Reflection loss from a "Pierson-Moskowitz" sea surface using the nonlocal small slope approximation

The lowest-order nonlocal small slope approximation (NLSSA) reflection coefficient is derived, and numerical results are presented for one-dimensional (1-D) surfaces, satisfying the Dirichlet boundary condition. Reduction to the perturbation expression occurs in the small height limit, and the first term of the reflection coefficient gives the Kirchhoff approximation (KA) result. Numerical results for the reflection loss at low grazing angles using a Pierson–Moskowitz spectrum are compared with those of other approximate methods as well as with exact integral equation (IE) results. For those cases when exact results are available, the NLSSA is found to give accurate results, comparable to those of the small slope approximation (SSA) and superior to those of classical perturbation theory (PT) and the KA.