Modeling Both Active and Passive Microwave Remote Sensing of Snow Using Dense Media Radiative Transfer (DMRT) Theory With Multiple Scattering and Backscattering Enhancement

In this paper, we incorporate the cyclical terms in dense media radiative transfer (DMRT) theory to model combined active and passive microwave remote sensing of snow over the same scene. The inclusion of cyclical terms is crucial if the DMRT is used to model both the active and passive contributions with the same model parameters. This is a necessity when setting out on a joint active/passive retrieval. Previously, the DMRT model has been applied to active and passive separately, and in each case with a separate set of model parameters. The traditional DMRT theory only includes the ladder terms of the Feynman diagrams. The cyclical terms are important in multiple volume scattering and volume-surface interactions. This leads to backscattering enhancement which represents itself as a narrow peak centered at backward direction. This effect is of less significance in passive remote sensing since emissivity is relating to the angular integral of bistatic scattering coefficients. The inclusion of cyclical terms in first-order radiative transfer (RT) accounts for the enhancement of the double bounce contribution and makes the results the same as that of distorted Born approximation in volume-surface interactions. In this paper, we develop the methodology of cyclical corrections within the framework of DMRT beyond first order to all orders of multiple scattering. The active DMRT equation is solved using a numerical iterative approach followed by cyclical corrections. Both quasi-crystalline approximation (QCA)-Mie theory with sticky spheres and bicontinuous media scattering model are used to illustrate the results. The cyclical correlation introduces around 1 dB increase in backscatter with a moderate snowpack optical thickness of similar to 0.2. The bicontinuous/DMRT model is next applied to compare with data acquired in the Nordic Snow Radar Experiment (NoSREx) campaign in the snow season of 2010-2011. The model results are validated against coincidental active and passive measurements using the same set of physical parameters of snow in all frequency and polarization channels. Results show good agreement in multiple active and passive channels.