ELSEVIER A Microwave Polarimetric Scattering Model for Forest Canopies Based on Vector Radiative Transfer Theory Mostafa A. Karam,* Faouxi Amar,** Adrian K. Fung,** Eric Mougin) Armand Lope$ David M. Le Vine,” and Andre Beaudoin? A microwave polarimetric scattering model for a forest canopy is developed based on the iterative solution of the vector radiative transfer equations up to the second order. The forest canopy constituents (branches, leaves, stems, and trunks) are embedded in a multi-layered medium over a rough interface. The branches, stems, and trunks are modeled as finite randomly oriented cylinders. Decid- uous leaves are modeled as randomly oriented discs and conifmous leaves are modeled as randomly oriented nee- dles. The vector radiative transfer equations contain non- diagonal extinction matrices that account for the differ- ence in propagation constants and the attenuation rates between the vertical and horizontal polarizations. For a plane wave exciting the canopy, the average Mueller ma- trix is formulated, and then used to determine the linearly polarized backscattering coeficients including both the copolarized and cross-polarized power returns. Compari- sons of the model with measurements from Les Landes Forest of France showed good agreements over a wide frequency band and gave a quantitative understanding of the relation between the backscattering coefficients and the age of the trees in the forest and forest biomass. INTRODUCTION This study is a sequel to an earlier one by Karam et al. (1992). In that paper, which we will refer to as the “ first * GenCorp Aerojet, Electronics System Division, Azusa, Cali- fornia. **Wave Scattering Research Center, Department of Electrical Engineering, University of Texas at Arlington. +Centre d’Etude Spatiale des Rayonnements, Toulouse Cedex, France. ‘NASA Goddard Space Flight Center, Greenbelt, Maryland. Address correspondence to Dr. Faouzi Amar, Electrical Engi- neering, Box 19016, University of Texas at Arlington, Arlington, TX 76019-0016. Received 23 November 1992. 0034-4257 I95 I $9.50 SSDI 0034-4257(95)00048-6 paper,” we developed a scattering model that general- ized the assumptions imposed by earlier models (Chau- han et al., 1991; Durden et al., 1989; Richard et al., 1987; and Ulaby et al., 1990), reported in the literature for closed canopies, to: include surface roughness effects from soil and canopy-soil interactions; account for cross-polarized scattering due to trunk-ground interactions and second-order volume scattering; use an extinction formulation that accounts for both ohmic and scattering losses when low fre- quency approximation is made; and include the second-order radiative transfer to ac- count for multiple scattering within the canopy. The model discussed in the first paper, which we refer to as the “two-layer model,” was shown to compare well with measurements from different forest canopies over a wide frequency range in the microwave bands (Karam et al., 1992; Mougin et al., 1993). However, it does not account for (a) the variation of the branch, stem, and leaf number densities with respect to the canopy depth, and for (b) the wide range of soil surface roughness. As a result, the two-layer model is limited in its applicability to cases where the trunk layer con- tains the trunk only, and where the crown layer contains all of the branches and leaves. In this study we extend the two-layer model to a multi-layer model over a rough surface. In the present model, forest components can be placed in any layer using different number densities. Furthermore, to ac- count for the wide range of soil surface roughness, a surface scattering model based on an integral equation method (IEM) is used (Fung et al., 1992). This model REMOTE SENS. ENVIRON. 53:16-30 (1995) OElsevier Science Inc., 1995 655 Avenue of the Americas, New York, NY 10010