Retrieval of nonlinear spectral information from ocean sunglint
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In this thesis we develop an inversion procedure which allows the retrieval of nonlinear characteristics of the ocean wave surface from observations of specularly reflected visible solar radiation, or sunglint. Knowledge of the higher order statistical properties of the wave surface enables us to gain an improved understanding of wave generation processes, to determine the degree of energy transfer between wave components, and to make statements about the likelihood of extreme or unlikely wave events. Apart from its scientific value, this information should be useful for the engineering of maritime structures, where account must be made of conditions occasionally exceeding what a structure is normally expected to withstand.Previous attempts at retrieving information about the ocean surface from sunglint data (Alvarez-Borrego, 1993) have used second order statistical descriptors, such as the variance and autocorrelation, to provide the connection between the slope and sunglint data. This approach results in the loss of phase information from the slope and sunglint statistical descriptors, which prevents the retrieval of the phase correlations between the wave components arising from nonlinear interactions.In order to address this deficiency, we derive the relationship between the slope and the sunglint data in terms of their respective third order cumulant functions. The glint function in this case is defined in terms of the corresponding joint slope probability density. This density function is developed using a perturbative approach, and consists of a Gaussian function (which characterises the second order statistical descriptors of the slope), and corrections which parameterise the higher order correlations between the slope variables. A consequence of this approach to synthesising the required slope density is a dependence on higher order, or Multidimensional Hermite Polynomials (MDHP). Accordingly, the differential and integral properties of these orthogonal polynomials are investigated with respect to their utility in formulating the slope density function.Using these tools, we develop an inversion procedure which exploits the generalised relationship connecting the statistical descriptors of the slope and glint to retrieve the slope descriptors, namely the slope cumulants and third order cumulant function. This technique is validated using synthetic ocean wave slope datasets with controlled phase correlations imposed on a subset of the wave spectrum components.
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