Circular polarization of scattered solar radiation is essentially zero for almost all aerosol and cloud cases. Required conditions for non-zero circular polarization include multiple-scattering and large scatterer size relative to wavelength. The single-scattering of incident solar radiation can produce linearly polarized light but not circularly polarized light. A second scattering event can transform some of the linearly polarized light into circularly polarized light. Additional scattering events can both create and destroy circular polarization via the transformation process with linear polarization. The peak in circular polarization ratio magnitude occurs at the optical depth for which the multiplescattering processes have maximized its creation-to-destruction rate. Provided multiple-scattering has occurred, circular polarization can only exist for scatterers of large size relative to the wavelength. For aerosols, this implies desert dust or oceanic aerosols and short wavelength observations (i.e., less than 0.5μm). All cloud particles are considered large as they are roughly an order of magnitude larger than aerosols.
This paper presents a conceptual approach toward the remote sensing of cirrus cloud particle size and optical depth using the degree of polarization and polarized reflectance associated with the first three Stokes parameters <i>I</i>, <i>Q</i>, and <i>U</i> for the 0.865 and 2.25 μm wavelengths. A vector line-by-line equivalent radiative transfer program including the full Stokes parameters based on the adding method was developed. The retrieval algorithm employs the steepest descent method in the form of a series of numerical iteration procedures to search for the simulated polarization parameters that best match the measured polarization parameters. Sensitivity studies were performed to investigate the behavior of phase matrix elements as functions of scattering angles for three ice crystal size-shape combinations. Overall, each phase matrix element shows some sensitivity toward ice crystal shape, size, and suface roughness due to the various optical effects. Synthetic retrievals reveal that the retrieval algorithm itself is highly accurate, while polarimetric and radiometric error sources cause very small retrieval errors. Finally, an illustrative example of applying the retrieval algorithm to airborne POLDER data during EUCREX is presented.
To support the verification and implementation of the Visible/Infrared Imaging/Radiometric Suites algorithms used for inferring cloud environmental data records, an inter-comparison effor has been carried out to assess the consistency between the simulated cloudy radiances/relectances from the University of California at Los Angeles line-by-line equivalent radiative transfer model (UCLA-LBLE RTM) and those from the Moderate-Resolution Transmission Model (MODTRAN) with the 16-stream Discrete Ordinate Radiative Transfer Model (DISORT) incorporated. For typical ice and water cloud optical depths and particle sizes, we find discrepancies in the visible and near-infrared reflectances from the two models, presumably due to the difference in phase function (non-spherical vs. Henyey-Greenstein), different numbers of phase function expansion terms (16-term vs. 200-term), and different treatment of forward peak truncation in each model. Using MODTRAN4, we also find substantial differences in the infrared radiances for optically thick clouds. These differences led to the discovery by MODTRAN4 developers of an inconsistency in the MODTRAN4/DISORT interface. MODTRAN4 developers corrected the inconsistency, which provided dramatic reductions in the differences between the two radiative transfer models. The comparison not only impacts the prospective test plan for the VIIRS cloud algorithms, but also leads to improvements in future MODTRAN releases.
We have developed a retrieval scheme for the inference of the emissivity and temperature of cirrus clouds using the data obtained from the advanced very high resolution radiometer (AVHRR) 3.7 and 10.9 micrometers channels. The scheme, which is applicable to the entire day, is based on the numerical solution of a set of nonlinear algebraic equations that are derived from the theory and parameterizations of infrared radiative transfer. The solution involves an effective extinction ratio for the two wavelengths, which is dependent on ice crystal size distribution. Based on radiative transfer calculations and cloud physics observations, the cloud optical depth and the ice crystal size distribution in terms of mean effective size can be determined from cloud emissivity and cloud temperature, respectively.