Accuracy of parabolic wave equation method in short propagation range

Modeling radio propagation over ocean surface is important for homeland security applications. Due to its fast simulation speed, the parabolic equation (PE) method is a good candidate for and has been used in such simulations for decades. Since PE method is based on paraxial approximation of wave equation, its accuracy is not guaranteed for short ranges and larger propagation angles. On the other hand, Finite Difference Time Domain (FDTD) method is well known as an accurate method in short range but not suitable for large regions (in terms of wavelengths). For homeland security applications, it is necessary to deal with both short and long range propagation problems and it is natural to integrate PE and FDTD for simulating such scenarios. To exploit the advantages of PE and FDTD, quantifying the ranges suitable for these two methods is important and practically useful. In this paper, we examine the accuracy of PE method as a function of range (in short range regime) for smooth/flat ocean surfaces.