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In this paper, we present a novel physical-statistical, generative model for the land mobile satellite (LMS), dual polarized, multiple-input-multiple-output (MIMO) channel along tree sided roads. Said model is parameterized by means of a physical model based on the Multiple Scattering Theory (MST) which accounts for the signal attenuation and scattering by trees. Moreover, Finite-Difference Time-Domain (FDTD) electromagnetic computations were performed to characterize the scattering pattern of an isolated tree, and to calculate the MIMO shadowing correlation matrix required by the model, and not provided by MST. This modeling framework also encompasses the single-input-multiple-output (SIMO)/space diversity case. To illustrate the capabilities of the developed model, time series were generated and used in system performance calculations. The obtained results give an insight into the advantages of dual polarized MIMO and SIMO/space diversity techniques in these very frequent scenarios, and may help service providers in evaluating the technical feasibility of such systems.