Full-Wave Electromagnetic Simulations of Forests at L-Band by Using Fast Hybrid Method

Wave propagation in forests at L-band has essential applications in satellite communication system design, foliage penetration (FOPEN), and remote sensing of forest canopy and soil using passive active and reflectometry techniques. In this work, we propose applying the fast hybrid method (FHM) for full-wave simulations of forests. The FHM significantly improves CPU time and memory efficiency for full-wave electromagnetic solutions. In this paper, we present simulations of forests of up to 72 trees with heights up to 13 m with FHM. Spatial distributions of electric fields at the bottom plane of the trees are illustrated showing constructive and destructive interferences. The electric field distributions show that the amplitudes of the electric fields can be as large as twice that of incident waves. The transmissivities are computed and averaged over realizations based on the electric fields underneath the forest. The simulations were performed on a desktop and required a CPU time of only 1346 seconds and the memory of 16.5 GB for the case of 72 13-m tall trees, demonstrating that the FHM method is substantially more efficient than the available commercial software. The results show that the L-band signals can penetrate forests to sense the soil moisture and detect targets hidden within forests, as evidenced by significant electric field intensities under forest canopies. Also, we illustrate that GPS signals can penetrate forests and be successfully received by GPS receivers. In the study on clustering effects, we present two distinct solutions for transmissivities, each corresponding to different spatial distributions of trees while maintaining the same average tree density.