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GRIDS AND DATUMS Cliff Mugnier C.P., C.M.S. LSU Center for GeoInformatics cjmce@LSU.edu
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
Historical maps • Reasonably accurate in North-South direction • East-West distorted due to systematic errors in timekeeping • (Pendulum clocks don’t work onboard ships).
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
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.
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.
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.
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.
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.
Surveying and Mapping • Interpolate, not extrapolate • Set control points along the perimeter • Interpolate for interior positions • Create baselines and work outward
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
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.
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
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
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
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
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
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.
Datums and control points I. • Traditional Military Secrets - WWII Nazis:
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!
Geocentric Coordinate System • Originally devised for use in astronomy • 3D Cartesian Orthogonal Coordinate • X-Y-Z right-handed • Units are in meters
a a a a a a a a a a a a a a a
Helmert transformations, I • Select common points in the two datums • Calculate the Geocentric coordinate differences and average them: • Use for several counties or for a small nation
Helmert transformations, II • Three parameter “Molodensky:”
Survey of India • Southeast Asia:Vietnam, Lao, Cambodia, Myanmar, Malaysia, Indonesia, Borneo, etc. • Bangladesh, India, Pakistan, Afghanistan, Iran, Iraq, Trans-Jordan, Syria • Indian Datum 1916, 1960, 1975, etc.
Datum Transformations, I • Be aware of (in)accuracies • DMA/NIMA published error estimates on the values in TR 8350.2 (now obsolete) • Lots of control points used = small errors • One or two points used = ±25 meters in each component which equates to ~ 43 meters on the ground!
Datum Transformations, II • LTCDR Warren Dewhurst modeled the NAD27-NAD83 for his dissertation • 3 maps – one each of: Δφ, Δλ, Δh • First Order Triangulation stations (280,000) • Two coordinate pairs at each station • Surface of Minimum Curvature • NADCON grids