Lattice Boltzmann Simulation of Water Isotope Fractionation During Growth of Ice Crystals in Clouds
Abstract
The isotopic composition of precipitation, especially that of snow, plays a special role in the global hydrological cycle and in reconstruction of past climates using polar ice cores. The fractionation of the major water isotope species (HHO, HDO, HHO-18) during ice crystal formation is critical to understanding the global distribution of isotopes in precipitation. Ice crystal growth in clouds is traditionally treated with a spherically- symmetric steady state diffusion model, with semi-empirical modifications added to account for ventilation and for complex crystal morphology. Although it is known that crystal growth rate, which depends largely on the degree of vapor over-saturation, determines crystal morphology, there are no existing quantitative models that directly relate morphology to the vapor saturation factor. Since kinetic (vapor phase diffusion-controlled) isotopic fractionation also depends on growth rate, there should be a direct relationship between vapor saturation, crystal morphology, and crystal isotopic composition. We use a 2D Lattice-Boltzmann model to simulate diffusion-controlled ice crystal growth from vapor- oversaturated air. In the model, crystals grow solely according to the diffusive fluxes just above the crystal surfaces, and hence crystal morphology arises from the initial and boundary conditions in the model and does not need to be specified a priori. The input parameters needed are the isotope-dependent vapor deposition rate constant (k) and the water vapor diffusivity in air (D). The values of both k and D can be computed from kinetic theory, and there are also experimentally determined values of D. The deduced values of k are uncertain to the extent that the sticking coefficient (or accommodation coefficient) for ice is uncertain. The ratio D/k is a length that determines the minimum scale of dendritic growth features and allows us to scale the numerical calculations to atmospheric conditions using a dimensionless Damkohler number: Da = kh/D, where h is the width of the 2D calculation domain. Varying the nondimensional Da in the model is equivalent to varying the scale (h) in the model. Our calculations confirm that the crystal/vapor isotopic fractionation approaches the equilibrium value, and the crystals are compact (circular in 2D) as the saturation factor approaches unity (S= 1.0). At higher oversaturation (e.g. S = 1.2), dendritic crystals of millimeter size develop on timescales appropriate to cloud processes, the isotopic fractionations are dominated by kinetic effects, and similar to those predicted by the spherical diffusion model. Dendritic crystals are constrained to be relatively large, with dimension much greater than D/k. The most difficult aspect of the modeling is to account for the large density difference between air and ice, which requires us to use a fictitious higher density for the vapor-oversaturated air and scale the crystal growth time accordingly. A different approach, using a larger scale simulation to derive boundary conditions for a nested smaller scale calculation is in progress. The results to date clarify the controls on dendritic crystal growth, the relationships between saturation state, growth rate, crystal morphology and isotopic fractionation, and provide limits on the value of the accommodation coefficient.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2006
- Bibcode:
- 2006AGUFM.H54D..08L
- Keywords:
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- 1009 Geochemical modeling (3610;
- 8410);
- 1012 Reactions and phase equilibria (3612;
- 8412);
- 1847 Modeling;
- 1854 Precipitation (3354);
- 1899 General or miscellaneous