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

Abstract

[1] 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. INDEX TERMS:4263 Oceanography: General: Ocean prediction; 4203 Oceanography: General: Analytical modeling; 3210 Mathematical Geophysics: Modeling; KEYWORDS: wave spectrum, wave development process, forecasting, nonstationary time series model, data assimilation Citation: Hokimoto, T., N. Kimura, K. Amagai, T. Iwamori, and M. Huzii, Effects of wind-forcing on the dynamic spectrum in wave development: A statistical approach using a parametric model,

An angular–linear time series model for waveheight prediction

“…This is ARIMA model with no MA parts, which was used as a basic model to express the sea surface movement in the wave development process in Hokimoto et al (2003). Since the time series data of WL t , WS t and WD t in Fig.…”

“…If the speed in changing statistical structure can be regarded to be slow, it may be reasonable to fit a stationary AR model to the time series data in the segment which can be regarded to be locally stationary (the theoretical background is given in Dahlhaus 1997;Dahlhaus and Giraitis 1998, and so forth). Hokimoto et al (2003) developed the nonstationary spectral model of the sea surface movement in the wave development process, based on the idea of local stationarity. We can also find the application of generalized autoregressive conditional heteroscedascity (GARCH) model to the wind speed observations (Toll 1997).…”

Improved Prediction of Local Significant Wave Height by Considering the Memory of Past Winds

“…Therefore, an accurate prediction of waves is of great importance to a better understanding of the physical process in marine environments and engineering design. Numerical models, for example, SWAN (Hsu & Holland, 2007;Muraleedharan et al, 2022;Rusu & Soares, 2013) or WAVE WATCH III (Campos et al, 2022;Zheng et al, 2021) are popular models of predicting waves nowadays, in which waves are simulated with the combination of physics-based models (Hokimoto et al, 2003;Reikard & Rogers, 2011), for example, energy balance equation (Nitsure et al, 2012). Although numerical models can capture the regional pattern by nesting global ocean wave models to coastal and near-shore high-resolution wave models (Sandhya et al, 2014), it sometimes fails to forecast local wave parameters.…”