A Model Predicting the Evolution of Ice Particle Size Spectra and Radiative Properties of Cirrus Clouds. Part I: Microphysics

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Abstract
A Lagrangian time-dependent three-dimensional model was developed that predicts the evolution of ice particle size spectra in cirrus clouds in terms of the growth processes of vapor diffusion and aggregation, as well as the cloud updraft profile. This was done by deriving moment conservation equations from a form of the ice particle number density equation, and parameterizing the moment conservation equations. Size distributions were parameterized by the form N(D) = N0Dv exp(−λD), where λ and N0 are functions of the growth processes. Growth by diffusion and aggregation were formulated to depend on the percentages of spatial and columnar crystal habits at a given level in the cloud. Two cirrus cloud field studies were simulated by the model, where the model was run in the one-dimensional, height-dependent mode that assumes steady-state, horizontally homogeneous ice water contents. Predicted and observed ice particle size spectra compared favorably. This implied that ice particles at lower levels evolved from higher levels. Although cirrus often exhibit banded layers, as found in both case studies, it appears that evaporating ice falling from a higher layer will initiate ice evolution in moist, lower layers. Model simulations indicated cloud updrafts have the general effect of increasing ice particle concentrations by increasing their residence time in the cloud. Size sorting occurs, by which the smaller ice particles are preferentially retained, and mean ice particle sizes decrease. The model indicates that transitions in ice crystal habit may strongly influence the evolution of ice particle size spectra. A transition from columnar to spatial habits produces a shift toward smaller but more numerous ice crystals. This has also been observed in field studies. It could not be determined whether aggregation was an important ice particle growth process, since model simulations using both high and low aggregation efficiencies yielded similar agreement with field data. The model described is fundamentally analytical and is computationally efficient. It may be used in large-scale models and may be useful in describing cloud-radiative interactions.

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