Sea Surface Height training course

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Part 1 - Oceanography
         Why the ocean surface is not plane?

         Dynamic topography and geostrophy
         Geostrophic current

Part 2 - Sea surface height measurement
         Observing the ocean with altimetry
         The altimeter measurement

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                            Part 1

  Atlantic ocean                        Pacific ocean

                                        Indian ocean

  Arctic ocean                          Polar ocean

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    Unequal repartition of the continents and oceans : this impact the
    atmospheric circulation and thus the oceanic circulation

                                 North Hemisphere : 61% of ocean

South Hemisphere: 81 % of
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                    General atmospheric circulation

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                    General oceanic surface circulation

  Wind induced circulation

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                  Why is the surface not plane?

   Because of the ocean-atmosphere interactions :

           Winds and associated mixing.

           Heat exchanges with the atmosphere modify the temperature and

            salinity, thus water mass density.

           Seasonal cycles: ocean temperature and volume grow in
            summer, leading to the mean sea level expansion over a all
            hemisphere. The opposite occurs in winter.

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               The ocean : a distorted surface
Sea level variations are due to:
    Tides
    Waves
    Water density :
      - the sea water density is related to the temperature and
      - the volume is related to the water density
      - If temperature decreases, density increases and volume
      decreases.         There is contraction of the water column.
     - If salinity decreases, density decreases and volume
      increases. There is expansion of the water column.
Density variations lead to appearance of bumps and holes on
the sea surface.
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                                   H1 < H’1                   H’1
                                   S2 > S1
                    T1,S2                             T1,S1

     H                                                              H’>H

                                   H2 < H’2                   H’2
                    T1,S2          T1 < T2            T2,S2

         H3         T3,S3          H3 = H’3           T3,S3   H’3
                               Bottom of the ocean

                            Piling up different density
                                 water quantities

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                           Pressure force

 The pressure at a given depth is essentially caused by
 the weight of the above water column.
 At two different locations in the ocean, at a given depth :
     if the above-water column have different density profiles, then the
       pressure will be different.
     an horizontal difference of pressure (“pressure gradient”) will
      produce a force which tends to push water from high to low

                                     --                        +++
                                          Pressure force

                                           Vertical section
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                         Geostrophic current
 BUT, because of the Coriolis force due to the Earth
  rotation, a current perpendicular to the sea surface
  slope is created. This current is called the
  geostrophic current.

                                                      Pressure force

                             !   In the Northern hemisphere
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The Coriolis force:

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          Dynamic topography and geostrophy

 The direction of geostrophic current is always
  perpendicular to the slope direction:
             In the northern hemisphere. The Coriolis force deflects
               movements to the right of the trajectory.

             In the southern hemisphere. The Coriolis force deflects
             movements to the left.

             WARNING : the Coriolis force vanishes at the equator. There
             is no geostrophic equilibrium at the equator : the slopes of the
             dynamic topography can NOT be related to geostrophic

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        Calculation of the geostrophic currents

 Current speed:
 The current speed is proportional to the sea surface slope.

        g      H                                      A
U           X
      2sin   X

H         : height difference between 2 points
X         : distance between the 2 points
g          : 9.81 gravity constant
          : 7.27 10-5 Earth angular rotation speed
          : latitude of the 2 points

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                No Coriolis force at the Equator

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     The ocean surface shows whirling structures, meanders and
      fronts witch size vary from a few tens to a few hundreds of
     The geostrophic velocity is minimum at the center of the eddy
      and gets higher away from it.

      Rotation of eddies :
                                      Anticyclonic eddies or       Cyclonic eddies
                                            “bumps”            (depressions or “holes”)

                  Contain generally        Warm water                Cold water

                     Northern              Clockwise                anticlockwise
                    hemisphere              rotation                   rotation

                       Southern           anticlockwise              Clockwise
                     hemisphere              rotation                 rotation
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    Fronts are found between positive eddies
     (anticyclones or “ bumps ”) and negative
     (depressions or “ holes ”), in areas of maximum
     current velocity.

    In the frontal areas take place convergence
     (sinking of surface water) and divergence
     (upwelling of cold water to the surface)

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                  MOVY: 4 years of general circulation in
                  the Atlantic ocean, an animation.

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                 Part 2
    sea surface height measurement

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                         Observing the ocean

                                   In-situ : poor space/time sampling of
                                    the ocean, remote regions (southern
                                    oceans), costly.

                                   Satellite Data/: space data can
                                    provide long-time, repeated and
                                    global measurements of ocean key
                                    parameters in real time.

                                   Numerical modeling : the only way to
                                    forecast the oceanic situation.

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                             Satellite altimetry

 Probably the most important satellite technique for oceanography.
 Very mature technique (20 years):
      GEOS-3 (1975), SEASAT (1978), GEOSAT (1985-1989), ERS-1
      (1991-1996), ERS-2 (1995- 2003) TOPEX/POSEIDON (1992 - ?), GFO,

 Major advances in sensor and processing algorithm performances
  over the last 20 years.

                         As a result, accuracy evolved from
                          several meters to a few cm only

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                      The altimeter measurement

                                                     SSH = S - R = G + 

                                                     SSH: absolute sea surface
                                                     topography / ellipsoid
                                                     S: position of the satellite /
  LASER                                              R: range
 STATION                       RANGE
 DORIS                                               G: marine geoid height
STATION                                              (motionless ocean)
                 ALTITUDE                            : dynamic topography.
                             DYNAMIC TOPOGRAPHY

                                 GEOID     SURFACE

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                          The geoid

The Earth is a quasi sphere in space

Flatened around the Poles because
of it’s rotation, it’s an inhomogeneous

This creates an irregular gravity
field: the geiod.

This surface is roughly known

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     SSH = S -R = G + 

   • the quantity we want to know: the dynamic topography .
   • because of the geoid imprécision we calculate sea level anomaly
     to a mean.

             mean sea surface height calculation
                   <SSH>= <G>+ <>
             man can then deduces the sea level anomalies
                   SSH - <SSH>= (G+) - (<G>+<>)
                              = -< >  SLA

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                  The radar altimeter : wave form

                Ideally calm sea             Rough sea

  Individual                                         Average of 90
return pulse:                                        return pulses

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                    Instruments characteristics

                            ENVISAT       GFO        JASON

              ALTITUDE       800 km      880 km     1300 km

              COUVERAGE     81°N-80°S   72°N-72°S   66°N-66°S

              INTER TRACk    85 km       160 km      300 km

              CYCLE         35 jours    17 jours    10 jours

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                              JASON (blue), ENVISAT(red) and GFO (green) ground tracks

Multi satellite combination
to increase the precision
of the maps.

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                          Sea level anomaly (cm)

“bump” of ocean
 topography, i.e
anticyclonic eddy
    (g. warm)

“hole” or cyclonic
  eddy (g. cold),
plankton can come
 up to the surface

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                    Part 3
          From scientific investigation
            Operational application

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                          Scientific results

 High precision of altimetric measurements : radar capable of
  detecting sea level changes of 1-2 cm at an ocean basin
 Global coverage of the whole ocean
 allow a great improvement in observing/understanding
     the global ocean circulation and climate:
     the mean sea level changes
     the ocean variability (seasonal cycle, a.s.o…)
     inter annual changes (El Nino)
     tides, ...
 Besides applications in meteorology, geophysics, and

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                         Dynamic topography (cm)

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               Ocean variability : El Nino 97-98

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               Who’s customers for altimetry ?
   « sea people », for whom the ocean is the essential environment
    (marine, fishing activities, navigation, oil exploration, ...),

   « scientific people », who study the “ocean system”, its balances,
    mechanisms and variability.

   “climate people”, who consider the ocean as a fundamental element
    which regulates the climate system (coupling between Earth-Ocean-

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                                    Fishing
                                        fishing helping tool: identification of
                                        the areas with higher fish

                                    Ship routing
                                        Optimization of maritime routes

                                       Scientific investigation
                                        Near real time help for campaigns
                                        at sea (in situ measurements)

                                       Oil exploration
                                         Help for planning operations at

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                         Albacore tuna campaign
                               (June 1993)
                                                         June, 9
                                                         June, 19
                                                         May, 30

                            lag between map and date (in day)
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