First-generation DP models and second-generation CH and CD models, which are based on fundamentally different pictures of the spectral energy balance, yield significantly different relations between space and time variables in the development of a windsea. It is therefore impossible to tune a DP model to agree with a CH or CD model for all types of wind fields. If the models are tuned to agree for fetch-limited growth, DP models will develop faster than CD or CH models in the duration-limited case by a factor of the order of 1.5.
DP models also differ from CH or CD models in the shape of the windsea spectrum. For the standard fetch- or duration-limited growth cases, DP models yield a nested family of spectral growth curves with no overshoot. For more complex wind fields, DP models generally develop a wider variety of spectral distributions than CH or CD models. Because different wave components evolve independently along different rays, the evolution of the spectrum in DP models is generally more sensitive to fetch variations with propagation direction. However, this is strongly dependent on the assumed directional distribution of the growth coefficients. In the cases studied, the effect was clearly pronounced in the DP model mri, which used relatively broad cos2 θ-dependent growth coefficients, but was insignificant for the second DP model venice, which assumed a narrower angular distribution for the growth coefficients.
Despite the basic incompatibility of first- and second-generation wave models, DP models remain attractive because of their greater computational simplicity. They can be useful if adapted and applied to a particular class of wave conditions. In the case of the two DP models considered in the present study, the mri model is used primarily for open-ocean, duration-limited conditions, while the venice model was originally designed for the typically fetch-limited wave conditions of the Adriatic.
All present second-generation models suffer from limitations in the parameterization of the nonlinear energy transfer, S nl This process largely controls the shape and growth of the windsea spectrum. The models perform satisfactorily for the standard fetch- and duration-limited growth situations for which the parameterizations were designed. This applies also to slowly varying large-scale wind fields, for which the internal nonlinear shape adjustment time of the spectrum is small compared with the characteristic time scale of the wind changes experienced by the waves. However, the case studies were designed to test the models under rather extreme conditions of rapidly changing winds. For these situations, the parameterizations of S nl generally contained too few degrees of freedom to cope with the wide variety of spectral distributions which may arise. In view of this shortcoming, which is common to both types of second-generation model, the potential advantage of CD models in providing a complete discretized 2d description of the windsea spectrum, as opposed to the parametrical description of CH models, could not be fully realized.
In the present stage of development, a CH model including a prognostic wave direction variable θ (hypa) generally yields predictions comparable to CD models with respect to directional relaxation effects. CD models have the advantage of predicting more detailed (but not necessarily correct) windsea directional distributions. As is to be expected, models which include no windsea directional relaxation show deficiencies for wind fields involving rapidly changing wind directions.
Many of these basic features distinguishing models of different classes become clearly recognizable in the case study analyses only if the individual model results were normalized in terms of the corresponding fetch-limited growth data of the model. Without this normalization, the variations in the basic fetch-limited growth rates of different models may mask the variations associated with different wind field geometries. This result was rather surprising in view of the fact that the calibration of most models rests heavily on fetch-limited growth data, and more data exist for this growth case than for any other growth situation. We attribute the differences in large part to uncertainties as to whether the wind speed (U 10 or U 19.5) or the friction velocity u * is the more appropriate parameter to characterize wave growth, and to the scatter in published drag coefficients relating the two. A contributing factor may be the uncertainty in the boundary layer formulation used to relate these surface velocities to the geostrophic wind, which is normally provided as the primary input by the atmospheric models used to drive the wave model. Other factors, such as the gustiness of the wind, may also contribute to the discrepancies.
Formal agreement on some standard fetch-limited growth law (whether correct or not) would facilitate future intercomparison studies and aid model development by providing a generally accepted reference baseline.
Another significant source of divergence in the model results which is not related to model class is the choice of directional distributions. This is seen most clearly in test cases involving the transition from windsea to swell in a turning or inhomogeneous wind field. Existing measurements of the frequency dependence of the directional spreading factor for a fetch-limited growing windsea are not incorporated into any of the models except sail, presumably because it is felt that a simple frequency-independent spreading factor is adequate for most applications. The test cases indicate that a more sophisticated treatment of the directional distribution is called for in all cases in which windsea directional relaxation effects come into play. However, the correct simulation of fetch-limited spreading factors is only a first step in this problem. An adequate treatment requires a more general parameterization of the nonlinear transfer, which controls the energy redistribution in a turning windsea and in the swell—windsea transition regime. A more detailed analysis of existing slanting-fetch growth data would provide a valuable test of the directional response of models.
Finally, the superposition of these many differences, related either to model class or to individual model assumptions, can result in substantial net discrepancies among different model predictions for complicated wind fields, such as the hurricane wind fields of Case VI. However, it should be recalled that the test wind fields were chosen to reveal and emphasize critical elements of the models. For more slowly varying wind fields more typical of the average case, the models may be expected to show greater agreement. On the other hand, wave models are frequently needed just for extreme-event forecasts and statistics. Our intercomparison study suggests that the reliable performance of the models in these situations, for which direct measurements are unfortunately sparse, must presently be regarded as highly questionable. A detailed analysis of the few existing hurricane wind and wave data sets in the light of the model intercomparison results for Case VI would clearly be valuable.
KeywordsWind Field Geostrophic Wind Directional Distribution Growth Coefficient Hurricane Wind
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