Basic Geodesy and Geographic Coordinate Systems Geometric Transformations

Basic Geodesy and Geographic Coordinate Systems

Geometric Transformations from The Earth to the Map

What if the Earth were … A Perfect Sphere

Modern Radius and Circumference Measurements Sphere equal in surface area to an oblate ellipsoid

Geographic Coordinate System: Parallels of Latitude and Meridians of Longitude

What if the Earth were … An Oblate Ellipsoid

Sir Isaac Newton’s Idea … Law of Gravity tells us the Earth must be oblate due to its rotation.

Radius of Curvature is Larger in Polar Areas than in Equatorial Areas So ground distance between equal increments of Latitude is greater in polar areas

Expedition to determine if the Earth is oblate or pr To Lapland in 1736

To Ecuador in 1736 Measurements showed Polar Distance per degre Of Latitude greater than Equatorial – It’s Oblate!

Historic and Current Oblate Ellipsoids Name Date Semi-major Axis (m) Maupertuis Airy Everest Bessel Clarke International Krasovsky Australian S. American Indonesian GRS 80 WGS 84 1738 1830 1841 1866 1880 1924 1940 1965 1969 1974 1980 1984 6, 397, 300 6, 377, 563. 4 6, 377, 276. 3 6, 377, 397. 2 6, 378, 206. 4 6, 378, 249. 1 6, 378, 388 6, 378, 245 6, 378, 160 6, 378, 137 Semi-minor Axis (m) 6, 363, 806. 3 6, 356, 256. 9 6, 356, 075. 4 6, 356, 079 6, 356, 583. 8 6, 356, 514. 9 6, 356, 911. 9 6, 356, 863 6, 356, 774. 7 6, 356, 774. 5 6, 356, 752. 3141 6, 356, 752. 3142

Different Ellipsoids Used as Best Fit Surfaces for Different Places

What if the Earth were … A Geoidal Surface ! North American Datum of 1927 (NAD 27)

Numerous Older Local Datums Used in Different Places across the Globe

Numerous Older Local Datums Used in Different Places across the Globe Afghanistan Herat North datum Of 1959 International Ellipsoid Datum Origin: 34° 23’ 09”N, 62° 10’ 59”E

Numerous Older Local Datums Used in Different Places across the Globe Philippines Philippine Reference System Of 1992 Clarke 1866 Ellipsoid Datum Origin: 13° 33’ 41”N, 121° 52’ 03”E

Numerous Older Local Datums Used in Different Places across the Globe Iraq Karbala datum Of 1979 Clarke 1880 Ellipsoid Datum Origin: 32° 34’ 14”N, 44° 00’ 50”E Being replaced by Iraqi Geospatial Reference System

NAD 27 vs. NAD 83 What if the Earth were …

What if. NAD the Earth were … Reference Frame 83 Terrestrial Thousands of Geodetic Control Points And more recently by Continuously Operating (GPS) Reference Stations

CORS ifdata What the allow Earth tectonic were … plate velocities to be Determined relative to the center of the continent So NAD 83 coordinates can be updated

NAD if 27 the to Earth were … What NAD 83 Latitude and Longitude Shifts 1” Latitude ≈ 30 meters 1” Longitude ≈ 28 m at 25°N 20 m at 50°N

What if the 27 Earth were 83…Geographic Coordinate The NAD to NAD Shift is large enough that we show it on Large-scale Topographic Maps

World Geodetic System of 1984 (WGS 84) is the best current global ellipsoid 6378137. 0 m semi-major axis 6356752. 3142 m semi-minor axis Flattening: 1/298. 257223

What if the Earth were …

The International Terrestrial Reference Frame is The WGS 84 Terrestrial Reference Frame

What. The if the Earth were difference on … the ground between NAD 83 and WGS 84 points with identical Latitidues and Longitudes varies from 1. 3 to 1. 9 meters, with most places about 1. 5 meter 1. 5 m 1. 3 m 1. 9 m

New Iraqi Geospatial Reference System GRS 80 Ellipsoid Datum Origin: Earth Center of Mass Terrestrial Reference Frame: • Several Continuously Operating Reference Stations (CORS) • High Accuracy Reference Network (HARN) of accurate GPS stations

What if the Earth were … A Geoid !

Global Geoid is the Average Mean Sea Level Surface for all the Oceans

Global Geoid Heights Relative to WGS 84 Ellipsoid Surface

Global vs. Local Geoid

For the North American Vertical Datum of 1988 (NAVD 88) the Local Geoid Mean Sea Level Datum Is defined by the Tidal Gauge at Rimouski, Quebec

North American Vertical Datum of 1988 What is Geodetic Leveling ? (NAVD 88) Terrestrial Reference Vertical surveying is the process of determining elevations above mean sea. Frame level. In geodetic surveys executed primarily for mapping, geodetic positions are referred to an ellipsoid, and the elevations of the positions are referred to the geoid. However, for satellite geodesy the geoidal heights must be considered to establish the correct height above the geoid. Precise geodetic leveling is used to establish a basic network of vertical control points. From these, the height of other positions in the survey can be determined by supplementary methods.

NAVD 88 Local Geoid heights relative to the GRS 80 Ellipsoid Surface Most places in the U. S. the Geoid is below the ellipsoi

Cartographic Uses of NAD 83 and NAVD 88

Cartographic Uses of the Ellipsoid Heights from GPS Receivers

Must Convert Ellipsoidal Height to Elevation H=h-N