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Published byRolf Kelley Modified over 8 years ago
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What is Geodesy ?
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Satellite Observations of the Earth European Remote Sensing satellite, ERS-1 from 780Km ERS-1 depicts the earth’s shape without water and clouds. This image looks like a sloppily pealed potato, not a smoothly shaped ellipse. Satellite Geodesy has enabled earth scienetists to gain an accurate estimate (+/- 10cm) of the geocentric center of the of the earth. A worldwide horizontal datum requires an accurate estimation of the earth’s center
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All right then – what is it ? "geo daisia" = "dividing the earth" Aim: determination of the figure of the earth or, more practically: determination of the relative positions on or close to the surface of the earth. oldest profession on earth but one geodesy, not geodetics
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Shape of the Earth flat large scale mapping street plans engineering surveys sphere small scale mapping, low accuracy geography survey calculations (medium accuracy) ellipsoid accurate (geodetic) mapping geodetic & survey calculations geoid accurate heighting satellite orbits high accuracy geodetic calculations
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Geoid equal gravity potential Locus (surface) of points with equal gravity potential approximately at Mean Sea Level must be measured ( errors) l difficult to describe mathematically l even more difficult to calculate with o reduction of survey observations o map projections l everyday heights are relative to geoid (MSL) l physically exists
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Geoid covering the USA (NGS96) 7.2 m - 51.6 m Note: This image shows the height of the geoid above the US reference ellipsoid
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Ellipsoid ( = spheroid) geoid Approximate the geoid ( not the earth's surface ) l good approximation possible variations ~10 -5 (±60 m over earth radius ~ 6,400,000 m) ellipsoidal calculus is feasible can be defined exactly: semi-major axis (size) and flattening (shape) l computational aid only; no physical reality ellipsoidal heights are not practical many choices possible (~50) optimum local fit with geoid (sometimes global fit) rotation axis parallel to mean earth rotation axis based on surface geodetic observations
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The geoid and two ellipsoids N N Europe N. America S. America Africa typically several hundreds of metres
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Ellipsoids - examples namesemi-major axisflattening Bessel 18416377397 m1/299.15 WGS846378137 m1/298.26 Clarke 18666378206 m1/294.979 Bessel 1841: usage: o Europe (German influence sphere), Namibia, Indonesia, Japan, Korea o National control network and mapping. WGS84: usage: o the entire world o the GPS system in conjunction with a datum of the same name. Clarke 1866: usage: o USA except Michigan, Canada, Central America, Philippines, Mozambique o National control network and mapping.
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Many ellipsoids …. many datums Approximate the local geoid with different ellipsoids... different origins different orientation of axes different shapes and sizes different GEODETIC DATUMS different GEODETIC DATUMS What is a ‘Geodetic Datum’? location (origin) orientation shape size of the ellipsoid in space
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Geographic coordinates P X-axis Y-axis Z-axis semi-major axis H Greenwich meridian semi-minor axis oblate at poles = Geographic Latitude = Geographic Longitude H = Ellipsoidal height
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Latitude is not unique ! 11 22 nor is Longitude 1 2 Due to different Geodetic Datums:
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President Ford’s secret Alaskan visit ?
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Washington to Tokyo - Orthographic Projection Tokyo Anchorage Washington
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Mercator projection Globular projection Orthographic projection Stereographic projection A familiarly shaped ‘continent’ in different map projections
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Easting Northing Longitude East Longitude West equator Latitude North Latitude South A A Geographic and map coordinates (N,E) = F (Lat, Lon) distortions
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What errors can you expect? Wrong geodetic datum: q several hundreds of metres Incorrect ellipsoid: q horizontally: several tens of metres q height: not effected, or tens to several hundred metres Wrong map projection: entirely the wrong projection: hundreds, even thousands of kilometres (at least easy to spot!) partly wrong (i.e. one or more parameters are wrong): several metres to many hundreds of kilometres No geodetic metadata coordinates cannot be interpreted datum ellipsoid prime meridian map projection Coordinate Reference System
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Types of Coordinate (Ref) System Coordinate Ref System Coordinate System Characteristics GeocentricCartesian or spherical Proper 3D spatial modeling; spatial applications Geographic 3DellipsoidalLocations described relative to ellipsoidal surface Geographic 2DellipsoidalLocations described on ellipsoidal surface; for large national/continental geodetic control networks ProjectedCartesianFor national mapping; smaller area than Geographic 2D. Carefully controlled mapping distortions EngineeringvariousEarth curvature ignored; mostly flat-earth model ImageCartesian or oblique Cartesian Distortions due to earth curvature determined by data acquisition characteristics Verticalgravity-related, depth,barometric Gravity-related means relative to geoid (~MSL) Depth: complex reference surfaces (tidal) Earth curvature modelling
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Geodesy, Map Projections and Coordinate Systems l Geodesy - the shape of the earth and definition of earth datums l Map Projection - the transformation of a curved earth to a flat map l Coordinate systems - (x,y) coordinate systems for map data
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Types of Coordinate Systems l (1) Global Cartesian coordinates (x,y,z) for the whole earth (2) Geographic coordinates ( , z) l (3) Projected coordinates (x, y, z) on a local area of the earth’s surface l The z-coordinate in (1) and (3) is defined geometrically; in (2) the z-coordinate is defined gravitationally
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Global Cartesian Coordinates (x,y,z) O X Z Y Greenwich Meridian Equator
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Geographic Coordinates ( , z) Latitude ( ) and Longitude ( ) defined using an ellipsoid, an ellipse rotated about an axis l Elevation (z) defined using geoid, a surface of constant gravitational potential l Earth datums define standard values of the ellipsoid and geoid
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Shape of the Earth We think of the earth as a sphere It is actually a spheroid, slightly larger in radius at the equator than at the poles
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Ellipse P F2F2 O F1F1 a b X Z An ellipse is defined by: Focal length = Distance (F1, P, F2) is constant for all points on ellipse When = 0, ellipse = circle For the earth: Major axis, a = 6378 km Minor axis, b = 6357 km Flattening ratio, f = (a-b)/a ~ 1/300
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Ellipsoid or Spheroid Rotate an ellipse around an axis O X Z Y a a b Rotational axis
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Standard Ellipsoids Ref: Snyder, Map Projections, A working manual, USGS Professional Paper 1395, p.12
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Horizontal Earth Datums l An earth datum is defined by an ellipse and an axis of rotation l NAD27 (North American Datum of 1927) uses the Clarke (1866) ellipsoid on a non geocentric axis of rotation l NAD83 (NAD,1983) uses the GRS80 ellipsoid on a geocentric axis of rotation l WGS84 (World Geodetic System of 1984) uses GRS80, almost the same as NAD83
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Definition of Latitude, (1) Take a point S on the surface of the ellipsoid and define there the tangent plane, mn (2) Define the line pq through S and normal to the tangent plane (3) Angle pqr which this line makes with the equatorial plane is the latitude , of point S O S m n q p r
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Cutting Plane of a Meridian P Meridian Equator plane Prime Meridian
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Definition of Longitude, Definition of Longitude, 0°E, W 90°W (-90 °) 180°E, W 90°E (+90 °) -120° -30° -60° -150° 30° -60° 120° 150° = the angle between a cutting plane on the prime meridian and the cutting plane on the meridian through the point, P P
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Latitude and Longitude on a Sphere Meridian of longitude Parallel of latitude X Y Z N E W =0-90°S P O R =0-180°E =0-90°N Greenwich meridian =0° Equator =0° =0-180°W - Geographic longitude - Geographic latitude R - Mean earth radius O - Geocenter
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Length on Meridians and Parallels 0 N 30 N ReRe ReRe R R A B C (Lat, Long) = ( , ) Length on a Meridian: AB = R e (same for all latitudes) Length on a Parallel: CD = R R e Cos (varies with latitude) D
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Example: What is the length of a 1º increment along on a meridian and on a parallel at 30N, 90W? Radius of the earth = 6370 km. Solution: A 1º angle has first to be converted to radians radians = 180 º, so 1º = /180 = 3.1416/180 = 0.0175 radians For the meridian, L = R e km For the parallel, L = R e Cos Cos km Parallels converge as poles are approached
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Representations of the Earth Earth surface Ellipsoid Sea surface Geoid Mean Sea Level is a surface of constant gravitational potential called the Geoid
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Geoid and Ellipsoid Ocean Geoid Earth surface Ellipsoid Gravity Anomaly Gravity anomaly is the elevation difference between a standard shape of the earth (ellipsoid) and a surface of constant gravitational potential (geoid)
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Definition of Elevation Elevation Z P z = z p z = 0 Mean Sea level = Geoid Land Surface Elevation is measured from the Geoid
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Vertical Earth Datums l A vertical datum defines elevation, z l NGVD29 (National Geodetic Vertical Datum of 1929) l NAVD88 (North American Vertical Datum of 1988) l takes into account a map of gravity anomalies between the ellipsoid and the geoid
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Converting Vertical Datums l Corps program Corpscon http://crunch.tec.army.mil/software/corpscon/corpscon.html Point file attributed with the elevation difference between NGVD 29 and NAVD 88 NGVD 29 terrain + adjustment = NAVD 88 terrain elevation
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Geodesy and Map Projections l Geodesy - the shape of the earth and definition of earth datums l Map Projection - the transformation of a curved earth to a flat map l Coordinate systems - (x,y) coordinate systems for map data
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Earth to Globe to Map Representative Fraction Globe distance Earth distance = Map Scale: Map Projection: Scale Factor Map distance Globe distance = (e.g. 1:24,000) (e.g. 0.9996)
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Geographic and Projected Coordinates ( ) (x, y) Map Projection
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Projection onto a Flat Surface
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Types of Projections l Conic (Albers Equal Area, Lambert Conformal Conic) - good for East-West land areas l Cylindrical (Transverse Mercator) - good for North-South land areas l Azimuthal (Lambert Azimuthal Equal Area) - good for global views
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Conic Projections (Albers, Lambert)
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Cylindrical Projections (Mercator) Transverse Oblique
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Azimuthal (Lambert)
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Albers Equal Area Conic Projection
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Lambert Conformal Conic Projection
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Universal Transverse Mercator Projection Universal Transverse Mercator Projection
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Lambert Azimuthal Equal Area Projection
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Projections Preserve Some Earth Properties l Area - correct earth surface area (Albers Equal Area) important for mass balances l Shape - local angles are shown correctly (Lambert Conformal Conic) l Direction - all directions are shown correctly relative to the center (Lambert Azimuthal Equal Area) l Distance - preserved along particular lines l Some projections preserve two properties
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Geodesy and Map Projections l Geodesy - the shape of the earth and definition of earth datums l Map Projection - the transformation of a curved earth to a flat map l Coordinate systems - (x,y) coordinate systems for map data
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Coordinate Systems l Universal Transverse Mercator (UTM) - a global system developed by the US Military Services l State Plane Coordinate System - civilian system for defining legal boundaries l California State Mapping System - a statewide coordinate system for California
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Coordinate System ( o, o ) (x o,y o ) X Y Origin A planar coordinate system is defined by a pair of orthogonal (x,y) axes drawn through an origin
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Universal Transverse Mercator l Uses the Transverse Mercator projection Each zone has a Central Meridian ( o ), zones are 6° wide, and go from pole to pole l 60 zones cover the earth from East to West Reference Latitude ( o ), is the equator l (Xshift, Yshift) = (x o,y o ) = (500000, 0) in the Northern Hemisphere, units are meters
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UTM Zone 21 &22 Equator -120° -90 ° -60 ° -102°-96° -123° Origin 6°
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State Plane Coordinate System l Defined for each State in the United States l East-West States (e.g. Texas) use Lambert Conformal Conic, North-South States (e.g. Indiana) use Transverse Mercator l Texas has five zones (North, North Central, Central, South Central, South) to give accurate representation l Greatest accuracy for local measurements
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California Mapping System l Designed to give State-wide coverage of California without gaps l Lambert Conformal Conic projection with standard parallels l 1927 Seven Zones - feet l 1983 Six Zones - meters
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Coordinate Systems l Geographic coordinates (decimal degrees) l Projected coordinates (length units, ft or meters)
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Summary Concepts Two basic locational systems: geometric or Cartesian (x, y, z) and geographic or gravitational ( , z) Mean sea level surface or geoid is approximated by an ellipsoid to define an earth datum which gives ( and distance above geoid gives (z)
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Summary Concepts (Cont.) l To prepare a map, the earth is first reduced to a spheroid and then projected onto a flat surface l Three basic types of map projections: conic, cylindrical and azimuthal l A particular projection is defined by a datum, a projection type and a set of projection parameters
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Summary Concepts (Cont.) l Standard coordinate systems use particular projections over zones of the earth’s surface l Types of standard coordinate systems: UTM, State Plane, California Coordinate System l Reference Frame in ArcInfo 8,& Geomedia requires projection and map extent
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