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Observations and measurements show that crystals remain relatively compact at low ice supersaturations, but become increasingly hollowed and complex as the ice supersaturation rises. Prior measurements at temperatures >−25°C indicate that the transition from compact, solid ice to morphologically complex crystals occurs when the excess vapor density exceeds a threshold value of about 0.05 g m⁻³. A comparable threshold is not available at low temperatures. A temperature-dependent criterion for the excess vapor density threshold (Δρ_thr) that defines morphological transformations to complex ice is derived from laboratory measurements of vapor grown ice at temperatures below −40°C. This criterion depends on the difference between the equilibrium vapor density of liquid () and ice (ρ_ei) multiplied by a measurement-determined constant,. The new criterion is consistent with prior laboratory measurements, theoretical estimates, and it reproduces the classical result of about 0.05 g m⁻³above −25°C. Since Δρ_thrdefines the excess vapor density above which crystals transition to a morphologically complex (lower density) growth mode, we can estimate the critical supersaturation (s_crit) for step nucleation during vapor growth. The derived values ofs_critare consistent with previous measurements at temperatures above −20°C. No direct measurements ofs_critare available for temperatures below −40°C; however, our derived values suggest some measurement-based estimates may be too high while estimates from molecular dynamics simulations may be too low.

 

Abstract An electrodynamic levitation thermal-gradient diffusion chamber was used to grow 268 individual, small ice particles (initial radii of 8–26 μ m) from the vapor, at temperatures ranging from −65° to −40°C, and supersaturations up to liquid saturation. Growth limited by attachment kinetics was frequently measured at low supersaturation, as shown in prior work. At high supersaturation, enhanced growth was measured, likely due to the development of branches and hollowed facets. The effects of branching and hollowing on particle growth are often treated with an effective density ρ eff . We fit the measured time series with two different models to estimate size-dependent ρ eff values: the first model decreases ρ eff to an asymptotic deposition density ρ dep , and the second models ρ eff by a power law with exponent P . Both methods produce similar results, though the fits with ρ dep typically have lower relative errors. The fit results do not correspond well with models of isometric or planar single-crystalline growth. While single-crystalline columnar crystals correspond to some of the highest growth rates, a newly constructed geometric model of budding rosette crystals produces the best match with the growth data. The relative frequency of occurrence of ρ dep and P values show a clear dependence on ice supersaturation normalized to liquid saturation. We use these relative frequencies of ρ dep and P to derive two supersaturation-dependent mass–size relationships suitable for cloud modeling applications. 

Abstract. Ice growth from vapor deposition is an important process for the evolution of cirrus clouds, but the physics of depositional ice growth at the low temperatures (<235 K) characteristic of the upper troposphere and lower stratosphere is not well understood. Surface attachment kinetics, generally parameterized as a deposition coefficient αD, control ice crystal habit and also may limit growth rates in certain cases, but significant discrepancies between experimental measurements have not been satisfactorily explained. Experiments on single ice crystals have previously indicated the deposition coefficient is a function of temperature and supersaturation, consistent with growth mechanisms controlled by the crystal's surface characteristics. Here we use observations from cloud chamber experiments in the Aerosol Interactions and Dynamics in theAtmosphere (AIDA) aerosol and cloud chamber to evaluate surface kinetic models in realistic cirrus conditions. These experiments have rapidly changing temperature, pressure, and ice supersaturation such that depositional ice growth may evolve from diffusion limited to surface kinetics limited over the course of a single experiment. In Part 1, we describe the adaptation of a Lagrangian parcel model with the Diffusion Surface Kinetics Ice Crystal Evolution (DiSKICE) model (Zhang and Harrington, 2014) to the AIDA chamber experiments. We compare the observed ice water content and saturation ratios to that derived under varying assumptions for ice surface growth mechanisms for experiments simulating ice clouds between 180 and 235 K and pressures between 150 and 300 hPa. We found that both heterogeneous and homogeneous nucleation experiments at higher temperatures (>205 K) could generally be modeled consistently with either a constant deposition coefficient or the DiSKICE model assuming growth on isometric crystals via abundant surface dislocations. Lower-temperature experiments showed more significant deviations from any depositional growth model, with different ice growth rates for heterogeneous and homogeneous nucleation experiments. 

Abstract Measurements show that after facets form on frozen water droplets, those facets grow laterally across the crystal surface leading to an increase in volume and surface area with only a small increase in maximum dimension. This lateral growth of the facets is distinctly different from that predicted by the capacitance model and by the theory of faceted growth. In this paper we develop two approximate theories of lateral growth, one that is empirical and one that uses explicit growth mechanisms. We show that both theories can reproduce the overall features of lateral growth on a frozen, supercooled water droplet. Both theories predict that the area-average deposition coefficient should decrease in time as the particle grows, and this result may help explain the divergence of some prior measurements of the deposition coefficient. The theories may also explain the approximately constant mass growth rates that have recently been found in some measurements. We also show that the empirical theory can reproduce the lateral growth that occurs when a previously sublimated crystal is regrown, as may happen during the recycling of crystals in cold clouds. 

Abstract Numerical cloud models require estimates of the vapor growth rate for ice crystals. Current bulk and bin microphysical parameterizations generally assume that vapor growth is diffusion limited, though some parameterizations include the influence of surface attachment kinetics through a constant deposition coefficient. A parameterization for variable deposition coefficients is provided herein. The parameterization is an explicit function of the ambient ice supersaturation and temperature, and an implicit function of crystal dimensions and pressure. The parameterization is valid for variable surface types including growth by dislocations and growth by step nucleation. Deposition coefficients are predicted for the two primary growth directions of crystals, allowing for the evolution of the primary habits. Comparisons with benchmark calculations of instantaneous mass growth indicate that the parameterization is accurate to within a relative error of 1%. Parcel model simulations using Lagrangian microphysics as a benchmark indicate that the bulk parameterization captures the evolution of mass mixing ratio and fall speed with typical relative errors of less than 10%, whereas the average axis lengths can have errors of up to 20%. The bin model produces greater accuracy with relative errors often less that 10%. The deposition coefficient parameterization can be used in any bulk and bin scheme, with low error, if an equivalent volume spherical radius is provided. 

Abstract In this study, processes that broaden drop size distributions (DSDs) in Eulerian models with two-moment bin microphysics are analyzed. Numerous tests are performed to isolate the effects of different physical mechanisms that broaden DSDs in two- and three-dimensional Weather Research and Forecasting Model simulations of an idealized ice-free cumulus cloud. Sensitivity of these effects to modifying horizontal and vertical model grid spacings is also examined. As expected, collision–coalescence is a key process broadening the modeled DSDs. In-cloud droplet activation also contributes substantially to DSD broadening, whereas evaporation has only a minor effect and sedimentation has little effect. Cloud dilution (mixing of cloud-free and cloudy air) also broadens the DSDs considerably, whether or not it is accompanied by evaporation. This mechanism involves the reduction of droplet concentration from dilution along the cloud’s lateral edges, leading to locally high supersaturation and enhanced drop growth when this air is subsequently lifted in the updraft. DSD broadening ensues when the DSDs are mixed with those from the cloud core. Decreasing the horizontal and vertical model grid spacings from 100 to 30 m has limited impact on the DSDs. However, when these physical broadening mechanisms (in-cloud activation, collision–coalescence, dilution, etc.) are turned off, there is a reduction of DSD width by up to ~20%–50% when the vertical grid spacing is decreased from 100 to 30 m, consistent with effects of artificial broadening from vertical numerical diffusion. Nonetheless, this artificial numerical broadening appears to be relatively unimportant overall for DSD broadening when physically based broadening mechanisms in the model are included for this cumulus case. 

There are few measurements of the vapor growth of small ice crystals at temperatures below -30°C. Presented here are mass-growth measurements of heterogeneously and homogeneously frozen ice particles grown within an electrodynamic levitation diffusion chamber at temperatures between -44 and -30°C and supersaturations ( s i ) between 3 and 29%. These growth data are analyzed with two methods devised to estimate the deposition coefficient ( α) without the direct use of s i . Measurements of s i are typically uncertain, which has called past estimates of α into question. We find that the deposition coefficient ranges from 0.002 to unity and is scattered with temperature, as shown in prior measurements. The data collectively also show a relationship between α and s i , with α rising (falling) with increasing s i for homogeneously (heterogeneously) frozen ice. Analysis of the normalized mass growth rates reveals that heterogeneously-frozen crystals grow near the maximum rate at low s i , but show increasingly inhibited (low α) growth at high s i . Additionally, 7 of the 17 homogeneously frozen crystals cannot be modeled with faceted growth theory or constant α. These cases require the growth mode to transition from efficient to inefficient in time, leading to a large decline in α. Such transitions may be, in part, responsible for the inconsistency in prior measurements of α. 

A major challenge in numerical weather prediction models is the ability to accurately simulate the microphysical properties and growth of ice hydrometeors in clouds. Eulerian bulk microphysics schemes in these models tend to obscure the properties and evolution of individual ice crystals, often resulting in inaccurate simulations of storm structures. To address this issue, this study presents a novel ice crystal trajectory growth (ICTG) model that simultaneously grows and advects individual ice crystals while tracking their evolving properties along their trajectories. The model is evaluated on a 3D quasi‐idealized leading‐convective, trailing‐stratiform squall line simulation. The ICTG model successfully produced a spatial distribution of ice crystal trajectories consistent with the simulated reflectivity structure of the storm above the melting level. Smaller initialized crystals (d ≤ 0.1 mm) were largely transported to the anvil and the trailing stratiform region. One primary trajectory involved sustained growth in the stratiform mesoscale updraft for ∼1.5 hr, resulting in a density reduction down to 600 kg m⁻³, a final particle size greater than 0.9 mm, and potential branching. In contrast, larger initialized crystals (d ≥ 0.5 mm) collected more rime and fell out primarily in the leading convective line. The ICTG model's realistic production of varied crystal growth properties owing to differences in transport and initial size suggests that it can be a valuable tool for learning about ice microphysical processes in a variety of cold cloud systems.

 

We present an analysis of long‐term data collected at Utqiaġvik, Alaska, to explore the impacts of cloud processes on the probability of finding supercooled water given cloud temperature,P(L|T), in the topmost unseeded liquid‐bearing layers.P(L|T) has local minima at temperatures around −6°C and −15°C. Simulations using habit‐evolving ice microphysics models suggest that these minima are the result of efficient vapor growth by non‐isometric habits found at these temperatures. We conclude that habit‐dependent vapor growth of ice crystals modulates the macrophysical occurrence of supercooled water in polar clouds, the effect of which should be included in model parametrizations to avoid biases and/or error compensation. Our methodology is adaptable for spherical ice treatments implemented in models (example parametrizations provided), amenable for use with satellite measurements to give global impartial observational targets for model evaluations, and may allow empirical characterization of bulk responses to seeding and possibly secondary ice effects.