Multiple scattering effects in vegetated surfaces at L-band and C-band for remote sensing of soil moisture

The goal of the NASA SMAP L-band Active and Passive mission is to retrieve soil moisture with 4% accuracy for vegetated surfaces that have vegetation water content (VWC) less than 5 kg/m2. The satellite was launched in January 2015. After the failure of the radar on July 7, 2015, there has been increasing interest in using the Sentinel C-band radar data for the active part of the mission. In using a physical model at L-band and C-band to treat the vegetation effects for such VWC, the common approaches were the distorted Born approximation [1] and the radiative transfer theory [2] under the single scattering approximation. However, the distorted Born approximation assumes small optical thickness which is not valid at C-band [3]. In treating the scattering from a collection of dielectric cylinders, the common approach is to use the independent scattering model by adding the scattering cross sections of cylinders. More advanced approaches include the coherent model [4, 5] which takes into account the phase difference among scatterers that are in close proximity of each other. To account for multiple scattering effects which are important when the optical thickness and scattering albedo of the vegetation layer are significant, we recently used an iterative approach of radiative transfer equation including backscattering enhancement for corn layer at L-band [6]. In this paper, we study two kinds of multiple scattering. One is continuing iterative radiative transfer with backscattering enhancement for various crop types at C-band. Using the iterative approach, the contribution to backscattering from each scattering mechanism is separated and thus the cyclical terms are also identified by examining the duality of the paths for each scattering mechanism. The second multiple scattering effects are more appropriately called near field wave interactions. For this case we consider cylinders in close proximity, and we solve Maxwell equations numerically. The near field interactions cause the internal field to be different from the independent scattering. The full wave solutions go beyond the coherent approach which only considers phase factor without accounting for the change of internal field. Numerical results of these multiple scattering models are illustrated and compared with the prior approaches of distorted Born approximation, independent scattering and coherent model. After taking into account the near field interaction between scatterers, the resulted absorption coefficient are different from the single scattering model, because the original internal field induced by the incident field alone is affected by the scattered field from the other scatters. The scattering pattern is also different from that of the coherent model [5]. In the coherent model which is the coherent addition of the scattering field from each scatterer, the effects of the scattered field from the other scatterers are ignored when calculating the scattering field from a scatterer. Thus the internal field of each cylinder calculated in the coherent model is inaccurate when the cylinders are in clusters.