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 (ηi) 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.