Characterization of ice crystals in clouds by simple mathematical expressions based on successive modification of simple shapes

The technique based on the concept of successive modification of simple shapes using elementary mathematical functions to represent the shape and size of ice crystals in clouds is discussed. Two hypothetical samples of ice crystals, a single-habit sample of hexagonal plates and a multihabit crystal sample, are generated using a formula developed previously to illustrate the use of this technique in generating ice crystal ensembles in cloud models. Next, a new expression representing columnar ice crystals is described. Finally, two new expressions that can be used to generate the three-dimensional combination of bullets and spatial dendrites are described. The parameters involved in these expressions are expected to be useful in characterizing the shape and size spectra of ice crystals found in cirrus clouds.