A FULLY NONLINEAR REGIONAL WAVE MODEL FOR THE BIGHT OF ABACO - 1 - NONLINEAR-TRANSFER COMPUTATION

This paper is the first in a series of papers describing a fully nonli near regional wave model for the Eight of Abaco, Bahamas. It discusses this model's hybrid representation for nonlinear transfer and the num erical errors associated with this representation. This discussion ext ends a number of results previously reported by Snyder et al. [1993], doubling both the Boltzmann integration resolution and the spectral re solution of the resulting nonlinear-transfer estimates and evaluating the errors associated with both resolutions. It also better resolves t he structure of the negative midfrequency lobe of the nonlinear transf er for JONSWAP input [Hasselmann et al, 1973], evaluates the errors as sociated with the diagnostic range of the nonlinear-transfer computati on, and extends the hybrid representation to various finite depths cha racteristic of the Abaco Eight. It also extends the previous discussio n of truncations of the hybrid representation, defining some renormali zed hybrid implementations of the discrete-interaction approximation [ Hasselmann et al., 1985] and generalizing its selection algorithm to i mprove the accuracy of this approximation (at some cost in efficiency) . Finally, it develops a systematic scheme for recursively selecting h ybrid coefficients to define a family of recursively optimized renorma lized hybrid truncations. Because this scheme selects coefficient grou ps (the interactions for which are scaled versions of one another or o f mirror images of one another) rather than individual coefficients an d because it optimizes over multiple spectral inputs, the resulting tr uncations perform well over a full range of peak frequency. The result ing truncations for a nominal spectral resolution of 16 prognostic and four diagnostic wave-number bands and 12 angle bands include some tru ncations that essentially trade a factor of 10 in efficiency for a fac tor of 10 in accuracy (relative to the discrete-interaction approximat ion). Other truncations, running only 600 times slower than the discre te-interaction approximation, give a very accurate representation of t he full nonlinear transfer. These truncations, employed in sequential fashion and extended to multiple spectral resolution, enable a relativ ely accurate and efficient staged inverse modeling of the action-balan ce equation. By first inverse modeling to convergence at nominal spect ral resolution, then inverse modeling to convergence at double spectra l resolution (starting from the converged results for nominal spectral resolution), it should be possible to extrapolate the results of the inverse modeling with an error no worse than a few percent (assuming t hat the errors in the results of the inverse modeling generated by err ors in the nonlinear-transfer computation are no worse than these gene rating errors and that the impact of other numerical errors can be sim ilarly contained).