LATTICE BOLTZMANN SIMULATION OF OXYGEN- AND HYDROGEN-ISOTOPE FRACTIONATIONS DURING SNOW CRYSTAL FORMATION

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. 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. We use a 2D lattice Boltzmann model to simulate 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. 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. Dendritic crystals are constrained to be relatively large, with dimension much greater than D/k. The results 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.