beauty grant
i am very pleased with both of us
curiously my old unreliable dictionary that i like to keep next to my old
unreliable atlas was misleading me by qualifying a spheroid as a particular
sort of ellipsoid that is generated by revolving an ellipse around one of
its axes
it defines ellipsoids generally as geometric surfaces whose plane sections
are all either ellipses or circles
so i am glad to gather from you that such distinctions are not operative in
the present cases or perspectives
& also glad to reduce the options from 4 to 3
so as to get at the 5 most interesting & actual ones
& authalic
what a handsome idea & so rare & mysterious a word for it
not in my old unreliable greek latin or english dictionaries
m
airy spheroid is a nice idea too for that matter
>
>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
>
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