Ellipsoids, Geoids, "Geographic Coordinates"

Objectives of lecture

Student introduction: Vertical Datums, Tiffany Vance
1 Abstractions about earth shape
2 Ellipsoids and Datums
3 Gravity and the differences between geoid and ellipsoid

Readings:

The NIMA document Geodesy for Laymen provides a thorough coverage.

Print it out if you must, but the virual copy might be easier to find in the future...

Reference Systems

Some really simple things (like the North Pole) turn out to be a lot more complicated in real life.

The International Terrestrial Reference System (now divided into:

• the International Celestial Reference System) consists of the Pole and the reference Meridian, corrected for the average tidal influences: an astronomical standard (note the use of seconds of arc to define the accuracy of the system).
• the Earth Orientation Program; with material about everything you need to know about the variability in the rotation of the Earth, hence the variation in "time" over time. (note in milliseconds); the movement of the polar axis; software (FORTRAN...)

Why does this matter? The location of the origin of the reference system is continuing to be tweaked. GPS is defined in terms of these astronomical standards (see International GPS Service). NGS reports that the 1996 and 1997 results are different (millimeters...)

Earth shape:

not a sphere: flattening of 1/298 or so; actually very close to spherical

Ellipsoid:

simplified, rotationally symmetric 3D solid created by rotating an ellipse around its minor axis.
center of earth given geometrically; "down" points to center of rotation;

Geoid:

the actual earth's shape (bumps and all)
gravitation pulls to center of mass (not always identical to geometric center)
Gravity measurements: (Gravity varies, Sea Level is a fiction...)
like horizontal position, gravity depends on a "datum" and adjustment of observations.

The Potsdam gravity datum was been replaced with an adjustment of 1854 stations worldwide International Gravity Standardization Net 1971; then replaced by the WGS 84 Earth Gravity Model (WGS-84). The work of estimating the geoid is never complete; A history of Gravity Datums.

NGS continues to make new version and corrections. The ellipsoidal heights are estimated for the world in the Joint Geopotential Project (funded by NASA and NIMA). 30 minute average (worldwide) plot;

GEOID 99

Different heights:

GPS produces ellipsoidal heights, heights above the ellipsoid.

Geodetic leveling traditionally produced orthometic heights. These can be different by relatively significant amounts. as GPS get into the field, the contours on the topo sheet will be useful only if you know how to translate... An explanation of these two height systems from NGS.

Geoidal height= geoid - ellipsoid: BUT it is really the rate of change (slope) of the geoidal height that makes the real difference. The "aspect" component of this slope is called:

Deflection of the vertical:

different "downs" (the gravity field points off toward denser mass, measured in north and east angular deflections (xi and eta)); the ellipsoid is creates a smooth surface with latitude longitude measured by the plane tangent to the ellipsoid at each point.

NOAA NGS has a 2minute by 2 minute estimate of the geoid for conterminous USA (called Geoid99), software to access it, and an on-line calculator for deflection of the vertical (DEFLEC96, now DEFLEC99). This research continues; check thier site...
GPS operates from orbital framework, hence flys around the center of mass, not around a geometric center. Recent standards have been influenced by this technology (eg. DoD adopts gravimetric definition of earth center and ellipsoid)

Some resources on geodesy:

NIMA Geospatial Sciences program
including Geodesy for Laymen (sic) publication

US National Geodetic Survey
Data sheets for control points

Monument data from WA DOT

Geographer's Craft Project

Dana's Coordinate Systems pages have a Geodetic Datums section

Watching the continent move and deform at Central Washington; elsewhere...

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Origins of Geodetic Information

a reminder that all geodetic sources are relative, connected in network
Originally: sparse triangulation; progressive densification
Adjustment techniques to deal with inevitable error
New technology permits monitoring of velocity of stations in a dynamic network (crustal movement) ITRF project.

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Living with the chaos: fixing standards

a history of datums (from DoD perspective...)
ellipsoids in common use (tuned to local shape of geoid); Clarke's 1866 for North America, etc.

World Geodetic System 80; 84: GPS redefines view of earth to center of mass.

What is a Datum?

an agreed selection of reference ellipsoid with a corresponding value given for at least one place on the earth. section in Geodesy for the Layman; NGS FAQ;
North American Datum 1927: (kept point in Kansas (Mead's Ranch) fixed);

NAD 1983 readjusted all horizontal measurements
Yes, the new datum moves the expected position of the lat/long corners. (see movement of tick marks on quadsheets); feds are meant to move to the new system (Federal Register 1995 pdf)

Tools: NADCON is "the federal standard" now to convert from one datum to the other. The datum shift in western Washington is around 4.5 second of arc in the longitude (much less change in the latitude). The read me file. USGS white paper on the shifts of topo quads (.html version);

No, unfortunately, the datum shift game hasn't finished...
There is a set of High Precision GPS Network revisions of NAD 83 that have been done around the USA. The City of Seattle specifies their datum as "HPGN" because it uses this NAD 83 (1992) revision...

AND there is the Vertical Datum to contend with as well... See A NOAA perspective from Tiffany Vance

Multiple Datums

problem occurs in many parts of the world (NIMA example for SE Asia horizontal datums)
even inside Europe the vertical datum for France is based on Mediterranean Sea at Marseilles, when it meets the North Sea datum used for Belgium there is a 5 meter jump...
See NIMA pamphlet on why Datum is important...

Exotic Objects

Other astronomic objects require other mathematics.

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Geographic coordinates:

Everyone uses latitude longitude: angles from plane of equator and plane of prime meridian.
Latitude and longitude have tricky problems computationally (at poles)
Full XYZ from earth center would not have any relationship to ellipsoid surface, yet this is the basis for geodetic calculations (the International Terrestrial Reference Frame, described above).

NGS provides a utility for going through these changes.

Direction cosines: an alternative reexpressing the lat/long... (See the software HIPPARCHUS deveopled by Hrvoje Lukatela, now Geodyssey Limited); if interested, look at the resources for a free programmer's toolkit.
[see also global tessalations as in QTM : Dutton ; now live on the web at QTM Comix (watch the dynamic gifs at the bottom left)]

Or look at the cutting edge of Global Grids research (conference at Santa Barbara in 2000)

So why do we need a projection anyway?

Most calculations (distance, intersection, buffer, overlay) can be done on geographic coordinates (at least on a spherical model), but projections of local scope are handled adequately by creating a projection onto some plane.