Inverse modeling of discrete interaction approximations for nonlinear interactions in wind waves

In the last two decades, the Discrete Interaction Approximation (DIA) has been the only economically feasible parameterization for nonlinear wave–wave interactions in operational wind wave models. Its major drawback is its limited accuracy. Several improvements to the DIA have been suggested recently. The present study summarizes these improvements and suggests some new modifications to the DIA. Using inverse modeling techniques, where the potential of various DIAs is assessed by optimal fitting to exact solutions, a comprehensive comparison of the potential of several such improvements is made. An in depth analysis of the behavior of DIAs in full wave models will be the subject of a second study, to be reported elsewhere. The major findings of this study are that: (i) An expanded definition of the representative quadruplet with additional degrees of freedom is necessary for an accurate representation of the exact interactions; (ii) Slowly varying the free parameters in such a DIA as a function of the spectral frequency f results in a (mostly qualitative) improvement; (iii) A DIA with expanded quadruplet definition and with four representative quadruplets is found to reproduce the exact source term accurately; (iv) Adding additional tunable constants to the equation for the strength of the interactions has little impact on the quality of the DIA.