Estimation of Directional Wave Spectra from Multicomponent Observations

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Abstract
An improved method for estimating the directional spectrum of linear surface gravity waves from in Situ observations is presented. The technique, a refinement and extension of the inverse method of Long and Hasselmann, is applicable to multicomponent wave measurements at fixed locations in constant or slowly varying depth water. On a frequency band by frequency band basis, an estimate of the directional distribution of wave energy S(θ) is obtained by minimizing a roughness measure of the form ∫dθ[d2S(θ)/dθ2]2 subject to the constraints: (i) S(θ) is nonnegative with unit integral, (ii) S(θ) fits the data within a chosen statistical confidence level, and (iii) S(θ) is zero on any directional sectors where energy levels are always relatively low because of the influence of geographic surroundings. The solution to this inverse problem is derived through a variational formulation with Lagrange multipliers. A series of simulations using the new estimator show the fundamental limitations of sparse array... Abstract An improved method for estimating the directional spectrum of linear surface gravity waves from in Situ observations is presented. The technique, a refinement and extension of the inverse method of Long and Hasselmann, is applicable to multicomponent wave measurements at fixed locations in constant or slowly varying depth water. On a frequency band by frequency band basis, an estimate of the directional distribution of wave energy S(θ) is obtained by minimizing a roughness measure of the form ∫dθ[d2S(θ)/dθ2]2 subject to the constraints: (i) S(θ) is nonnegative with unit integral, (ii) S(θ) fits the data within a chosen statistical confidence level, and (iii) S(θ) is zero on any directional sectors where energy levels are always relatively low because of the influence of geographic surroundings. The solution to this inverse problem is derived through a variational formulation with Lagrange multipliers. A series of simulations using the new estimator show the fundamental limitations of sparse array...

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