A Sea State Parameterization with Nonarbitrary Wave Age Applicable to Low and Moderate Wind Speeds

Abstract

A simple coupled flux and sea state model is developed. It is applicable to low, moderate, and high wind speeds, with a nonarbitrary wave age. It is fully consistent with an atmospheric flux parameterization. The flux model includes the influence of capillary waves on surface stress, which dominate surface stress on a wave-perturbed surface for U10 < 7 m s−1. The coupled model is verified for conditions of local equilibrium and it is used to examine the influences of surface tension and capillary waves on the equilibrium sea state at low and moderate wind speeds (U10 < 7 m s−1). Capillary waves can directly influence characteristics of the airflow (roughness length and friction velocity), and surface tension can directly influence wave characteristics (period, phase speed, and wave age). The influences of capillary waves and surface tension on wave characteristics are found to be noticeable for U10 < 6 m s−1, and are likely to be significant in most applications when U10 < 5 m s−1. The conditions under which relations valid for higher wind speeds break down are discussed. The new sea state parameterization is an improvement over previous relations (which apply well for U10 > 7 m s−1) because it is also applicable for low and moderate winds. The mean wind speed over most of the world's oceans is less than 7 m s−1, so there is considerable need for such a parameterization. The nonarbitrary wave age is particularly important because of the influence of wave age on the shape and size of waves, as well as fluxes of momentum, heat, and moisture. Additional results include a criterion for the capillary cutoff, significant wave height, and dominant wave period (as functions of wind speed and wave age). Consistency with a flux parameterization is crucial because of the influence of atmospheric stability on surface stress, which influences wave characteristics. The modeled significant wave height for local equilibrium is shown to be consistent with several parameterizations. The modeled dominant period is a good match to that of the Pierson–Moskowitz spectrum when U10 > 13 m s−1; however, for lower wind speeds, the modeled period differs significantly from that of the Pierson–Moskowitz spectrum. The new model is validated with field observations. The differences are largely due to the capillary cutoff, which was not considered by Pierson and Moskowitz.