Effects of wind-forcing on the dynamic spectrum in wave development: A statistical approach using a parametric model

Previously, studies on the dynamic structure of the spectrum in the wave development process have considered only the physical mechanism of the transmission of energy from wind to wave or have considered purely mathematical methodologies. Few studies have examined the statistical mechanism of the dynamic relationship between sea surface movement, wind motion, and the time‐varying spectrum of the sea surface movement. In the present paper, we investigate the statistical structure of the sea surface movement and the wind motion in developing wind waves and propose a spectral model to estimate the time‐varying spectral density function. The validity of the proposed model is demonstrated through numerical experiments to evaluate the forecasting accuracy. The proposed model is used to examine the degree of the influence by wind motion, which affects the spectral density function. In the present study, we analyzed the time series record in the wave development process measured in Uchiura (Funka) Bay, Hokkaido, Japan. The basic results are summarized as follows: (1) the nonstationary statistical structure presented herein yields one of the effective classes by which to explain the dynamic mechanism between the time‐varying spectral density function of sea surface movement and wind motion, and (2) in our numerical experiments the spectral model allowed effective forecasting, especially in the case of high wind speed.