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A computational model for radio wave propagation through tree orchards is presented. Trees are modeled as collections of branches, geometrically approximated by cylinders, whose dimensions are determined on the basis of measurements in a cherry orchard. Tree canopies are modeled as dielectric spheres of appropriate size. A single row of trees was modeled by creating copies of a representative tree model positioned on top of a rectangular, lossy dielectric slab that simulated the ground. The complete scattering model, including soil and trees, enhanced by periodicity conditions corresponding to the array, was characterized via a commercial computational software tool for simulating the wave propagation by means of the Finite Element Method. The attenuation of the simulated signal was compared to measurements taken in the cherry orchard, using two ZigBee receiver-transmitter modules. Near the top of the tree canopies (at 3 m), the predicted attenuation was close to the measured one-just slightly underestimated. However, at 1.5 m the solver underestimated the measured attenuation significantly, especially when leaves were present and, as distances grew longer. This suggests that the effects of scattering from neighboring tree rows need to be incorporated into the model. However, complex geometries result in ill conditioned linear systems that affect the solver's convergence.

A Computational Model for Path Loss in Wireless Sensor Networks in Orchard Environments