3.10

**A Combination of Empirical Orthogonal Function and Neural Network Approaches for Parameterizing Nonlinear Interactions in Wind Wave Models**

Vladimir M. Krasnopolsky, NOAA/NCEP/EMC, Camp Springs, MD; and H. L. Tolman and D. V. Chalikov

The nonlinear interaction parameterization represents the core of a third-generation wind wave model. In principle, an exact formulation of this source term is well known. However, exact calculations are too expensive by several orders of magnitude to be economically feasible in practical wave models. Presently the only feasible parameterization of the nonlinear interactions is the Discrete Interaction Approximation (DIA, Hasselmann et al 1985). This parameterization is very successful, as it allowed for the development of the first operational third generation wave models, but its large errors are generally recognized as being one of the main deficiencies of such models. Moreover, such errors hamper further development of third-generation wave models.

We are presently developing a Neural Network Interaction Approximation (NNIA) for the nonlinear interaction. This approximation considers the interaction source term as a nonlinear mapping of the spectrum on the source term. Both the spectrum and source term are decomposed into basis functions to reduce the number of degrees of freedom, and to make the approximation independent of the actual spectral resolution. The basis functions are derived from empirical orthogonal functions for spectra and nonlinear interaction separately. A NN is used to predict coefficients of the basis functions of the interaction decomposition from the coefficients of the basis functions of the spectrum decomposition.

We have tested the feasibility of the NNIA by constructing large independent training and testing ensembles of realistic spectra and their corresponding exact interactions according to Web-Resio-Tracy (Van Veldder et al 2000). These experiments have shown that an economical NNIA can be constructed with resulting errors less than half those of the DIA, at computing times comparable with that of the DIA. As might have been expected, however, the training dataset was insufficiently divers to result in a generally applicable NNIA.

We are presently expanding our study by: (i) broadening the training datasets by considering modeled and/or observed spectra, (ii) including scaling properties directly into the NNIA. Both activities are aimed at obtaining a more generally applicable (and more economical) NNIA.

References:

Hasselmann, S, and K. Hasselmann, 1985: Computations and parametrizations of the nonlinear energy transfer in a gravity wave spectrum. Part I: a new method for efficient computations of the exact nonlinear transfer integral. J. Phys. Oceanogr., 15, 1369-77

Van Veldder, G.Ph., T.H.C. Herbers, B. Jensen, D.T. Resio, and B. Tracy: Modelling of nonlinear quadruplet wave-wave interactions in operational coastal wave models. Abstract, accepted for presentation at ICCE 2000, Sydney

Session 3, Neural Networks

**Tuesday, 11 February 2003, 8:30 AM-12:15 PM**** Previous paper
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