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Karissa Oleyanin
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Posts: 4127

« on: February 01, 2009, 02:00:55 am »

Satellite Altimetry
According to the laws of physics, the surface of the ocean is an "equipotential surface" of the earth's gravity field. (Lets ignore waves, winds, tides and currents for the moment.) Basically this means that if one could place balls everywhere on the surface of the ocean, none of the balls would roll down hill because they are all on the same "level". To a first approximation, this equipotential surface of the earth is a sphere. However because the earth is rotating, the equipotential ocean surface is more nearly matched by an ellipsoid of revolution where the polar diameter is 43 km less than the equatorial diameter. While this ellipsoidal shape fits the earth remarkably well, the actual ocean surface deviates by up to 100 meters from this ideal ellipsoid. These bumps and dips in the ocean surface are caused by minute variations in the earth's gravitational field. For example the extra gravitational attraction due to a massive mountain on the ocean floor attracts water toward it causing a local bump in the ocean surface; a typical undersea volcano is 2000 m tall and has a radius of about 20 km. This bump cannot be seen with the naked eye because the slope of the ocean surface is very low.

These tiny bumps and dips in the geoid height can be measured using a very accurate radar mounted on a satellite (Figure). For example, the Geosat satellite was launched by the US Navy in 1985 to map the geoid height at a horizontal resolution of 10-15 km (6 - 10 mi) and a vertical resolution of 0.03 m (1 in). Geosat was placed in a nearly polar orbit to obtain high latitude coverage (+- 72 deg latitude). The Geosat altimeter orbits the earth 14.3 times per day resulting in an ocean track speed of about 7 km per second (4 mi/sec). The earth rotates beneath the fixed plane of the satellite orbit, so over a period of 1.5 years, the satellite maps the topography of the surface of the earth with an ground track spacing of about 6 km (4 mi).

Two very precise distance measurements must be made in order to establish the topography of the ocean surface to an accuracy of 0.03 m (1 in) (Figure). First, the height of the satellite above the ellipsoid h* is measured by tracking the satellite from a globally-distributed network of lasers and/or doppler stations. The trajectory and height of the satellite are further refined by using orbit dynamic calculations. Second, the height of the satellite above the closest ocean surface h is measured with a microwave radar operating in a pulse-limited mode on a carrier frequency of 13 GHz. (The ocean surface is a good reflector at this frequency.) The radar illuminates a rather large spot on the ocean surface about 45 km (28 mi) in diameter. A smaller effective footprint (1-5 km in diameter = 0.6 - 3 mi)) is achieved by forming a sharp radar pulse and accurately recording its 2-way travel time. The footprint of the pulse must be large enough to average out the local irregularities in the surface due to ocean waves. The spherical wavefront of the pulse ensures that the altitude is measured to the closest ocean surface. A high repetition rate (1000 pulses per second) is used to improve the signal to noise ratio, especially when the ocean surface is rough. Corrections to the travel time of the pulse are made for ionospheric and atmospheric delays and known tidal corrections are applied as well. The difference between the height above the ellipsoid and the altitude above the ocean surface is approximately equal to the geoid height N = h* - h.

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