Retrieval of tropical cirrus thermal optical depth, crystal size, and shape using a dual-view instrument at 3.7 and 10.8 mu m

In this paper the authors derive thermal optical depth at 3.7 and 10.8 mu m for tropical cirrus utilizing Along Track Scanning Radiometer data under n ighttime conditions. By analytically solving the equation of radiative tran sfer, inclusive of scattering, a pair of nonlinear equations can be solved for the optical depth. Stable and unique solutions for the optical depth ar e found by combining nadir and forward (55 degrees) views. The accuracy of the analytic solution is compared with solutions from a numerical radiative transfer model assuming an isothermal cirrus cloud. Numerical solutions fo r two nonisothermal cirrus clouds are also compared with the analytic solut ion for an equivalent mean cloud temperature. The numerical model uses appr opriate hexagonal column scattering phase functions at 3.7 and 10.8 mu m. T he 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 t hen applied to obtain the likely true optical depth. The retrieved true optical depths at 3.7 and 10.8 mu m are combined to form a ratio that is related to the ratio of extinction coefficients between th e two wavelengths and thus to the crystal size and shape. Predictions of cr ystal size and shape are made for tropical cirrus using anomalous diffracti on theory as geometric ray tracing is nor applicable for typical ice partic les at thermal wavelengths. Crystal median mass dimension in the range 40 t o 110 mu m is derived for columns and planar polycrystals, whereas for rose ttes predicted sizes are much larger than this range and outside the range found by the Central Equatorial Pacific Experiment (CEPEX) for crystals nea r 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 a nd planar polycrystals, a finding consistent with the CEPEX field results. In addition to the optical depth ratio between 3.7 and 10.8 mu m being sens itive to crystal size and shape, it is shown that this sensitivity can be u sed to locate underlying water clouds below semitransparent cirrus during n ightime conditions.