  Over-water communication has been an important research field of wireless
communications and radar. Since there are so many parameters in this
environment that are changing continuously in the spatial and temporal domains
such as weather and sea surface parameters. Hence, accurately modeling the
over-water propagation channel is very crucial and challenging at the same
time. In this report, we will shed some light on the parabolic equation (PE)
method which is one of the main methods used to model the radio waves
propagation over variable terrain and through the homogeneous and inhomogeneous
atmosphere. Besides ray-tracing, PE is among the most widely used approaches
nowadays for deterministically analyze over-water channels. We are trying to
pave the way for better understanding of the mathematical background for the PE
and develop a tool to perform advanced analysis for the over-water
communication channel taking into consideration its spatial and temporal
behavior.
