The Soil Moisture Active Passive (SMAP) satellite has provided soil moisture estimates in the top 5 cm of the soil surface by measuring the brightness temperature at L-band ($f$=1.41 GHz, $\lambda$=21 cm) emitted from the earth at a spatial resolution of 33 km. The SMAP products have been assessed by comparing them with ground-based in \emph{situ} soil moisture observations. It was found that cropland such as the South Fork located in Iowa is problematic, not satisfying the SMAP accuracy goal. This is due to the vegetation scattering effect which the SMAP algorithm ($\tau-\omega$ model) inherently ignores. Thus, we hypothesize that vegetation scattering effect can not be negligible because of the electrical size of plants comparable to the observation wavelength.

In order to address our hypothesis, we model the vegetation canopy consisting of an infinite number of finite-length cylinders using the Floquet port and periodic boundary condition in the HFSS (high-frequency structure simulator). S-parameters are utilized to derive the reflection and transmission coefficients. The accuracy of this method is validated by comparing it with analytical solutions and the literature.

Three cases are studied: (a) reflection and transmission coefficients for the 2-layer (soil and air) case, (b) vegetation scattering effect for 3-layer (soil, vegetation canopy, and air) case, and (c) transmissivity for the vegetation canopy itself. The results of case (c) show that vegetation optical depth from our HFSS model is about 6.9 times lower than that from the VRT (vector radiative transfer model). Also, the result of the periodically distributed case from our HFSS model falls within the range of results of the sparsely distributed case from the NMM3D (Numerical Maxwell Model in 3D simulations). It is because our HFSS model and the NMM3D take into account the scattered fields and coherent wave interactions by solving Maxwell equation directly. Through these cases, we show that the vegetation scattering effect becomes larger as plants grow taller, and the proposed approach can provide the vegetation optical depth for grass canopy.