Optimal Smoothing of the Wave Spectrum using HeMOSU-1 Data

Abstract

The optimal model based on water surface elevation can be considered as the optimal smoothing model, which is the model for estimating the optimal range of smoothing. The optimal model is a process of classifying observation data into a structure that can be statistically analyzed or a signal and noise component that can be given meaning, and the signal component is an optimal estimation model. In general, wave spectral analysis for irregular waves is carried out using water surface elevation data. In this study, errors that occur in the process of smoothing the estimated spectrum were minimized using the statistical estimation method that tracks the optimal bandwidth. For optimal smoothing, a total of 169 data (excluding missing and unobserved data) were used as wave data observed from the HeMOSU-1 observation station near Wido island located in the west sea of Korea from 2013.07 to 2014.07. The extracted spectrum used raw data observed in WaveGuide Rader, and the equipment used standard wave analysis package (SWAP) method to estimate 10 mHz wave energy density spectrum after applying 10% COSINE Tapering, Fast Fourier Transform (FFT). In order to optimize the estimated spectrum, the optimal bandwidth was estimated using the local linear regression function (dpill) in the ‘KernSmooth’ package included in R, one of the data analysis programs, and the estimated value was plotted by constructing a linear function. Optimal smoothing is based on the theory of bias-variance trade off, and the optimal bandwidth value occupies 50% within the range of 0.0201 to 0.0207.