Modeling multiple wave systems in the eastern equatorial Pacific

Abstract

While moderate wind and wave conditions prevail in the eastern equatorial Pacific, modeling waves in this area remains challenging due to the presence of multiple wave systems converging from different parts of the ocean. This area is covered by swells originated far away including the storm belts of both hemispheres, coexisting with local generation due to the regular action of both the southern trade winds and the wind jets from Central America. In this context, our ability to predict waves in the area depends on the overall quality (i.e., at Pacific scale) of the meteorological input, and also on the skills of the wave model itself. Clearly any error at the remote generation areas translates into larger errors the further waves go, especially if attention is focused on coastal areas. A relevant aspect is that the traditional integral parameters do not offer the possibility to properly assess the errors associated with the different parts of the spectrum (e.g., wind sea and swell). To gain insight in this direction, we make use of partitioning techniques, which enables us to neatly cross-assign and evaluate three spectral components. Not surprisingly, the performance for the swell part is lower than that of the corresponding wind sea. This is further explored with a couple of tests modifying both the wind input and the wave model physics. We find that although at first sight the initial scheme (i.e., ST4) seems to provide the better estimate, the spectral analysis reveals a substantial underestimation of wind sea, compensated with a substantial overestimation of swell. This suggests a problem with too high winds and wave generation in the storm belts together with a likely lack of dissipation or dispersion of swell. In turn, local waves are generally underestimated due to a corresponding underestimation of the local winds. This insight emphasizes the need and advantages of evaluation methods able to look at the different sectors of the wave spectrum.

Appendix. Statistical parameters

The statistical parameters for comparisons between model results and observations are root mean square error (RMSE), bias, scatter index (SI), and the coefficient of determination (R²). The corresponding formulations as given by Van Vledder (1993) are:

$$ RMSE={\left\{\frac{1}{N}\sum \limits_{i=1}^N{\left({x}_i-{y}_i\right)}^2\right\}}^{1/2} $$

(1)

$$ BIAS=\frac{1}{N}\sum \limits_{i=1}^N\left({y}_i-{x}_i\right) $$

(2)

$$ SI=\frac{RMSE}{\left|\overline{x}\right|} $$

(3)

$$ {R}_{x,y}=\frac{\sum \limits_{i=1}^N\left({x}_i-\overline{x}\right)\left({y}_i-\overline{y}\right)}{{\left\{\sum \limits_{i=1}^N{\left({x}_i-\overline{x}\right)}^2\right\}}^{1/2}{\left\{\sum \limits_{i=1}^N{\left({y}_i-\overline{y}\right)}^2\right\}}^{1/2}} $$

(4)

where x is the measured and y the modeled variable.