Oceanography
CRN # 10053
Lecture 4b
Debbie Reynolds Lecture Certification:
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Lectures 1
a)
b)
Properties of sea water, ocean physics, ocean basins, explorers
Meteorology, heat balance, geostrophic circulation
Lectures 2
a)
b)
Surface ocean winds, currents, temperature and salinity
Deep circulation, instruments
Lectures 3
a)
b)
El Niño
Climate change in the oceans, including sea level rise
Lectures 4
a)
b)
Wind waves, rogue waves and tsunami
Tides
Lectures 5
a)
b)
Sea-floor spreading, continental drift − Plate Tectonics
Ocean basins, ocean sediments, coasts and estuaries
Lectures 6
a)
b)
Food web, plankton, invertebrate animals
Vertebrate animals, communities tidal to abyssal
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Introduction
•
•
•
•
•
•
The ocean tides on the earth are driven by the
gravitation attraction of the sun and the moon
Lunar tides are roughly twice as strong as solar
tides
Regions have diurnal (once a day), semidiurnal
(twice a day) or mixed tides
Tides can be predicted
Spring Tides occur when the moon and sun line
up and reinforce the tides
Neap Tides occur when the moon and sun are
roughly 90° apart and weaken the tides
3
Tidal Theories
• Equilibrium Theory of Tides






Earth is a water world
No land or ocean topography
No inertial delay, tidal forces act instantly
Realistic: Earth rotates in 24 hours
The moon is considered first
Then the sun is added
• Dynamic Theory of Tides
 Earth has land and ocean topography which impacts
the tides
 Tide waves are forced waves driven by the moon and
sun
4
Tides
1) Tides are Gravitational Forced Shallow Water
Waves
2) Tidal forces from the moon (and the sun) are
Not Constant across the earth
3) The oceans closer to the moon are more
strongly attracted to the moon causing a high
tide
4) The oceans opposite the moon also have a high
tide!
5
Center of Mass (CM)
The Center of Mass is the unique point
where the weighted relative positions
of the distributed masses sum to zero
Two bodies
rotate
about their
Center of Mass
6
Why are there 2 High Tides
on Opposite Sides of the Earth?
The Earth and Moon System rotates about the Center of Mass
The Center of Mass is NOT at Center of the Earth!
7
Tidal Forces
• Tidal Forces are
differential
• Tidal Forces act
on:
Moon
 The Atmosphere
 The Solid Earth
 As well as the
Ocean
Jupiter’s Tidal Forces
tore apart the Shoemaker
Levy Comet
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Why the Moon has a stronger
tidal force on the earth than the Sun
• Earth Tidal forces are proportional to: m / r3


m = mass of moon or sun
r = distance between the moon and the earth
or the sun and the earth
• The sun’s influence on the tides on earth is
46% of the moon’s influence


The sun is 27 million times more massive than
the moon
The sun is 390 times as far away as the moon

(27,000,000)/(390)3 = 0.46
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Spring and Neap Tides
Spring Tides: Moon and
sun reinforce each other
to produce stronger tides
• Occurs at full and new
moons
Spring Tide
Neap Tides: Moon and
sun offset each other to
produce weaker tides
• Occurs at first and
last quarter moons
Neap Tide
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Spring and Neap Tides
Lunar orbit is
• 29.5 days with
respect to the
Earth
• Spring tides
occur twice a
month (at full
and new
moon)
• Neap tides
occur twice a
month (at first
and last
quarter)
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Spring and Neap Tides
Lunar orbit is
• 29.5 days with
respect to the
Earth
• Spring tides
occur twice a
month (at full
and new
moon)
• Neap tides
occur twice a
month (at first
and last
quarter)
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Lunar orbit is 29.5
days with respect to
the earth
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Classification
of Tides
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The Tidal Bulge is NOT symmetric
with respect to the equator
Why
Mixed
Tides
occur
?
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Tidal Complications − 1
•
•
Continents and Ocean Topography interfere with
tidal motions
Tidal waves move as Forced shallow water waves

On the equator tidal waves would have to move at
roughly 1600 km/hr (1000 mi/hr)

Free shallow water speed,
𝐂=

C = 712 km/hr (442 mi/hr)

h = 4000 m (13,000 ft):
𝐠∙𝐡
, too slow
Water must actually be forced to keep up
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Tidal Complications − 2
•
•
•
The earth is tilted by 23.5° so the sun is not
always over equator
The moon’s orbit is tilted 5° with respect to the
orbit of the earth around the sun (the ecliptic)
Both the earth’s orbit around the sun and the
moon’s around the earth are elliptical
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Tidal Complications − 3
•
•
The sun is at its highest
point overhead every 24
hours
The moon is at its highest
point overhead every 24
hours and 50 minutes

With respect to the earth the
moon completes an orbit in
29.5 days
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Bathymetry
Atlantic
Topography
•
•
•
Abyssal Plain
Continental Shelf
& Margins
Ridges
•
Trenches
Ocean topography
interferes with
tidal motions
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Rogue Waves
• Interaction of
two waves
leads to
constructive
or destructive
interference
1. Constructive
Interference:
Add Waves
2. Destructive
Interference:
Subtract
Waves
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Harmonic Tidal Prediction
•
•
•
•
We know the orbital and rotational parameters of
the earth, sun and moon system (ephemerides)
We can compute the period of each of the tidal
components from the ephemerides
There are at least 388 of them (using 62 is OK)
The first 6 are
Name
1.
2.
3.
4.
5.
6.
Symbol
Principal lunar semidiurnal
Principal solar semidiurnal
Larger lunar elliptic semidiurnal
Lunar diurnal
Lunar diurnal
Solar diurnal
M2
S2
N2
K1
O1
P1
Period
12.4206012 hr
12 hr
12.65834751 hr
23.93447213 hr
25.81933871 hr
24.06588766 hr
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Harmonic Tidal Procedure
• Measure the tidal height, H(t), for a month to a year where
t is time

H(t) → Measured
• Find the unknown amplitudes A and phases φ (timing) of
each of the tidal components
• Using computed amplitudes and phases predict tides
into future

H(t) → Predicted
• Problems


Meteorological signals (strong winds, storm surge, etc.)
add noise
Short tuning period used to get coefficients
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Tidal Harmonics
• Example shows a 3
semidiurnal and 3
diurnal constituents
• Differences in
constituent periods
are due to the orbital
parameters
(ephemerides)
• Combining the 6
components gives
the composite
• Once this is done we
can predict the tides
by extending the
composite into the
future
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Historical Context
• Tidal information in the 1800s was critical for
sailing ships to be able to leave harbor; the
information was kept secret by private firms and
sold to ship captains
• The Method of Harmonic Tidal Prediction was
developed in by William Thomson (Lord Kelvin),
George Darwin and others in the 1860s
• It was latter improved with 388 components by
Arthur Thomas Doodson in the 1920s
• The computations were tedious to compute by
hand to determine the harmonic constants
• It was even more tedious to compute tidal
predictions
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Analog Computation
•
•
Rollin A. Harris and E.G. Fischer constructed
this machine in 1912 for the U.S. Coast and
Geodetic Survey
The machine summed 37 harmonics and was
capable of producing results graphically
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Measuring Tides
Older
Tide
Houses
In Situ
Nice House
In Russia
Newer
Houses
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Hopewell Rocks
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Low Tide
Hopewell Rocks
Provincial Park
New Brunswick
Canada
High Tide
Incoming Tide
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Low Tide
Mont Saint-Michel
Normandy, France
Began as a monastery
in the 8th Century
High Tide
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Intertidal Zones
•
•
Life may have started in tide
pools
Reproductive Activities



Turtles lay eggs at high tide
Fish (grunion) spawn at high
tide on the beach
Some corals spawn during
Spring Tides
• Some animals (for example
crabs) hide in the sand at high
tide and forage at low tide
• Animals and plants sort
themselves into several tidal
zones where they are best
adapted
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Macton River, Canada
Tidal
Bore
Flood: Incoming Flow
Ebb: Outgoing Flow
River Ribble, England
Qiantang River, China
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Low Tide, Gorey Harbour, Jersey, England
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Summary
•
•
•
•
The ocean tides on the earth are driven by the
gravitation attraction of the sun and the moon
Because the moon is closer than the sun, lunar
tides are roughly twice as strong as solar tides
Regions have diurnal, semidiurnal or mixed tides
Tides can be predicted using tidal harmonics
• Spring Tides occur when the
moon and sun line up and
reinforce the tides
• Neap Tides occur when the
moon and sun are roughly
90° apart and weaken the
tides
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