The second-order shallow-water hydrodynamic coupling coefficient in interpretation of HF radar sea echo

Extraction of wave.height directional spectral information from high-frequency (HF) radar sea echo requires the use of hydrodynamic and electromagnetic second-order coupling coefficients obtained from a perturbational expansion of the nonlinear boundary conditions at the ocean surface. To present, the hydrodynamic coupling coefficient derived for deep water has been given. Since most coastal HF radar observations are made in water shallow compared with the dominant ocean wavelength, that solution has proven inadequate for those applications. This paper derives the more general expression for water of arbitrary depth, and demonstrates its validity against measured data. The hydrodynamic contribution increases in importance as waves of constant energy move into shallow water. The use of these results for interpretation of both narrow-beam and CODAR data is discussed.