Geoid Totally Explained

Everything about The Geoid totally explained

The geoid is that equipotential surface which would coincide exactly with the mean ocean surface of the Earth, if the oceans were to be extended through the continents (such as with very narrow canals). According to C.F. Gauss, who first described it, it's the "mathematical figure of the Earth," a smooth but highly irregular surface that corresponds not to the actual surface of the Earth's crust, but to a surface which can only be known through extensive gravitational measurements and calculations. Despite being an important concept for almost two hundred years in the history of geodesy and geophysics, it has only been defined to high precision in recent decades, for instance by works of P. Vaníček and others. It is often described as the true physical figure of the Earth, in contrast to the idealized geometrical figure of a reference ellipsoid.

Description

The geoid surface is irregular, unlike the reference ellipsoids often used to approximate the shape of the physical Earth, but considerably smoother than Earth's physical surface. While the latter has excursions of +8,000 m (Mount Everest) and −11,000 m (Mariana Trench), the total variation in the geoid is less than 200 m (-106 to +85 m(compared to a perfect mathematical ellipsoid).
   Sea level, if undisturbed by tides and weather, would assume a surface equal to the geoid. If the continental land masses were criss-crossed by a series of tunnels or narrow canals, the sea level in these canals would also coincide with the geoid. In reality the geoid doesn't have a physical meaning under the continents, but geodesists are able to derive the heights of continental points above this imaginary, yet physically defined, surface by a technique called spirit leveling.
   Being an equipotential surface, the geoid is by definition a surface to which the force of gravity is everywhere perpendicular. This means that when travelling by ship, one doesn't notice the undulations of the geoid; the local vertical is always perpendicular to the geoid and the local horizon tangential component to it. Likewise, spirit levels will always be parallel to the geoid.
   Note that a GPS receiver on a ship may, during the course of a long voyage, indicate height variations, even though the ship will always be at sea level. This is because GPS satellites, orbiting about the center of gravity of the Earth, can only measure heights relative to a geocentric reference ellipsoid. To obtain one's geoidal height, a raw GPS reading must be corrected. Conversely, height determined by spirit leveling from a tidal measurement station, as in traditional land surveying, will always be geoidal height.

Spherical harmonics representation

Spherical harmonics are often used to approximate the shape of the geoid. The current best such set of spherical harmonic coefficients is EGM96 (Earth Gravity Model 1996), determined in an international collaborative project led by NIMA. The mathematical description of the non-rotating part of the potential function in this model is ť

V=frac=360

). For many applications the complete series is unnecessarily complex and is truncated after a few (perhaps several dozen) terms.
New even higher resolution models are currently under development. For example, many of the authors of EGM96 are working on an updated model that should incorporate much of the new satellite gravity data (see, for example, GRACE), and should support up to degree and order 2160 (1/6 of a degree, requiring over 4 million coefficients).

Precise geoid

The 1990s saw important discoveries in theory of geoid computation. The Precise Geoid Solution by Vaníček and co-workers improved on the Stokesian approach to geoid computation. Their solution enables millimetre-to-centimetre accuracy in geoid computation, an order-of-magnitude improvement from previous classical solutions .

Further Information

Get more info on 'Geoid'.

External Link Exchanges

Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:

<a href="http://geoid.totallyexplained.com">Geoid Totally Explained</a>

Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned.