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Advanced Series on Ocean ~ n ~ i n e e r ~ ~ g - Volume 16 
AND ~ N A G E ~ E N T 
J. William ~ ~ r n p h u ~ ~ 
Queen’s University, Canada 
WpVVorld Scientific 
Singapore *NewJersey* London 4Hong Kong 
~ u b l i s ~ d by 
World Scientific Publishing Co. Pte. Ltd. 
P 0 Box 128, Farrer Road, Singapore 912805 
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British Library Cataloguing-in-Publication Rab 
A catalogue record for this book is available from the British Library. 
~ R O ~ ~ ~ ~ N TO COASTAL E ~ G ~ ~ N G AND M A ~ A ~ E M ~ N T 
C o ~ ~ g h t Q 2000 by Worfd Scientific Pubiishing Co. Pte. Ltd. 
Al l rights resewed. This book, or parts thereoj m y not be reproduced in any form or by any means, 
electronic or m e c ~ n ~ c a l , includingpho~ocopying, recording or any i ~ ~ o r ~ t ~ o n storage and retrieval 
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ISBN 981-02-3830-4 
ISBN 981-02-4417-7 (pbk) 
Printed in Singapore. 
6. Tides and Water Levels 
6.1 Introduction 
Although coastal design is normally considered to be a function of wave conditions, 
it is primarily a fbnction of water levels. It is water levels that control both flooding 
and wave exposure. Imagine a simple structure close to shore that is subject to 
waves. When the water level rises, the structure will be exposed to larger waves 
because the water depth determines where waves break and loose most of their 
energy (Ch. 7). This results in increased forces on the structure and overtopping of 
water that will damage the structure and areas behind it. Conversely, when the water 
level drops, the same structure may not be exposed to waves at all. Thus most 
damage to structures occurs when the water levels are high. 
Similarly, high water levels cause retreat of sandy shores, even if they are backed by 
substantial dunes. The higher water levels allow larger waves to come closer into 
shore. These waves will erode the dunes and upper beach and deposit the sand 
offshore. If the water level rise is temporary, most of this loss will be regained at the 
next low water (Ch 11). Permanent water level rise, however, will result in 
permanent loss of sand (Ch 12). Shorelines consisting of bluffs or cliffs of erodable 
material, such as glacial till or sol3 rock are continuously eroded by wave action. (Ch 
11). High water levels, however, will allow larger waves to attack the bluffs 
directly, causing a temporary rapid rate of shoreline recession. 
There are several types of water level fluctuations and they can be classified 
according to their return period as: 
118 Introduction to Coastal Engineering and Management 
Short Term 
- Tides 
Long Term 
- Climatic Fluctuations 
- Eustatic (Sea) Level Rise 
- Climate Change 
Storm Surge and Barometric Surge 
- Seiche 
Isostatic (Land) Emergence and Subsidence 
6.2 Tides 
Astronomic tides are often the defining water motion in coastal areas. They cause 
the water levels to rise and fall and cause large-scale currents patterns, sometimes 
with large velocities. Tides directly affect coastal morphology, navigation, fisheries, 
habitat and recreational activity. Because of their relative importance they are 
discussed extensively in this chapter. 
The tides are the result of a combination of forces acting on individua~ water 
particles. These are: 
gravitational attraction of the earth, 
centrifugal force generated by the rotation of the earth - moon combination, 
gravitational attraction of the moon, 
gravitational attraction of the sun. 
6.2. I Equilibrium Tide (Moon) 
Let us first neglect the force of the sun and assume t..dt the whole earth is covered 
with water. The resultant force on the water particles is a small horizontal force. It 
moves the water particle A in Fig. 6.1 toward the moon and particle B away from 
the moon, resulting in two bulges of high water, (Defant, 1961; Ippen, 1966; 
Marchuk and Kagan, 1984; Neumann and Pierson, 1966). As we turn with the 
earth's angular velocity, wE, around the earth's axis at CE in the direction of the 
arrow, we turn through this deformed sphere of water and experience two high water 
levels and two fow water levels per day. The resulting tidal period would be 12 hrs, 
however, the moon-earth system also rotates around CME with velocity oME in the 
same direction as the earth's rotation. The bulges follow the position of the moon 
and hence the tidal period is 12.42 hrs. 
Chapter 6 - Tides and Water Levels 119 
The tide in Fig. 6.1 is called equilibrium tide since it results from the assumption 
that the tidal forces act on the water for a long time so that equilibrium is achieved 
between the tide generating force and gravity (the slope of the water surface). 
Figure 6.1 Equilibrium Tide 
6.2.2 Equilibrium Tide (Sun and Moon) 
The sun's gravity forms a second, smaller set of bulges toward the sun and away 
from the sun. Since our day is measured with respect to the sun, the period of the 
tide generated by the sun is 12 hrs. 
Both these equilibrium tides occur at the same time and they will add up when the 
moon and sun are aligned (at new moon and full moon). At those times, the tides 
are higher than average. At quarter moon, the forces of the sun and moon are 90" 
out of phase and the equilibrium tides subtract from each other and at such a time, 
the tides will be lower thah average. The higher tides are called spring tides and the 
lower ones neup tides. Fig. 6.2a demonstrates this. The phases of the moon are 
shown at the bottom of the figure and it is seen that, except for some phase lag, the 
maximum tides (spring tides) in Fig. 6.2a correspond to new and full moon, while 
the neap tides correspond to the quarter moon. 
120 Introduction to Coastal Engineering and Management 
I 1 
I I 
A S 
I - 
Figure 6.2 Tide Recordings (after Forrester, 1983) 
Chapter 6 - Tides and Water Levels 121 
6.2.3 Daily Inequality 
Figure 6.1 was drawn looking down on the earth's axis. Since the equilibrium tide 
is three dimensional in shape (it forms a distorted sphere), the picture is the same 
when the earth is viewed from the side, as shown in Fig. 6.3. An observer, C, 
travelling along a constant latitude would experience two tides of equal height per 
day. However, the moon or sun is seldom in the plane of the equator. When the 
moon or sun has a North or South Declination with respect to the equator, as shown 
in Fig. 6.4, one bulge of the equilibrium tide will lie above the equator and one 
below the equator. An observer moving along a constant latitude would now 
experience two tides per day of unequal height. This is called daily inequality. The 
daily inequality is most pronounced when the moon or sun is furthest North or South 
of the equator. There is no daily inequality at the equator and it increases with 
latitude. Lunar daily inequality is demonstrated in Fig. 6.2b. The letters E, N and S 
at the top of Fig. 6.2 denote when the moon is in the plane of the equator, at the 
maximum North declination and maximum South declination. It is seen that the 
largest daily inequalities indeed correspond to N and S, except again for some phase 
lag. The daily inequality cycle generated by the moon's forces repeats itself every 
lunar month (29.3 days). For the tide generated by the sun, the daily inequality 
cycle has a period of a year and is greatest shortly after mid-summer and mid-winter, 
causing higher tides in early January and early July. 
t " 
Figure 6.3 Equilibrium Tide (2) 

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