In microwave remote sensing of vegetated land surfaces, there are volume scattering from the vegetation and rough-surface scattering of the interface between the vegetation and the ground. However, the coupling of volume scattering and surface scattering and its impact on microwave emission have not been fully studied, particularly when multiple scattering effects are to be considered as in forested scenarios. Earlier treatment with the Kirchhoff approximation neglects the incoherent bistatic scattering components from the rough soil interface and thus overestimates the transmitted upward emission from the soil half space and underestimate the reflected upward emission from the downward-going intensity streams arising from the vegetation layer in non-specular directions. To address this issue, bistatic scattering coefficients are introduced into the boundary conditions and an interpolation-accelerated numerical iterative method is employed to solve the passive radiative transfer equation to rigorously couple the volumesurface scattering interactions at the vegetation/soil interface. In this paper, the rough-surface bistatic scattering is modeled using the advanced integral equation method (AIEM). The volume scattering model is derived from a radiative transfer based multiple scattering model that accounts for the vertical profile of the vegetation structure. The SMAPVEX12 forest dataset is utilized to validate the proposed model, encompassing L-band radiometric brightness temperature observations corresponding to extensive variations in soil moisture. Comparisons are made between the brightness temperatures simulated by the model with and without considering the incoherent bistatic scattering coefficients, under diverse vegetation water contents (VWCs) and varying soil roughness conditions. Notable features are observed in the angular pattern of the vegetated surface emission by fully accounting for the multiple scattering effects and the incoherent bistatic scattering effects of the rough soil. These features become more evident at smaller observation angles, lower VWCs, and greater soil roughness. The findings reveal that the model incorporating the bistatic scattering coefficient of rough surfaces exhibits improved agreement with the measured brightness temperatures. Furthermore, the proposed model is parameterized by matching the high-order solutions to the RT equation to the widely adopted albedo-tau formalism, i.e., the zero-order solution to the passive radiative transfer equation with a flat lower boundary. The resulting equivalent optical thickness and the equivalent scattering albedo incorporates the multiple scattering effects within the vegetation layer and they are solely associated with the geometries and the electromagnetic properties of the vegetation layer. Additionally, the equivalent reflectivity of the soil is proposed to characterize the scattering properties of rough surfaces and the scattering coupling between the rough surface and the vegetation layer. The new model developments will significantly enhance the prediction and interpretation of vegetated land surface emission characteristics and thus improve the remote sensing of the vegetation and the underlying soil parameters.

A multiple scattering model for passive radiative transfer (RT) in vegetation that accounts for the vertical profile of the plant structure is developed, offering advancements over the commonly-used single-layer uniform scattering models prevalent in the vegetated land surface microwave remote sensing. The proposed model takes into account the complexities of the canopy morphology with vertical heterogeneity, enabling the representation of overlapping vegetation species applicable to diverse plant types and growth stages. Additionally, it serves as a valuable tool for understanding the influence of the vegetation vertical structure on the microwave brightness temperatures. The model is constructed based on high-order solutions to the RT equations, obtained through a numerical iterative approach with an efficient interpolation scheme for algorithm acceleration. This methodology facilitates the accurate distinction of the contributions to the brightness temperature from each scattering order and scattering mechanism, ensuring a comprehensive consideration of multiple scattering effects within various vegetated scenarios. The model is validated using the SMAPVEX12 L-band forest data set, encompassing a wide range of soil moisture variations. Comparisons are made between the brightness temperatures simulated by the newly developed multiple-scattering model with a continuous profile or layered profile and those obtained from a uniform single-layer model. Results demonstrate significant improvements in the multi-layered or the continuously profiled model, showing improved agreement with the measured brightness temperatures. Furthermore, the proposed model is parameterized by matching the high-order solutions to the RT equation to the widely adopted reduced order albedo-tau formalism. The resulting equivalent parameters are linked to the geometries and the electromagnetic properties of the vegetation layer, while also incorporating the effects of multiple scattering. Comparative analysis of the equivalent parameters derived from the layered model and those derived from the single-layer model reveals that the vertical heterogeneity of the vegetation structure has a notable influence on the effective scattering albedo and it yields a value more consistent with the albedo as chosen in the SMAP/SMOS inversion algorithms. Meanwhile, the impact of the vegetation vertical profile on the effective optical thickness and the effective transmissivity of the vegetation layer is weak.These insights are essential for the retrieval of soil moisture and vegetation characteristics including the plant vertical structures in microwave remote sensing.

The Radiative Transfer (RT) theory has been widely utilized for wave propagation in random media, but it faces challenges in situations involving strong forward scattering, such as in forests with electrically large trunks, due to the singularity of the scattering phase matrix. In this paper, we present an effective approach to compute multiple scattering solutions to RT equations with singular phase matrix by combining the strategy of forward scattering extraction with an efficient numerical iterative procedure through interpolation. We evaluate the effectiveness and efficiency of our technique through simulations using a layer of vertically oriented, electrically large long cylinders to represent a layer of trunks over the ground. The results demonstrate that the proposed approach increases the computational efficiency by one to two orders of magnitude in cases where forward scattering is dominant. Additionally, a parameterized model is derived by matching the higher-order RT results with the ω − τ formalism under catered conditions. An explicit physical definition of the equivalent scattering albedo and equivalent optical thickness are proposed under boundary-free conditions. The multiple scattering effects are included in the physically derived equivalent parameters of the plant layer, which are independent of ground conditions by definition. Tests verify that the applicability of the parameterized model with ω−τ form can be extended to a wider range of vegetation and ground conditions. Besides, these equivalent parameters are directly linked to the geometric structures and electromagnetic properties of the vegetation layer, allowing their values to be frequency- and angle-dependent. Compared to the single-scattering albedo and optical thickness, the effective albedo derived from the RT model exhibits relatively weak polarization and angle dependence. This is consistent with many empirically derived parameterizations while providing a physically plausible origin for these equivalent parameters. Remarkably, we find that the transmittance linked to the parameterized tau value, incorporating multiple scattering effects, is similar to that obtained through full-wave simulations.