Retrieval of Tropical Cirrus Thermal Optical Depth, Crystal Size, and Shape Using a Dual-View Instrument at 3.7 and 10.8 μm

Abstract

In this paper the authors derive thermal optical depth at 3.7 and 10.8 ?m for tropical cirrus utilizing Along Track Scanning Radiometer data under nighttime conditions. By analytically solving the equation of radiative transfer, inclusive of scattering, a pair of nonlinear equations can be solved for the optical depth. Stable and unique solutions for the optical depth are found by combining nadir and forward (55°) views. The accuracy of the analytic solution is compared with solutions from a numerical radiative transfer model assuming an isothermal cirrus cloud. Numerical solutions for two nonisothermal cirrus clouds are also compared with the analytic solution for an equivalent mean cloud temperature. The numerical model uses appropriate hexagonal column scattering phase functions at 3.7 and 10.8 ?m. The largest analytic model error is shown to occur at nadir, and it is shown that this error is not overly sensitive to crystal size and is independent of cloud-top temperature. A correction to the retrieved optical depth is then applied to obtain the likely true optical depth. The retrieved true optical depths at 3.7 and 10.8 ?m are combined to form a ratio that is related to the ratio of extinction coefficients between the two wavelengths and thus to the crystal size and shape. Predictions of crystal size and shape are made for tropical cirrus using anomalous diffraction theory as geometric ray tracing is not applicable for typical ice particles at thermal wavelengths. Crystal median mass dimension in the range 40 to 110 ?m is derived for columns and planar polycrystals, whereas for rosettes predicted sizes are much larger than this range and outside the range found by the Central Equatorial Pacific Experiment (CEPEX) for crystals near the tops of tropical cirrus. The authors therefore conclude that near the tops of tropical cirrus the crystal habits are most likely to be columns and planar polycrystals, a finding consistent with the CEPEX field results. In addition to the optical depth ratio between 3.7 and 10.8 ?m being sensitive to crystal size and shape, it is shown that this sensitivity can be used to locate underlying water clouds below semitransparent cirrus during nightime conditions.