Vol.:(0123456789) 1 3 Model. Earth Syst. Environ. DOI 10.1007/s40808-017-0348-2 ORIGINAL ARTICLE Advanced spectral analysis of sea water level changes Mohamed Elsobeiey 1   Received: 3 June 2017 / Accepted: 22 July 2017 © Springer International Publishing AG 2017 Introduction The word “tides” is the term used to defne the response of the ocean to the periodic fuctuations of the gravitational attraction of the moon and the sun. This response is in the form of long waves that are generated throughout the ocean. They propagate from place to place, are refected, refracted, and dissipated just as other long waves. Like the open oceans, lakes are also afected by tides, and the solid Earth crust is afected by the same gravitational force of the sun and the moon. Moreover, other factors such as the coastline shape hydrographic conditions can play an essen- tial role in the tidal range, the diference tidal range, and the duration and occurrence time of the tides. As the tides rise and fall, it produces food and ebb currents, respectively. Gravity is the main force that creates tides. Tides are the results of the gravitational force of the moon and the sun as explained by Isaac Newton in 1978. Newton’s uni- versal gravitation law states that the gravitational attraction between two objects has a directly proportional to the cor- responding masses, and inversely proportional to the square of the distance between the bodies (Sumich and Morrissey 2004). The gravitational attraction force F between any two masses, m 1 and m 2 apart with distance d is given by: where G is constant depends upon the units employed. Therefore, the gravitational attraction force between two objects depends mainly on the mass of the objects and the distance between them. So, tidal forces are the result of the gravitational force. In case of the objects on the Earth’s sur- face, the distance between the two objects is more impor- tant than their masses. If we consider the Earth-moon (1) F = Gm 1 m 2 d 2 , Abstract Navigation in coastal areas requires accurate water levels modeling and prediction. Basically, tides are generated as a response to the attraction forces exerted by the moon and the sun. However, such attraction forces are not the only factors afecting water levels. The shape of bays, local wind and weather patterns also can afect tides. In this paper, the least-squares spectral analysis (LSSA) approach is used to analyze long series of tidal data, atmospheric pressure, and wind speed extended more than 9 years. The tide prediction model is developed by deter- mining the harmonic constituents of the tidal data using LSSA approach. It is found that the resultant spectrum still contains diferent peaks after forcing all tidal constituents. The water level response to atmospheric pressure is also investigated. The amplitude and phase response of tidal data to atmospheric pressure are determined. It is shown that the response of water level to the atmospheric pressure has an average of about 4.5 mm/millibar. Moreover, the amplitude and phase response of tidal data to wind speed is also investigated. It is found that the power ratio of pressure efect to wind efect is about 1.64 × 10 6 . That means the efect of wind is too small compared to the efect of atmos- pheric pressure, which can be considered a special case for this location as it is surrounded by mountains that afect the wind speed and its variation. Keywords Water level · Atmospheric pressure · Spectral analysis · Least-squares * Mohamed Elsobeiey melsobeiey@kau.edu.sa 1 Department of Hydrographic Surveying, Faculty of Maritime Studies, King Abdulaziz University, P. O. Box 20807, Jeddah 21589, Saudi Arabia