Lecture # 7 Coordinate systems and georeferencing

Transcription

1 Lecture # 7 Coordinate systems and georeferencing

2 Coordinate Systems Coordinate reference on a plane Coordinate reference on a sphere

3 Coordinate reference on a plane Coordinates are a convenient way of locating points on a two-dimensional plane Two usually employed systems are Rectangular cartesian coordinate system that makes use of linear measurements in two directions from a pair of fixed axes, usually orthogonal (or rectangular) Polar coordinate position defined with reference to the origin or pole, the polar axis, radius vector (distance), and the vectorial angle

4 Cartesian (x,y)

5 Polar coordinates O- origin or pole OA- radius vector QOA- vectorial angle r φ A O Q

6 Coordinate reference on a sphere For unique references for locations on the surface of earth, a system of three dimensional polar coordinates may be used Two orthogonal planes are chosen, which intersect the origin (centre of earth) one plane goes through equator second plane is perpendicular to the equatorial plane (Greenwich, UK, 1884)

7 Referencing location on the earth s surface latitude and longitude reference system Equator Prime Meridian Parallels of Latitude Meridians of Longitude Graticular Network

8 Grids vs. Graticules Graticule - 3 dimensional network of lines that wrap around the earth (lat./long) Grid - flat 2 dimensional network of lines (x, y plane) A grid is on a flat piece of paper, while a graticule is on the round earth

9 Referencing location on the earth s surface latitude φ: angle from the equator to the parallel longitude λ: angle from Greenwich meridian

10 Referencing location on the earth s surface

11 Geographic Coordinate System INTERNATIONAL DATE LINE -180 Longitude NORTH POLE +90 Latitude CENTRAL MERIDIAN LATITUDE LINES (PARALLELS) EQUATOR 0 Lat. LONGITUDE LINES (MERIDIANS)

12 Earth Surfaces Ellipsoid or spheroid - smooth mathematical models of the shape of the earth Geoid - Geoid models attempt to represent the surface of the entire earth over both land and ocean as though the surface resulted from gravity alone Topographic surface - the actual surface of the land and sea at some moment in time

13 The earth as a spheroid

14 Ellipsoid Geoid

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16 Reference Ellipsoid b a Ellipsoidal Parameters a - semi-major axis b - semi-minor axis f = (a-b)/a - flattening used to establish a datum: reference point for large scale mapping

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19 Heights Elevation - Mean Sea Level - the average surface of the oceans. Tidal forces and gravity differences from different locations cause variations of hundreds of meters. Ellipsoid height - the height from the ellipsoid Orthometric height - the height from the geoid.

20 Datums The datum is where zero is, it is where you start measuring from A datum is a mathematical model of the earth we use to calculate the coordinates on any map, chart, or survey system

21 Geodesy Modern geodetic datums range from flat-earth models used for plane surveying to complex models used for international applications which completely describe the size, shape, orientation, gravity field, and angular velocity of the earth Cartography, surveying, navigation, and astronomy all make use of geodetic datums, and the science of geodesy is the central discipline for the topic Referencing geodetic coordinates to the wrong datum can result in position errors of hundreds of meters

22 Geodetic Datums Geodetic datums define the size and shape of the earth and the origin and orientation of the coordinate systems used to map the earth Hundreds of different datums have been used to frame position descriptions since the first estimates of the earth's size were made by Aristotle Datums have evolved from those describing a spherical earth to ellipsoidal models derived from years of satellite measurements

23 Datum Selection Different nations, states, and agencies use different datums as the basis for coordinate systems used to identify positions in geographic information systems, precise positioning systems, and navigation systems. The diversity of datums in use today and the technological advancements that have made possible global positioning measurements with sub-meter accuracies requires careful datum selection and careful conversion between coordinates in different datums

24 Why do the themes on a map need to have the same datum? Datum shift- the coordinates for a point on the Earth s surface in one datum will not match the coordinates from another datum for the same point A shift exists between datums because each datum has a different origin. Sometimes the shift is obvious, but sometimes it is very subtle

25 History of Datums Flat Earth models are still in use for plane surveying over distances less than 10 km; because earth s curvature is insignificant Spherical Earth models are still used for short range navigation and global distance approximation Ellipsoidal Earth models

26 Two Types of Datum Horizontal Datum forms the basis for computations of horizontal control surveys in which the curvature of the Earth is considered Vertical Datum almost always use mean sea level for elevation

27 History of the North American Datum New England Datum first official US geodetic datum referenced to Clarke 1866 ellipsoid Renamed United States Standard Datum in 1901 after network extensions to the south and west. Official origin was the triangulation station in Meades Ranch, Kansas.

28 History of the North American Datum, Cont Canada and Mexico agreed to base there triangulations on the US system and it was renamed the North American Datum After many adjustments to the new networks the system was called the North American 1927 Datum (NAD27). Its origin is still Meades Ranch, Kansas and it is computed on the Clarke 1866 ellipsoid

29 History of the North American Datum, Cont. The NAD27 system was adjusted in to become a geocentric datum. Geocentric means the center of the ellipsoid is referenced to Earth s center of mass This new system is North American Datum 1983 (NAD83). Its origin is Earth s center of mass and it is referrenced to the GRS80 ellipsoid Because it is geocentric, it is the datum commonly used by GPS

30 Projections Definition: a mathematical transformation that projects the Earth s surface from 3D to some 2D representation that can be drawn on paper. Since this cannot be done without distortion, a characteristic must be chosen to be portrayed accurately at the expense of others, or a compromise of several characteristics. This can be done in infinite number of ways.

31 Map Projections Curved surface of the earth needs to be flattened to be presented on a map projection is the method by which the curved surface is converted into a flat representation

32 Map Projections defined as a mathematical function to convert between the surface location on the earth and the projected location on the map conversion from a geographic (spherical) reference system to a planar (Cartesian) system; e.g., lat/long -> x/y

33 Map Projections we can literally think of it as a light source located inside the globe which projects the features on the earth s surface onto the flat map map p q p earth s surface q

34 Three Levels of Recognition Class Aspect Property

35 Basic Classes of map projections Cylindrical Conical Azimuthal

36 The Aspect of Map Projection The Normal Aspect The Transverse Aspect The Oblique Aspect

37 Properties of Map Projection Conformality Equivalence (equal area) Equidistance

38 Cylindrical Projections

39 Conic Projections

40 Azimuthal Projections Aspect

41 Azimuthal Projections

42 Distortion in Map Projections some distortion is inevitable less distortion if maps show only small areas, but large if the entire earth is shown projections are classified according to which properties they preserve: area, shape, angles, distance

43 Conformal When the scale of a map at any point on the map is the same in any direction, the projection is conformal. Meridians (lines of longitude) and parallels (lines of latitude) intersect at right angles. Shape is preserved locally on conformal maps.

44 Equal area projections area on the map is proportional to the true area on the earth s surface required when area measures are made popular in GIS

45 Equal area projections

46 Equidistant projections represent the distances to other locations from either one or two points correctly

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49 UTM coordinates are usually measured in meters from the central meridian (x) and the equator (y) minimal distortions of area, angles distance and shape at large and medium scales very popular for medium scale mapping

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52 GPS Coordinates Hundreds of geodetic datums are in use around the world. The Global Positioning system is based on the World Geodetic System 1984 (WGS- 84). Parameters for simple XYZ conversion between many datums and WGS-84 are published by the Defense Mapping Agency.

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55 Lat/Long can also be represented in planar form (but is not technically a projection)