The ocean waveheight nondirectional spectrum from inversion of the HF sea-echo Doppler spectrum

Abstract

The measured HF sea-echo Doppler spectrum consists of prominent first-order peaks, around which exist second-order sidebands of a continuous nature. Theoretical models developed elsewhere are interpreted here and shown to satisfactorily account for these first and second-order measured spectral features. Employing these theoretical models, this paper derives a simple inversion technique for obtaining the waveheight nondirectional spectrum. The result is a closed-form expression, independent of the wave directionality factor, the radar look direction, or the stage of development of the waveheight spectrum. Approximations required in the derivation are stated along the way, and are shown to become increasingly valid in the limit of high seas and/or radar frequencies. The technique is tested by attempting to recover several input waveheight nondirectional spectra for various radar look directions. Comparisons show that the technique produces acceptable results for koh > 0.2, where ko is the radar wavenumber and h is the rms waveheight. Application of the inversion technique to measured data is straightforward. One employs one of the stronger second-order Doppler sidebands (vs. Doppler frequency with respect to the first-order Doppler-peak frequency) and divides it by a parameterless, dimensionless weighting function derived in this paper. He then divides this result by the adjacent first-order spectral energy. The latter normalization (i) serves to remove any unknown radar path loss or system gain factors, and (ii) also eliminates the need for any a priori knowledge of the wave or radar directionality and/or the assumption of a model for these latter quantities. © 1977.