Michael:
>1 spherical
>2 spheroidal
>3 ellipsoidal
>4 geoidal
Actually only three - "spheroid" and "ellipsoid" are interchangeable
terms, the first being a little antique. In the U.K. we had until
recently the venerable "Airy spheroid" (1830) as the basis for our
mapping, but it was an oblate ellipsoid like all the others.
1) The basic global mapping sphere is the "authalic" sphere, which
has the same surface area as the real Earth - it's 6371km in radius,
so has an error of 0.1% to 0.2%.
2) The WGS84 ellipsoid is the best fit for the whole Earth, but fits
quite badly at some locations - the biggest bulge occurs around New
Guinea, where sea level is 75m above the ellipsoid, and the deepest
depression is near Sri Lanka, -104m.
Hence the adoption of various local standards (a hundred or so as I
recall) - differently shaped ellipsoids (some of them nudged slightly
off-centre relative to the Earth), which better fit the shape of the
Earth in the area of interest. My estimate of a "few metres" error
applies to these local ellipsoids only - there is an irreducible
error of tens of metres for any global standard ellipsoid.
Although these ellipsoids have been overtaken to some extent by 3)
below, they are still relevant to us, since most of the maps and
treaties we think about predate satellite mapping technology.
3) On top of the WGS84 ellipsoid you can lay a geoid model - a lot of
data points and interpolation software to derive the true Earth
radius at any given point. Once you have this in place you don't need
to worry about the local ellipsoids any more. Local WGS84 variants
are defined, however, to take into account the fact that the various
continents are drifting at various (centimetre/year) rates relative
to the basic WGS84.
There is also the residual problem of "sea surface topography". The
geoid is the calculated equilibrium mean sea level, but the global
oceans are never in equilibrium - regional variations in salinity and
temperature cause variations in the density of sea water from place
to place - abnormally cold salty water "sits lower" than surrounding
water, like a fat person and a thin person sitting side by side on a
water bed. The U.K. for instance sits at the bottom of an 80cm trough
in mean sea level, and so has its own local variant of the global
geoid model for GPS mapping purposes.
The vertical errors in MSL are therefore of the following order.
1) Spherical: kilometres
2a) Ellipsoidal: tens of metres
2b) Local ellipsoidal: metres
3a) Geoidal: tens of centimetres
3b) Local geoidal: ?centimetres?
Grant