Application of Radon Transform to Multi-angle Measurements Made by the Research Scanning Polarimeter: Test of a Cloud Tomography Concept

Abstract:

The Research Scanning Polarimeter (RSP) is an airborne along-track scanner measuring the polarized and total reflectances in 9 spectral channels. Its uniquely high angular resolution coupled with the high frequency of measurements allows for characterization of liquid water cloud droplet sizes using the polarized rainbow structure, and also provides geometric constraints on the cumulus cloud's 2D cross section between a number of tangent lines of view. The latter yields cloud geometric shape estimates which depend on thresholds in total reflectance used to separate bright cloud from darker background in each RSP scan. The nested family of "cloud shapes" corresponding to a range of reflectance thresholds can be viewed as level curves of an abstract 2D "reflectance distribution" (RD), which can be used for interpolation of the observed reflectances to any virtual line of view (chord). This allows us to create a complete regularly-spaced set of chords to be used in Radon Transform (the mathematical basis of the X-ray computer tomography). Our chord’s value is the maximum of RD along it, while in Radon Transform the chord’s value is the integral of the spatial distribution (to be determined) along the chord. Thus, we convert chord’s reflectances into directional optical thicknesses, which are integrals of the scattering coefficient along these chords. This conversion can be made using the regression between nadir-view reflectances and cloud optical thickness retrievals from the standard RSP product. Then the inverse Radon Transform will be used to obtain 2D spatial distribution of the scattering coefficient. An extension of this method to a pair of spectral channels (absorbing and non-absorbing) can be contemplated. It may be able to provide distributions of droplet size and number concentration. We will apply the proposed algorithm first to synthetic data (LES cloud model coupled with 3D RT computations) where scattering-coefficient distribution is known, and learn from the comparison how to improve the algorithm (mitigating shadowing, in particular). After that we plan to apply the new technique to the real RSP measurements from NASA's Cloud, Aerosol and Monsoon Processes Philippines Experiment (CAMP2Ex) conducted in 2019.