining two new variables, growth latency and growth direction, our improved model gives a realistic model not only for dendrite but also for plate forms.

Solidification of a disk-shaped crystal from a weakly supercooled binary melt.

The physics of ice crystal growth from the liquid phase, especially in the presence of salt, has received much less attention than the growth of snow crystals from the vapor phase. The growth of so-called frazil ice by solidification of a supercooled aqueous salt solution is consistent with crystal growth in the basal plane being limited by the diffusive removal of the latent heat of solidification from the solid-liquid interface, while being limited by attachment kinetics in the perpendicular direction. This leads to the formation of approximately disk-shaped crystals with a low aspect ratio of thickness compared to radius, because radial growth is much faster than axial growth. We calculate numerically how fast disk-shaped crystals grow in both pure and binary melts, accounting for the comparatively slow axial growth, the effect of dissolved solute in the fluid phase, and the difference in thermal properties between solid and fluid phases. We identify the main physical mechanisms that control crystal growth and show that the diffusive removal of both the latent heat released and the salt rejected at the growing interface are significant. Our calculations demonstrate that certain previous parametrizations, based on scaling arguments, substantially underestimate crystal growth rates by a factor of order 10-100 for low aspect ratio disks, and we provide a parametrization for use in models of ice crystal growth in environmental settings.

Physical Improvements to a Mesoscopic Cellular Automaton Model for Three-Dimensional Snow Crystal Growth

We motivate and derive the dynamical rules for a computationally feasible three-dimensional cellular automaton model of snow crystal growth. The model improves upon points of weak physical connections identified in other similar models which have produced morphological features observed in many snow crystal photographs. A systematic survey of the morphologies resulting from our model illustrates the degree to which these features persist in our results, and the trends that appear as model parameters are varied.

Finite Element Approximation of One-Sided Stefan Problems with Anisotropic, Approximately Crystalline, Gibbs--Thomson Law

We present a finite-element approximation for the one-sided Stefan problem and the one-sided Mullins--Sekerka problem, respectively. The problems feature a fully anisotropic Gibbs--Thomson law, as well as kinetic undercooling. Our approximation, which couples a parametric approximation of the moving boundary with a finite-element approximation of the bulk quantities, can be shown to satisfy a stability bound, and it enjoys very good mesh properties, which means that no mesh smoothing is necessary in practice. In our numerical computations we concentrate on the simulation of snow crystal growth. On choosing realistic physical parameters, we are able to produce several distinctive types of snow crystal morphologies. In particular, facet breaking in approximately crystalline evolutions can be observed.

Numerical computations of faceted pattern formation in snow crystal growth

Faceted growth of snow crystals leads to a rich diversity of forms with 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 spacial dimensions using a computational method recently introduced by the present authors. We present both qualitative and quantitative computations. In particular, a linear relationship between tip velocity and supersaturation is observed. In our computations, surface energy effects, although small, have a pronounced effect on crystal growth. We compute solid plates, solid prisms, hollow columns, needles, dendrites, capped columns, and scrolls on plates. Although all these forms appear in nature, it is a significant challenge to reproduce them with the help of numerical simulations for a continuum model.

A ROBUST AND ACCURATE PHASE-FIELD SIMULATION OF SNOW CRYSTAL GROWTH

In this paper we introduce 6-fold symmetry crystal growth using new phase-field models based on the modified Allen-Cahn equation. The proposed method is a hybrid method which uses both analytic and numerical solutions. We then show this method can be extended to <TEX>$k$</TEX>-fold case. The Wulff construction procedure is provided to understand and predict the shape of crystals. We also present a detailed mathematical proof of the validity of the Wulff construction. For computational results, we verify the accuracy and efficiency of the method for snow crystal growth.

A Multisensor Approach Toward a Better Understanding of Snowfall Microphysics: The TOSCA Project

The Towards an Optimal estimation based Snow Characterization Algorithm (TOSCA) project addresses possible novel measurement synergies for deriving snowfall microphysical parameters from the ground by combining the unique information obtained from a suite of ground-based sensors: microwave radiometers (22–150 GHz), 24- and 36-GHz radar, lidar, and in situ optical disdrometer methods. During the winter of 2008/09, such instruments were deployed at the Environmental Research Station Schneefernerhaus (UFS; at 2650 m MSL) at the Zugspitze Mountain in Germany for deriving microphysical properties of snowfall. This contribution gives an overview of the measurements carried out and discusses the potential for the developments of synergetic retrieval algorithms for deriving snow water content within the vertical column. The identification of potentially valuable ground-based instrument synergy for the retrieval of snowfall parameters from the surface will also be of importance for the development of new space-borne observational techniques. Microwave radiometer measurements show that brightness temperature enhancements at 90 and 150 GHz are correlated with the radar-derived snow water path, which is supported by radiative transfer simulations. The synergy of these measurements toward an improved snow mass content, however, needs to be augmented by knowledge on water vapor, supercooled liquid water, particle size distribution, and shape, thus making clear the necessity of synergetic remote sensing and in situ measurements. The radiometric measurements also reveal the very frequent presence of supercooled water within snow clouds and its importance to microphysical diffusion and aggregation growth of snow crystals. Analysis of the disdrometer measurements shows a “secondary aggregation peak” around −12° to −15°C, a temperature range where the Wegener–Bergeron–Findeisen process is most effective and typically dendrite snow crystals forms dominate.

On stable parametric finite element methods for the Stefan problem and the Mullins–Sekerka problem with applications to dendritic growth

We introduce a parametric finite element approximation for the Stefan problem with the Gibbs–Thomson law and kinetic undercooling, which mimics the underlying energy structure of the problem. The proposed method is also applicable to certain quasi-stationary variants, such as the Mullins–Sekerka problem. In addition, fully anisotropic energies are easily handled. The approximation has good mesh properties, leading to a well-conditioned discretization, even in three space dimensions. Several numerical computations, including for dendritic growth and for snow crystal growth, are presented.

Lattice Boltzmann simulation of snow crystal growth in clouds

The Lattice Boltzmann (LB) method can be used to simulate aspects of chemical reactions such as mineral precipitation from a fluid phase or condensation from a vapor phase. The LB method has the advantage of allowing the shape of the condensing phase to evolve depending on local conditions rather than being specified, so that the controls on condensed phase grain shape can be studied simultaneously with the controls on chemical composition and growth rate. We have used the LB approach to simulate the growth of ice crystals from water vapor‐oversaturated air as a first step in developing methods for treating more complex chemical reaction problems, including isotopic effects. The formation of ice crystals (i.e., snow) in air is a classic problem in diffusion‐limited crystal growth. There are many complexities, but the process is attractive for modeling purposes because it involves only one chemical component and there is abundant information on reaction kinetics and the relationships between crystal morphology and growth conditions. In this paper we describe the LB approach used, and address strategies for properly conserving mass at a surface of a growing “crystal,” the scaling of the calculations to the actual physical problem, and the conditions for growth of dendritic versus compact crystals.

Modeling snow-crystal growth: A three-dimensional mesoscopic approach

We introduce a three-dimensional, computationally feasible, mesoscopic model for snow-crystal growth, based on diffusion of vapor, anisotropic attachment, and a boundary layer. Several case studies are presented that faithfully replicate most observed snow-crystal morphology, an unusual achievement for a mathematical model. In particular, many of the most striking physical specimens feature both facets and branches, and our model provides an explanation for this phenomenon. We also duplicate many other observed traits, including ridges, ribs, sandwich plates, and hollow columns, as well as various dynamic instabilities. The concordance of observed phenomena suggests that the ingredients in our model are the most important ones in the development of physical snow crystals.

A microstructural dry-snow metamorphism model for kinetic crystal growth

AbstractHistorically, dry-snow metamorphism has been classified by the thermal environment and thermodynamic processes in a snowpack. Snow experiencing predominantly macroscopic isothermal conditions develops different microstructure than snow subjected to large temperature gradients. As such, much previous research has been categorized by and limited to specific thermal conditions. The current research expands a generalized approach for the movement of heat and mass to include a snow crystal kinetic growth model. An existing spiral defect propagation theory for kinetic growth on simple faceted geometry is utilized. Primary crystal habit as a function of temperature is incorporated. A model of heat and mass transfer through an ice and pore structure is coupled with phase-change thermodynamics during kinetic growth. A kinetic growth microstructure model is developed and integrated into heat and mass transfer representations, which are solved using finite-difference techniques. The kinetic morphology model approximates frequently observed hopper-type crystals. The snow microstructure is allowed to change at every step, resulting in a transient description of kinetic growth metamorphism. Variable kinetic growth rates are demonstrated based on temperature and on crystallographic orientation relative to a temperature gradient. Crystals preferentially aligned with the temperature gradient have significantly higher growth rates, supporting previous observations of predominant crystal habits developing under temperature gradient conditions. Grain-size dispersion increase with time is demonstrated and supported experimentally in the literature. A dominant grain growth theory based on crystallographic orientation that has been previously postulated is supported. A broad range of metamorphic geometric parameters and thermal conditions may now be simulated with a single model.

Modeling snow crystal growth II: A mesoscopic lattice map with plausible dynamics

We present a local lattice model for the evolution of snow crystals that combines diffusion-limited aggregation with anisotropic attachment kinetics and an idealized quasi-liquid layer. Despite a voluminous modeling literature, this is apparently the first approach that successfully captures the essential form of core and tip instabilities, branch faceting, and other aspects of real snow crystal growth. As parameters are varied, our nearest neighbor system reproduces the basic features of most of the observed varieties of planar snowflakes and offers new insights into their genesis.