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