Semi-Analytic Functions to Calculate the Deposition Coefficients for Ice Crystal Vapor Growth in Bin and Bulk Microphysical Models.

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.

Approximate Models for Lateral Growth on Ice Crystal Surfaces during Vapor Depositional Growth

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.

Estimating Surface Attachment Kinetic and Growth Transition Influences on Vapor-Grown Ice Crystals

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 si between 3% and 29%. These growth data are analyzed with two methods devised to estimate the deposition coefficient α without the direct use of si. Measurements of si 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 si, with α rising (falling) with increasing si for homogeneously (heterogeneously) frozen ice. Analysis of the normalized mass growth rates reveals that heterogeneously frozen crystals grow near the maximum rate at low si, but show increasingly inhibited (low α) growth at high si. 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.

Fluvial landscape evolution controlled by the sediment deposition coefficient: Estimation from experimental and natural landscapes

The evolution of a fluvial landscape is a balance between tectonic uplift, fluvial erosion, and sediment deposition. The erosion term can be expressed according to the stream power model, stating that fluvial incision is proportional to powers of river slope and discharge. The deposition term can be expressed as proportional to the sediment flux divided by a transport length. This length can be defined as the water flux times a scaling factor ζ. This factor exerts a major control on the river dynamics, on the spacing between sedimentary bedforms, or on the overall landscape erosional behavior. Yet, this factor is difficult to measure either in the lab or in the field. Here, we propose a new formulation for the deposition term based on a dimensionless coefficient, G, which can be estimated at the scale of a landscape from the slopes of rivers at the transition between a catchment and its fan. We estimate this deposition coefficient from 29 experimental catchment–alluvial fan systems and 68 natural examples. Based on our data set, we support the idea of Davy and Lague (2009) that G is a relevant parameter to characterize the erosional and transport mode of a fluvial landscape, which can be field calibrated, with a continuum from detachment-limited (G = 0) to transport-limited behavior (G >0.4 from the studied examples).

Analytical Solution for One-Dimensional Transport of Particles considering Dispersion in Deposition Kinetics

The study of particle transport in porous media is of great significance for pollution mitigation, grouting reinforcement, municipal solid waste landfill management, and groundwater exploitation. We developed an analytical solution for a corrected convection-dispersion model that takes into account the effects of dispersion on deposition kinetics with regard to the particle concentration decay type. The rationality and correctness of the solution were verified using time, distance, deposition coefficient, diffusion coefficient, and decay coefficient. As the time increased, the particle concentration increased from zero to the peak value, then decreased to zero. However, as distance increased, the peak value of particle concentration gradually decreased. The deposition coefficient affected the magnitude of the peak value and the distance corresponding to the peak value. In addition, the greater the attenuation coefficient, the smaller the peak value. Overall, our method’s prediction results showed that considering the effect of dispersion on deposition kinetics produces better results than when this is not considered.