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Mass and Water
IFAE THURSDAY MEETING October 23th, 15.30h, at
IFAE meeting room
Carolina Deluca Silberberg
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INDEX
Introduction 1st PART Tide - Producing
Forces The Earth Moon System Points where
the TPF would have most effect in generating
tides Equilibrium tidal bulges Variations in
lunar induced tides The Earth Sun system
Interaction of solar and lunar tides 2nd PART
Satellite Oceanography Brew history of
Altimetry and TOPEX/Poseidon Altimetric
studies of ocean tidal dynamics Earths geoid
Mean dynamic topography Significant wave height
and wind speed modulus Conclusions
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INTRODUCTION
Visible ocean phenomena Sea movement originated
by Earths rotation OCEAN CURRENTS Sea
movement originated by the wind WAVES
Sea movement as a consequence of geological
movements TSUNAMIS... Sea movement due to
relation between Earth and our Solar system
TIDES
Tides
Tides are the sea level differences as a
consequence of the interaction between the Earth
and the heavenly bodies of our Solar System
Because of that, it is very common to see empty
beaches...
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And sometimes, absentminded people...
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TIDE-PRODUCING FORCES The Earth-Moon system
Earth Moon single system rotating about a
common CM. (T27.3 days) All points on and
within the Earth will experience the same
centrifugal force.(Fc) Fc acting on the
Earth-Moon system Fg Earth-Moon
system in equilibrium
Gravitational force
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Points where the TPF would have most effect in
generating tides
Are those points where the horizontal component
of the TPF (tractive force) is at maximum

• Tractive Force
• unopposed by another lateral force
• (negligible friction sea-bed)
• causes water to move
• is greatest at points along this circles
• this points have nothing to do with lattitude or
  longitude

Gravitational attraction at point P (1st
approximation)
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EQUILIBRIUM TIDAL BULGES
The two bulges mantain their prositions
relative to the Moon So, they would travel around
the world at the same rate but in opposite
direction as the Earth rotates In any point on
the Earths surface would encounter 2 high and 2
low tides during each day
Earth circumference 40000 Km
tide wavelenght 20000 Km Average depth of
the ocean basinis lt 4 Km
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VARIATIONS IN LUNAR INDUCED TIDES
The Moons declination Plane Moons orbit
Plane Earths orbit angle between them
declination When declination 0 - There
is an offset between the plane of the two tidal
bulges and Equator. - The tides at a given
lattitude will be unequal (particularly at
mid-lattitudes)
Angle between lunar and Earth orbit 5º Angle
between Earths equator and
ecliptic 23 .4º
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VARIATIONS IN LUNAR INDUCED TIDES II
The Moons elliptical orbit Elliptical orbit
variation in distance Earth-Moon
variations in TPFs Difference in Earth-Moon
distance (apogee perigee) about 13 Moon in
apogee TPF reduced about 20 below the
average value Tidal ranges greater if Moon in
perigee
Precession of the Moons elliptical orbit
18.6-years This cycle can be identified in
long-term tidal records Maximum declination of
the Moon ranges from 18.4º to 28.4º during the
18.6-years precession cycle
Moon travels faster at perigee than at apogee
Variations in tidal cycles
average 12h 15 All his causes small
variations in Earth-Moon period, declination
cycle and in perigee-apogee-perigee cycle
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The Earth-Sun system
There are tractive forces and two equilibrium
tidal bulges TPFSUN 0.46 TPFMOON (Sun
is some 360 times further and
) Semidiurnal period of solar tides of 12h
Solar declination also produces variations in the
relative heights of the semidiurnal solar tides
Difference in distance Earth-Sun between aphelion
and perihelion is only about 4
Changes in the orbit of the Earth around the
Sun over periods of tens of thousands of years
will affect the tides
Variation of the Sun declination over the
seasonal yearly cycle
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INTERACTION OF SOLAR AND LUNAR TIDES
a c The Moon and the Sun are in phase so they
reinforce each other They are said to be in
conjunction (New Moon) or in opposition (Full
Moon) Spring tide (long tide)
b d The solar and lunar tides are out of
phase so the tidal range is smaller than
average The Moon is said to be in quadrature
Neap tide (short tide)
Declinations of the Sun and the Moon 0
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INTERACTION OF SOLAR AND LUNAR TIDES II
Synodic month period between successive new
months (T 29.5 days) Sidereal month period
of rotation of the Moon about the Earth-Moon CM
(T 27.3 days)
The complete cycle of the Moon takes 29.5
days It is different from the Earth-Moon
rotation period!! Why? Because while the Moon
is orbiting the Earth, the Earth-Moon system is
orbiting the Sun The Moon has to return to the
same position relative to both Earth and Sun
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Brew history of ALTIMETRY AND TOPEX/Poseidon
Satellite Oceanography major
component ALTIMETRY Altimeter Microwave
radar pulse sent from an orbiting satellite,
bounces the Earths surface an returns to the
orbiting spacecraft Same principle as GPS,
aiplane altimeters and radars An altimeter
meaures the height of the ocean ATTENTION!!
Oceans height Oceans level
Seamounts and trenches which changes the
gravitational pull on the ocean surface
Tide-producing forces Ocean currents Winds
which cause waves and also force ocean currents
Sun heating the ocean, which causes it to
expand Atmpospheric storms, which cahnge the
pressure on the ocean surface
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Brew history of ALTIMETRY AND TOPEX/Poseidon II
Seasat The first true oceanographic altimetric
mission (1978) Was able to detect global
features associated with the bottom of the ocean
changes in depth of the ocean that affect the
ocean surface Could not detect how the major
currents chande over time or El Niño Seamounts
push up the ocean, opposite over a trench
This causes changes in the ocean surface of 100
meters
Now we are able to see El Niño
Highs marked by red to white, lows by blue
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Brew history of ALTIMETRY AND TOPEX/Poseidon III
TOPEX/Poseidon Seamounts and trenches might
change on geological time scales but not on
scales of El Niño So, any changes over a
year-period must be due to other forces
TOPEX/Poseidon is able to see how the ocean
changes from one year to the next For El Niño
of 1998 TOPEX/Poseidon allowed for first time
global observations of how sea level was changing
in the Pacific Seasat see changes about meters,
TOPEX/Poseidon about 2 centimeters Changes in
sea level can be used to predict
Fisheries
Coral reefs
Regional applications (ocean eddies) PRIMARY
CONTRIBUTION UNDERSTANDING OF CLIMATE
AND THE OCEANS
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ALTIMETRIC STUDIES OF OCEAN TIDAL DYNAMICS
This tecnology allows to study in a serious
way Tidal energy dissipation Dynamics of
long-period tides Improve the existing tidal
models Better observation of internal tides
TIDAL ENERGETICS Nature and location of tidal
energy dissipation Most tidal energy is
dissipated in shallow seas However, about 25
to 30 of the global energy dissipation occurs in
the open ocean
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EARTHS GEOID
The height Earths oceans changes by about 150
m from the south coast of India and western
Pacific ocean (New Guinea) This smoothed map
does not include the effect of seamounts,
trenches, etc., on the oceans surface height
Earths geoid is a calculated surface of equal
gravitational potential energy and represents the
shape the sea surface would be if the ocean were
not in motion How the real ocean surface
differs from the geoid gives ocean currents
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MEAN DYNAMIC TOPOGRAPHY
Variations observed in mean surface height are
between 110 cm (deep blue) and 110 cm (light
blue) This sea surface height (dynamic
topography) is directly related to large scale
ocean currents These flow along the lines of
equal dynamic topography (red lines)
Northern hemisphere CLOCKWISE FLOW Southern
hemisphere COUNTER-CLOCKWISE FLOW
Map showing all the features of general
circulation
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SIGNIFICANT WAVE HEIGHT AND WIND SPEED MODULUS
Satellite altimetry also used to map surface
wind speed and wave-height Figures Units in
mm (wave heigh) and m/s (wind speed) Time
interval between two consecutive maps 3
months These figures highlight the seasonal
variations in wave fields and the relationship
between wind speed and wave height Observe
trade winds, Equatorial calms, Mid-latitude lows
...
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CONCLUSIONS
The tides are the sea level differences mainly
as a consequence of the interaction between the
Earth and the Moon The tide producing force is
proportional to distance (Moon-Earths surface)
The points where the TPF would have most effect
in generating tides are those points where the
horizontal component of the TPF is at maximum
There are two equilibrium tidal bulges The most
important variations in lunar induced tides are
produced by the Moons declination and by the
Moons elliptical orbit The solar induced tides
are very similar to that the Moons induced tides
but about 0.46 that of the Moon When the Sun
and the Moon are in phase we said to have Spring
tides, and when there are out of phase we said to
have Neap tides Satellite oceanography and in
particular Altimetry are the sciences that
investigate the changes in the sea surface The
heights ocean is affected by various factors
such as the gravitational pull on the ocean
surface, the tides, the ocean currents, the
winds, the Sun heating the ocean and the
atmospheric storms