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  1. 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 andmore »bin scheme, with low error, if an equivalent volume spherical radius is provided.« less
  2. 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.
  3. 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, theremore »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.« less
  4. 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 tomore »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.« less