Time Variant Wave-Signal-Amplitude Trigonometry Regression of Latitudes and Longitudes of the Belmullets of the Atlantic Ocean

Abstract

This paper introduces time variant wave-signal-amplitude cosine and sine regression as an extension to wave signal Fourier function and Wave-Shape Function (WSF) model. A full-scale conditional characterization of the linear time variant wave-signal-amplitude cosine and sine model of cosine and sine function with random errors (η_i) was proposed. The associated regression coefficients were estimated via the Ordinary Least Square (OLS) technique, such that, the model wave signal, frequency, and phase were carved-out. In application to real life problem, the wave-signal-amplitude trigonometry model was applied to the real-time observations of the latitude and longitude of the wave buoys’ Belmullets of the Atlantic Ocean. The full-scale real-time observations of the wave climate are the time-variant significant wave height (in metre), peak wave (in ^oC) and sea temperature (in ^oC) from 2012 to 2022.