A fully nonlinear regional wave model for the Bight of Abaco. Part 1: Nonlinear-transfer computation

This paper is the first in a series of papers describing a fully nonlinear regional wave model for the Bight of Abaco, Bahamas. It discusses this model's hybrid representation for nonlinear transfer and the numerical errors associated with this representation. This discussion extends a number of results previously reported by Snyder et al. [1993], doubling both the Boltzmann integration resolution and the spectral resolution of the resulting nonlinear-transfer estimates and evaluating the errors associated with both resolutions. It also better resolves the structure of the negative midfrequency lobe of the nonlinear transfer for JONSWAP input [Hasselmann et al., 1973], evaluates the errors associated with the diagnostic range of the nonlinear-transfer computation, and extends the hybrid representation to various finite depths characteristic of the Abaco Bight. It also extends the previous discussion of truncations of the hybrid representation, defining some renormalized hybrid implementations of the discrete-interaction approximation [Hasselmann et al., 1985] and generalizing its selection algorithm to improve the accuracy of this approximation (at some cost in efficiency). Finally, it develops a systematic scheme for recursively selecting hybrid coefficients to define a family of recursively optimized renormalized hybrid truncations. Because this scheme selects coefficient groups (the interactions for which are scaled versions of one another or of mirror images of one another) rather than individual coefficients and because it optimizes over multiple spectral inputs, the resulting truncations perform well over a full range of peak frequency. The resulting truncations for a nominal spectral resolution of 16 prognostic and four diagnostic wave-number bands and 12 angle bands include some truncations that essentially trade a factor of 10 in efficiency for a factor of 10 in accuracy (relative to the discrete-interaction approximation). Other truncations, running only 600 times slower than the discrete-interaction approximation, give a very accurate representation of the full nonlinear transfer. These truncations, employed in sequential fashion and extended to multiple spectral resolution, enable a relatively accurate and efficient staged inverse modeling of the action-balance equation. By first inverse modeling to convergence at nominal spectral resolution, then inverse modeling to convergence at double spectral resolution (starting from the converged results