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Download GEOGRAPHIC INFORMATION SYSTEMS Lecture 07: Earth
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GEOGRAPHIC INFORMATION SYSTEMS Lecture 07: Earth Ellipsoids and Horizontal Datums Earth Ellipsoid and Horizontal Datums Shape of the Earth - the Earth rotates on its polar axis once every 24 hours - this rotation creates a centrifugal force which causes the planet to bulge at the Equator - the equatorial diameter (12,756 km) is about 42 km greater than the polar diameter (12,714 km) - thus, the Earth is better described as an ellipsoid or oblate spheroid (a slightly flattened sphere) - this centrifugal force is caused by the speed of Earth’s rotation - the circumference of the Earth is about 40,076 km – and the Earth rotates once every 24 hours - if we divide 40,076 km / by 24 hours – the speed of rotation is about 1,669 kph – or about 1,000 mph Earth Ellipsoids - the shape of the Earth ellipsoid is described in terms of the flattening ratio f = (a – b) / a - where “a” is equatorial radius and “b” is the polar radius - so we have f = (equatorial radius – polar radius) / equatorial radius the flattening ratio for the Earth is approximately 1/298 - over the years, the exact shape of the Earth has been very difficult to calculate and there have been many different estimates of the flattening ratio - the flattening ratio and resulting ellipsoid are very important because we are trying to apply a spherical coordinate system (latitude and longitude) to an object that is not perfectly spherical - lines of latitude and longitude must therefore be compressed to fit the ellipsoid - for the U.S., the three most important ellipsoids are: - the Clark Ellipsoid of 1866 (Clark_1866 ellipsoid, f = 1/294.9786982) - the Geodetic Reference System of 1980 (GRS_80 ellipsoid, f = 1/298.257222101) - the World Geodetic System of 1984 (WGS_84 ellipsoid, f = 1/298.257223563) Copyright© 2015 Kevin Mulligan, Texas Tech University Horizontal Datums - a horizontal datum provides a reference framework for the measurements of latitude and longitude - there are two components to a datum: 1) the ellipsoid and 2) the origin - the ellipsoid is defined by the flattening ratio - the origin determines how the ellipsoid is aligned to the Earth (or more precisely, the geoid) Historical Use of Datums in the United States - most early U.S. maps used the Clarke Ellipsoid of 1866, where f = 1/294.97… - in 1924 an international convention was held to select an international standard - most countries agreed to use the International Datum of 1924 where f = 1/297 - the U.S. did not adopt this standard - rather, the U.S. established the North American Datum of 1927 (NAD_27) North American Datum of 1927 (NAD_27) - the NAD_27 datum is based on the Clarke Ellipsoid of 1866 - the origin for NAD_27 is a physical benchmark placed in the ground on Meades Ranch in Kansas - NAD_27 is the datum used on most topo maps and held as the U.S. standard datum until 1983 North American Datum of 1983 (NAD_83) - with satellites, it became possible to measure the shape of the Earth more precisely from space - the NAD_83 datum is based on the Geodetic Reference System 1980 ellipsoid (GRS_80) - the NAD_83 datum is an Earth-centered datum – so there is no physical benchmark on land World Geodetic Reference System of 1984 (WGS_84) - today, most of the world uses the World Geodetic Reference System of 1984 (WGS_84) - the WGS_84 datum is based on the WGS_84 ellipsoid (a slight refinement of GRS_80) - like the NAD_83 datum, the WGS_84 datum is also Earth-centered - for most general mapping purposes, NAD_83 and WGS_84 are the same - the Global Positioning System uses WGS_84 – so GPS coordinates are referenced to the WGS_84 datum - most GIS data layers for the United States are referenced to NAD_83, but a few layers still use NAD_27 - until recently, U.S. layers from Esri and U.S. government agencies were almost always referenced to NAD_83 - Esri has now begun to release U.S. data layers referenced to WGS_84 - most global GIS data layers from Esri and other organizations are referenced to WGS_84 - both Google (Google Maps and Google Earth) and Microsoft (Bing Maps) use the WGS_84 datum Copyright© 2015 Kevin Mulligan, Texas Tech University GIST 3300 / 5300 Geographic Information Systems Earth Ellipsoids and Horizontal Datums The Shape of the Earth - Earth rotation and centrifugal force - comparing the polar vs equatorial diameter Earth Ellipsoids - describing the Earth ellipsoid (the flattening ratio) - Clarke Ellipsoid of 1866 (Clark 1866 ellipsoid) - Geodetic Reference System of 1980 (GRS 80 ellipsoid) - World Geodetic System of 1984 (WGS 84 ellipsoid) Horizontal Datums - North American Datum of 1927 (NAD 27) - North American Datum of 1983 (NAD 83) - World Geodetic System of 1984 (WGS 84) Geographic Information Systems Shape of the Earth - the Earth rotates on its polar axis once every 24 hours - this rotation creates centrifugal force on the planet - causes the Earth to bulge at the equator equatorial diameter 12,756 km polar diameter 12,714 km 42 km … but where does this centrifugal force come from if the Earth is rotating so slowly? Geographic Information Systems Shape of the Earth - the equatorial circumference of the Earth is 40,076 km - the Earth rotates once in 24 hours Equatorial Circumference 40,076 km - divide 40,076 km / 24 hours = 1669 km/hr - or about 1000 mph! Geographic Information Systems Shape of the Earth - the Earth is not a true sphere - it is best described as an ellipsoid (or oblate spheroid) - it is slightly flattened at the poles N equatorial diameter 12,756 km S polar diameter 12,714 km Geographic Information Systems Ellipsoids - the ellipsoid is described in terms of the flattening ratio f = (a - b) / a = approximately 1/298 b a Geographic Information Systems Ellipsoids - the exact shape (axes lengths) was very difficult to calculate - there have been many estimates of the flattening ratio Geographic Information Systems Horizontal Datums - the flattening ratio is very important - trying to apply a spherical coordinate system (latitude, longitude) to a object (the Earth) that is not spherical - lines of latitude and longitude must be compressed to fit the ellipsoid Clarke 1866 Ellipsoid - historically, in the U.S., most maps used the Clarke Ellipsoid of 1866 f = 1/294.9786982 International 1924 Ellipsoid -1924 International convention - most countries agreed to a standard ellipsoid - known as the International 1924 ellipsoid f = 1/297 - the U.S. did not adopt the 1924 datum Geographic Information Systems Horizontal Datums North American Datum of 1927 (NAD 27) - 1927 U.S. created the North American Datum of 1927 (NAD_27) - physical benchmark located on Meades Ranch, Kansas - NAD_27 is based on the Clarke Ellipsoid of 1866, with f = 1/294.9786982 Meades Ranch benchmark – set in 1891 Geographic Information Systems Horizontal Datums U.S.G.S. topographic maps produced prior to 1980 NAD_27 Geographic Information Systems Horizontal Datums NAD_27 works well for North America only North America Clark 1866 Ellipsoid f = 1/294.9786… ellipsoid is aligned to the geoid using a benchmark in Kansas geoid Geographic Information Systems Horizontal Datums North American Datum of 1983 (NAD_83) - during the 1970’s satellites were used to measure the shape of the Earth - the U.S adopted a new reference ellipsoid and horizontal datum - ellipsoid is called the Geodetic Reference System of 1980 (GRS 80) f = 1/298.257222101 - this is an earth-centered ellipsoid - no physical benchmark on land - horizontal datum is called North American Datum of 1983 (NAD 83) - based on the GRS_80 ellipsoid - in the U.S. - most GIS data layers are referenced to NAD_83 Geographic Information Systems Horizontal Datums NAD_83 works well for North America – and much better for the rest of the world North America GRS 80 Ellipsoid f = 1/298.2572… geoid Earth-centered ellipsoid Geographic Information Systems Horizontal Datums revised U.S.G.S. topographic maps NAD_83 Geographic Information Systems Horizontal Datums World Geodetic System (WGS_84) - today, most of the world has adopted the - World Geodetic System of 1984 (WGS_84) - the new ellipsoid is based on a slight refinement of GRS 80 - in the World Geodetic System of 1984 (WGS_84 ellipsoid) f = 1/298.257223563… (in GRS_80, f = 1/298.257222101…) - the horizontal datum is called the WGS_84 datum - used by the U.S. military for the Global Positioning System - GPS coordinates are therefore referenced to WGS_84 - WGS_84 is the default datum in most GPS receivers - most global data layers are referenced to WGS_84 - adopted by Google and Microsoft for Internet mapping applications Geographic Information Systems Horizontal Datums WGS_84 Datum: works well for world North America WGS 84 Ellipsoid f = 1/298.2572… geoid Earth-centered ellipsoid Geographic Information Systems Comparison of NAD-83 & WGS-84 – – – NAD 1983 is tied to the North American and Pacific tectonic plates WGS 1984 is tied to the International Terrestrial Reference System (ITRF) which is independent of the tectonic plates Over time the two coordinate systems have become increasingly different (1 – 2 cm /yr) Geographic Information Systems Horizontal Datums Summary - a datum provides a reference framework for a geographic coordinate system. - there are two components to a datum: 1) the ellipsoid, 2) the origin - the ellipsoid is defined by the flattening ratio - the origin determines how the ellipsoid is aligned to the Earth (geoid) North American Datum of 1927 (NAD_27) ellipsoid: Clark Ellipsoid of 1866 (f = 1/294.9786982) origin: physical benchmark located on Meades Ranch, Kansas North American Datum of 1983 (NAD_83) ellipsoid: GRS_80 Ellipsoid (f = 1/298.257222101) origin: Earth-centered World Geodetic System of 1984 (WGS_84) ellipsoid: WGS_84 Ellipsoid (f = 1/298.257223563) origin: Earth-centered Geographic Information Systems
