Recent developments in wave modelling

How can we improve ocean wave model simulations during hurricanes? One approach is to focus on nonlinear wave – wave interactions. The wave-wave interactions serve to transfer and distribute energy and momentum throughout the wave spectrum, allowing the spectral peak frequency to downshift and the associated waves to grow and develop. Biases and errors in the manner in which this done, result in biases in parameterizations for transfer of energy and momentum from wind to waves, and in parameterizations for wave dissipation, transfers to currents and white-capping. This is relevant to severe sea-state conditions, for example during hurricanes.

A new method for estimating the transfer rates in wind wave spectra is presented and tested, based on a two-scale approximation (TSA) to the total integral for quadruplet wave-wave interactions (Resio and Perrie, J. Phys. Oceanogr., 2008, submitted 2010; Perrie and Resio, J. Phys. Oceanogr., 2009). The TSA formulation involves functional decompositions of given wave spectra. It is important for the parametric terms in the TSA to capture much of the broad-scale behavior of the spectra. However, as has been shown, even for relatively complicated cases in which observed spectra deviate significantly from simple parametric forms (either in their directional distributions of energy or their directionally integrated shapes), the perturbation component of the TSA appears to do a relatively good job of allowing the total TSA solution to accurately represent the nonlinear energy transfer due to wave-wave interactions.

Comparisons of this new estimation method to the full integral are given for several idealized spectra, including JONSWAP spectra with different peakedness, a finite depth case, and cases with perturbations added to underlying parametric spectra. In particular, these comparisons show that the TSA is a significant improvement over the Discrete Interaction Approximation (DIA) in deep water and an even greater improvement in shallow water.

We show that TSA is suitable for operational wave model implementations, with tests and examples where TSA is implemented in WAVEWATCHIII, the operational wave model used by NOAA, in simulations of dedicated field experiments such as JONSWAP and real hurricane-generated wave data collected off North Carolina, including cases of the stages of simple fetch-limited wave growth, shearing wind cases, swell- windsea interactions, and discussion of equilibrium range fluxes. These comparisons include data collected by the Field Research Facility (FRF) at Duck North Carolina during hurricane Wilma in 2005, as well as later North Atlantic hurricanes. Results show that TSA performs very well, and that this new approximation is a notable improvement over results attained by DIA, which is the formulation used in all operational third generation, state-of-the-art wave forecast models, today.