Passive and Active Multiple Scattering of Forests Using Radiative Transfer Theory With an Iterative Approach and Cyclical Corrections

Abstract

In this article, a unified framework of vegetation scattering using radiative transfer (RT) theory for passive and active remote sensing of vegetated land surfaces, especially those associated with moderate-to-large vegetation water contents (VWCs), e.g., forest field, is presented. The framework allows for modeling passive and active microwave signatures of the vegetated field with the same physical parameters describing the vegetation structure. RT equations are solved by a numerical iterative approach for both passive and active configurations. This approach allows including higher order scattering, which represents multiple scattering. In fields such as forests with large VWCs, associated with large scattering albedo and optical thickness, multiple scattering effects are critical. In the active iterative approach, cyclical terms are identified and backscattering enhancement is included by doubling contributions from cyclical terms. The method is applied to aspen trees in forest fields to compute the brightness temperatures and backscattering coefficients for passive and active remote sensing configurations, respectively. In the passive configuration, for forest field with VWC of 15 kg/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\text{m}^{2}$ </tex-math></inline-formula> , the deviation between the zeroth-order brightness temperature, i.e., the tau–omega model results, and multiple scattering results around 40° observation angle, can be as large as 50 K for vertical polarization and 35 K for horizontal polarization. In the active configuration, the deviation between first-order results, which is identical to the distorted Born approximation, and the multiple scattering results around 40° incidence angle, is about 1.6 dB for VV and 0.7 dB for HH polarization. Multiple scattering is shown to be crucial for accurate forward modeling, especially over forested areas. The proposed approach is thus suitable for vegetation scattering with large VWCs. Furthermore, the proposed model is validated with the passive and active L-band sensor (PALS) acquired in SMAPVEX12 measurements in 2012, which demonstrates the applicability of this model.