The dimensional characteristics of ice crystal aggregates from fractal geometry

Ice crystal aggregates imaged by aircraft particle imaging probes often appear to be fractal in nature. As such, their dimensional properties, mass, and projected area can be related using fractal geometry. In cloud microphysics, power-lawmass (m)- and area (A)-dimensional (D) relationships (e.g.,m=aD^b) incorporate different manifestations of the fractal dimension as the exponent (b). In this study a self-consistent technique is derived for determining the mass and projected area properties of ice particles from fractal geometry. A computer program was developed to simulate the crystal aggregation process. The fractal dimension of the simulated aggregates was estimated using the box counting method in three dimensions as well as for two-dimensional projected images of the aggregates. The two- and three-dimensional fractal dimension values were found to be simply related. This relationship enabled the development of mass-dimensional relationships analytically from cloud particle images. This technique was applied to data collected during two field projects. The exponent in the mass-dimensional relationship, the fractal dimension,was found to be between 2.0 and 2.3with a dependence on temperature noted for both datasets. The coefficient a in the mass-dimensional relationships was derived in a self-consistentmanner. Temperature-dependent mass-dimensional relationships have been developed. Cloud ice water content estimated using the temperature-dependent relationship and particle size distributions agreed well with directly measured ice water content values. The results are appropriate for characterizing cloud particle properties in clouds with high concentrations of ice crystal aggregates.