In some cases, it may be preferred to characterize the ocean surface or
bottom by a complex reflection coefficient as a function of grazing
angle. Such a reflection coefficient may be specified by tabulating the
magnitude and phase at a discrete set of -values. To
completely define the normal mode problem, must be defined
continuously for some range of -values. A routine (REFCO)
accomplishes this by linearly interpolating the magnitude and phase of
the reflection coefficient. In addition, the reflection coefficient
must be converted to an equivalent Robin style boundary condition with
coefficients which are a function of horizontal propagation number, **k**.

Note that a surface reflection coefficient asserts a relationship between an upgoing and downgoing wave of the following form.

where

is the vertical wavenumber. Then,

which implies that,

Thus, the reflection coefficient implies an impedance or Robin style boundary condition of the form,

For bottom reflection we use the form

which leads to,

In general, the reflection coefficient is a function of the grazing angle which is related to by

Tue Oct 28 13:27:38 PST 1997