Parameterization of Photon Tunneling with Application to Ice Cloud Optical Properties at Terrestrial Wavelengths

Sometimes deep physical insights can be gained through the comparison of two theories of light scattering. Comparing van de Hulst's anomalous diffraction approximation (ADA) with Mie theory yielded insights on the behavior of the photon tunneling process that resulted in the modified anomalous diffraction approximation (MADA). (Tunneling is the process by which radiation just beyond a particle's physical cross-section may undergo large angle diffraction or absorption, contributing up to 40% of the absorption when wavelength and particle size are comparable.) Although this provided a means of parameterizing the tunneling process in terms of the real index of refraction and size parameter, it did not predict the efficiency of the tunneling process, where an efficiency of 100% is predicted for spheres by Mie theory. This tunneling efficiency, Tf, depends on particle shape and ranges from 0 to 1.0, with 1.0 corresponding to spheres. Similarly, by comparing absorption efficiencies predicted by the Finite Difference Time Domain Method (FDTD) with efficiencies predicted by MADA, Tf was determined for nine different ice particle shapes, including aggregates. This comparison confirmed that Tf is a strong function of ice crystal shape, including the aspect ratio when applicable. Tf was lowest (< 0.36) for aggregates and plates, and largest (> 0.9) for quasi- spherical shapes. A parameterization of Tf was developed in terms of (1) ice particle shape and (2) mean particle size regarding the large mode (D > 70 mm) of the ice particle size distribution. For the small mode, Tf is only a function of ice particle shape. When this Tf parameterization is used in MADA, absorption and extinction efficiency differences between MADA and FDTD are within 14% over the terrestrial wavelength range 3-100 mm for all size distributions and most crystal shapes likely to be found in cirrus clouds. Using hyperspectral radiances, it is demonstrated that Tf can be retrieved from ice clouds. Since Tf is a function of ice particle shape, this may provide a means of retrieving qualitative information on ice particle shape.