Utilization of Equivalent Spheres of Equal Volume and Surface Area for Estimation of the Asymmetry Parameter from Microphysical Observations

Understanding the scattering properties of complex ice particles is essential to understanding the role of clouds in climate. Ray-tracing studies (Fu, 1998; Takano and Liou, 1989a; Takano and Liou, 1995) have focused on simple ice crystal shapes such as columns and plates. The scattering properties of highly complex ice crystals would be computationally prohibitive to calculate using traditional ray-tracing techniques. Korolev and Sussman, (2000) noted that most ice particles observed in clouds are irregular in shape. Examples of irregular ice crystals as well as rarely seen pristine ice crystals observed by the Stratton Park Engineering Company (SPEC Inc.) cloud particle imager probe (CPI) during the Cirrus Regional Study of Tropical Anvils and Cirrus Layers Florida Area Cirrus Experiment (CRYSTAL-FACE) field project in southern Florida in July 2002 are shown in figure 1. To simplify cloud radiative property calculations, cloud particles are often represented as equivalent spheres. This approach facilitates the use of the computationally simple Mie theory for the calculation of the scattering properties. Ice particles have been represented by spheres with equal volume as well as spheres with equal projected area. These equivalent sphere theories require one sphere for each particle in the cloud. Liou and Takano (1994) have shown that equal volume and equal area spheres are inadequate for modeling purposes. The third equivalent sphere type, studied by Grenfell and Warren (1999), Neshyba et al (2003) and Grenfell et al (2005), uses spheres with an equal volume to surface area ratio (hereafter EVSA). Grenfell and Warren (1999) give a numerical description of EVSA spheres. For the EVSA sphere theory, numerous spheres can be used to represent single complex ice crystals. The inside surface of internal or concave structures is represented by outside surfaces of the spheres (Neshyba et al, 2003), giving the EVSA sphere population a higher optical depth than the ice cloud that it is representing. Two-stream radiation transfer models use the asymmetry parameter and cloud optical depth to Figure 1: Ice particles observed during the CRYSTAL-FACE field project. The ice crystals were imaged with the Cloud Particle Imager (CPI) probe. Examples of highly irregular particles are shown above, some pristine particles (which represent less than 0.1% of observed particles during CRYSTAL-FACE) are shown below.