The fractal dimension of ice cloud particles and particle ensembles for the determination of mass dimensional relationships

In some circumstances, mass-dimensional relationships for ice crystal ensembles can be determined by fractal geometry techniques. This is accomplished by using projected area measurements to determine the exponent in the area-dimensional relationship. The area dimensional exponent can then be converted to account for the third dimension. This technique has been shown to work well in cases with high concentrations of ice crystal aggregates. Some ice clouds are dominated by single particle types such as bullet rosettes, needles, plates or dendrites. The fractal dimension of individual pristine particles can be easily calculated and is shown to agree with the fractal dimension determined by using the area-fractal technique calculated for an ensemble of pristine particles in different stages of growth. The fractal dimension of aircraft particle ensembles of pristine and irregular particles are calculated in an effort to better understand the changing properties of cloud particles in different temperature and particle growth regimes. Results are used to determine mass dimensional relationships which are tested by calculating the total ice water content (IWC) for particle size distributions and comparing the results to directly measured IWC values.