Mass and Water
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Mass and Water. IFAE THURSDAY MEETING October 23th, 15.30h, at IFAE meeting room. Carolina Deluca Silberberg. 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

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Mass and Water


October 23th, 15.30h, at IFAE meeting room

Carolina Deluca Silberberg


· 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

· Earth’s geoid

· Mean dynamic topography

· Significant wave height and wind speed modulus

· Conclusions


Visible ocean phenomena

· Sea movement originated by Earth’s 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 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...

And sometimes, absentminded people...


The Earth-Moon system

· Earth + Moon = single system rotating about a common CM. (T=27.3 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


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)


·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 Earth’s 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 < 4 Km


The Moon’s declination

· Plane Moon’s orbit Plane Earth’s 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

Earth’s equator and ecliptic: 23 .4º


The Moon’s 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

·Precessionof the Moon’s 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

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


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


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

Brew history of ALTIMETRY AND TOPEX/Poseidon

·Satellite Oceanography major component = ALTIMETRY

·Altimeter = Microwave radar pulse sent from an orbiting satellite, bounces the Earth’s surface an returns to the orbiting spacecraft

· Same principle as GPS, aiplane altimeters and radars

· An altimeter meaures the heightof the ocean

·ATTENTION!! Ocean’s height Ocean’s 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

Brew history of ALTIMETRY AND TOPEX/Poseidon II


· 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

Brew history of ALTIMETRY AND TOPEX/Poseidon III


· 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

· Seasatsee changes about meters, TOPEX/Poseidon about 2 centimeters

· Changes in sea level can be used to predict:


Coral reefs

Regional applications (ocean eddies)



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


· 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


· The height Earth’s oceans changes by about 150 mfrom 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 ocean’s surface height

·Earth’s 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


· 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


·Southern hemisphere


Map showing all the features of general circulation


· Satellite altimetry also used to map surface wind speed and wave-height


· Units in mm (wave heigh) and m/s (wind speed)

· Time interval between two consecutive maps = 3 months

· These figures highlight the seasonal variationsin wave fields and the relationship between wind speed and wave height

· Observe trade winds, Equatorial calms, Mid-latitude lows ...


·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-Earth’s 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 Moon’s declination and by the Moon’s elliptical orbit

· The solar induced tides are very similar to that the Moon’s 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 height’s 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

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