Parameterization scheme of the sea surface drag coefficient considering the influence of wave states and sea spray stress

The drag coefficient of the sea surface is crucial for the exchange of momentum between the ocean and atmosphere. The wave state significantly influences the variability of the drag coefficient. In the past, researchers commonly employed single-parameterization methods to describe this influence. However, the influence of wave conditions on drag coefficient is complex and variable, and it is difficult to accurately describe it with a single parameter alone. Wave age represents the ability of wind-induced waves to input energy, while wave steepness reflects the stability of the waves. By simultaneously considering wave age and wave steepness, a more accurate characterization of the dynamic nature of waves can be achieved. Additionally, the presence of sea spray profoundly impacts the distribution of the momentum flux between the ocean and atmosphere, thereby influencing the drag coefficient of the sea surface. In this study, we established a novel sea spray generation function that bases on both the wind speed and wave states (wave steepness and wave age). Considering this function, the momentum flux of sea spray droplets was analyzed under different wave states. Moreover, with increasing wave age or wave steepness, the effective sea surface drag coefficient is attenuated at low to moderate wind speeds. Considering the challenge of simultaneously obtaining wave age and wave steepness data, this paper proposes a relationship equation between the two wave state parameters. When the wave age is greater than 0.4, the correlation between the wave age and the wave steepness is strong. As the wind speed increases from low to high, there is a noticeable decrease in the effective sea surface drag coefficient with the corresponding increase in wave age. When the wave age is less than 0.4, the wave steepness reaches a maximum value, and the effective sea surface drag coefficient increases with the increase of the wave age at medium and low wind speed. With further increases in wind speed, the momentum flux derived from the air also increases. Simultaneously, the effective sea surface drag coefficient exhibits a decrease as wave age increases.