Equilibrium Wave Spectrum and Sea State Bias in Satellite Altimetry

Abstract

For a well-developed sea at equilibrium with a constant wind, the energy-containing range of the wavenumber spectrum for wind-generated gravity waves is approximated by a generalized power law ?(U2/g)2?k?4+2?Y(k,?), where Y is the angular spread function and ? can be interpreted as a fractal codimension of a small surface patch. Dependence of ? on the wave age, ?=C0/U, is estimated, and the ?Phillips constant,? ?, along with the low-wavenumber boundary, k0, of the inertial subrange are studied analytically based on the wave action and energy conservation principles. The resulting expressions are employed to evaluate various non-Gaussian statistics of a weakly nonlinear sea surface, which determine the sea state bias in satellite altimetry. The locally accelerated decay of the spectral density function in a high-wavenumber dissipation subrange is pointed out as an important factor of wave dynamics and is shown to be also highly important in the geometrical optics treatment of the sea state bias. The analysis is carried out in the approximation of a unidirectional wave field and confined to the case of a well-developed sea characterized by ?>1.