GRIDS AND DATUMS

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##### GRIDS AND DATUMS

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1. GRIDS AND DATUMS Cliff Mugnier C.P., C.M.S. LSU Center for GeoInformatics cjmce@LSU.edu

2. Object Space Coordinate Systems • Orderly arrangement for displaying locations • Mapping requires interpolation in-between known control points • Historical origins at observatories • Precise location observed astronomically • Basis for a datum definition

3. Historical maps • Reasonably accurate in North-South direction • East-West distorted due to systematic errors in timekeeping • (Pendulum clocks don’t work onboard ships).

4. Latitude (Φ) and Longitude (Λ) • Latitude (Φ) is measured positive north of the equator, negative south of the equator. • Can be determined very accurately with astronomical techniques. • Longitude (Λ) is measured east and west from a chosen (Prime) meridian. • Time-based measurement

5. The Longitude Lunatic

6. Measuring Longitude • Relative calculation based on distance from zero meridian. • Chronometer – navigation instrument with known (and constant) error rate. • Lunar Distances could find Longitude. • Moons of Jupiter could find Longitude.

7. The Prize - £10,000 Sterling:

8. Inventor of the Chronometer

9. Systematic errors in historical data • Longitude errors 5-7x larger than latitude errors • Biases often due to different time-keeping • Rotations are gravity-related • French navigators once sailed between Caribbean islands 7 times with different chronometers and then averaged the results.

10. Ephemeris • Astronomical almanac of predicted positions for heavenly bodies • Countries had Royal Astronomers with observatories in capitol cities • Datum origins were mainly at observatories • New England Datum origin was at the U.S. Naval Observatory in Washington, D. C.

11. Datum Origin Point • Observations based on time-keeping at the observatory • One known point measured over decades • Astronomic position: • Φo based on vertical angle to Polaris • Λo zero longitude is the observatory pier • αo azimuth from Polaris (or mire) to another point.

12. Classical Astro Stations • 12 sets of directions • 2 nights of observation • 1 day of computation • Determination of: • Φ, Λ, α, (ξ, η) • Positional accuracy of ~ 100 meters.

13. Surveying and Mapping • Interpolate, not extrapolate • Set control points along the perimeter • Interpolate for interior positions • Create baselines and work outward

14. Law of Sines

15. Historical Distance Tools • Wooden rods or staffs • Magnolia wood boiled in paraffin • Glass rods (encased in wood boxes) • Platinum caps (expansion same as glass) • Metal chains made of “links” • Gunter’s chain = 66ft = 100 links • Length increases due to repeated use

16. Baselines • Use baselines and trigonometry to calculate other positions • Used to form a triangulation “chain” • With one known length and known interior angles of a triangle, we can calculate the positions of other points with the Law of Sines.

17. Shape of the Earth • Pendulum clock’s rate varies at different latitudes. • Sir Isaac Newton concluded that the Earth is an oblate ellipsoid of revolution. • Equatorial axis is larger • C. F. Cassini de Thury disagreed – it’s a prolate ellipsoid of revolution. • Polar axis is larger

18. Christiaan Huyens invented the pendulum-regulated clock.

19. Sir Isaac Newton

20. French Meridian Arcs

21. Ellipsoids • Published by individuals for local regions • Everest 1830 • Bessel 1841 • Clarke 1858, 1866, 1880 • Hayford 1906/Madrid/Helmert 1909/International • Recent ones are by committees

22. U. S. Ellipsoids • Used Bessel 1841 through the Civil War (1860s) • Clarke 1866 (used for 100+ years) • COL. Alexander Ross Clarke, R.E., used Pre-Civil War triangulation arcs of North America. • a = 6,378,206.4 meters • b = 6,356,583.6 meters

23. U. S. Ellipsoids, continued • GRS 80 / WGS 84 • a = 6,378,137.0 meters • b (GRS 80) = 6,356,752.314 14 meters • b (WGS 84) = 6,356,752.314 24 meters • Defined the gravity field differently • NAD 83 was the same as WGS84, has changed • centimeter/millimeter level

24. Survey Orders • 4th Order – ordinary surveying • 3rd Order – Topographic/Planimetric mapping, control of aerial photography • 2nd Order – Federal / State, multiple county or Parish control • 1st Order – Federal primary control • Zero Order – Special Geodetic Study Regions

25. Triangulation • Primary triangulation is North – South • Profile of the ellipse is North – South • Profile of a circle is East – West • Baselines control the scale of the network • LaPlace stations control azimuth and the correction for deflection of the vertical where Latitude and Longitude are observed astronomically.

26. Datums and control points I. • Traditional Military Secrets - WWII Nazis:

27. Datums and control points II. • Datum ties done via espionage & stealth. • The Survey of India is military-based and data is/was denied to its own citizens. • South America–triangulation data along borders is commonly a military secret. • China and Russia–ALL data still secret mapping (unauthorized) in China is now espionage!

28. Geocentric Coordinate System • Originally devised for use in astronomy • 3D Cartesian Orthogonal Coordinate • X-Y-Z right-handed • Units are in meters

29. a a a a a a a a a a a a a a a