EPSc 407 IP07

1. EPSc 407 � IP07

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3. 3 Map projection general concepts Map projections attempt to display a portion of a planet's surface on a flat plane Distortion in area, shape, scale, or direction occurs in creating the projection There is no �best� map projection Each projection is designed to minimize distortion in area, shape, scale, or direction Projections that accurately portray area are known as equal-area projections A circle placed on anywhere on map represents the same amount of area Also known as equivalent projections Conformal projections show objects on a map without shape distortion All lines of latitude and longitude intersect at right angles Local scale is the same in all directions around any point Areas are generally distorted, except along certain lines

4. 4 Map projection general concepts Scale is the ratio of a distance portrayed on a map to the same distance on the planet No map projection correctly shows scale throughout the map Usually one or more lines on the map has a constant scale Equidistant projections show true scale between the center of map and other points Directions (azimuths) on a map are shown correctly relative to the center of the map on azimuthal projections Some azimuthal projections are also equal-area, conformal, or equidistant Some map projections have special characteristics Lines of constant direction shown as straight lines (Mercator), good for navigating over long distances Great circle arcs shown as straight lines (gnomonic) or as circles (stereographic)

5. 5 Map projection general concepts Reference ellipsoid used to approximate planets that are flattened at poles (polar axis is shorter than equatorial axis) Reference ellipsoids can be designed for local or global applications Earth ellipsoids for global use refined over past 200 years Geopotential surface is the surface of equal gravity potential Gravity vector is perpendicular to geopotential surface Geoid is geopotential surface at mean sea level Varies from ellipsoid by up to � 100 m. Elevations on maps are usually relative to a geoid; latitude, longitude, and planar coordinates are relative to reference ellipsoid

6. 6 Map projection general concepts Reference Ellipsoids a = semi-major axis (ellipsoid equatorial radius) b = semi-minor axis (ellipsoid polar radius) f = flattening e = eccentricity

7. 7 Selected reference ellipsoids

8. 8 Latitude and longitude coordinate systems Planetocentric is relative to ellipsoid center Latitude is angle between equator and line from surface point to ellipsoid center Longitude uses right-hand rule (east positive) Planetographic (geodetic) is relative to ellipsoid normal Latitude is angle between equator and normal to ellipsoid at a surface point Longitude direction depends on planet rotation: west positive for prograde planets; Earth is east positive for global areas or west positive locally Planet Centered Cartesian have x, y, z coordinates

9. 9 Geodetic datums Provides framework for referencing planar coordinates Horizontal and/or vertical reference Requires reference ellipsoid and coordinate system origin Hundreds of datums in use for different regions of the Earth Datums can differ from each other by up to one kilometer in x, y planar coordinates Conversion from one datum to another will also change values of geodetic latitude and longitude. It is important to know what datum is being used Do not mix data that use different datums Common datums for maps and remote sensing of North America NAD27: Clark 1866 ellipsoid WGS84: WGS84 ellipsoid These differ by about 150 - 200 meters

10. 10 Datum conversion

11. 11 Map projections Projection Types Cylindrical Conic Azimuthal Pseudocylindrical

12. 12 Cylindrical projections Regular cylindrical projections partly formed by projecting points onto a cylinder wrapped around a globe at the equator Longitude lines are equidistant parallel straight lines on the projection Latitude lines cross longitude lines at right angles, but are not equally spaced Oblique or transverse projections result from rotating the cylinder relative to the globe

13. 13 Mercator projection Longitude lines are vertical, equally spaced, and parallel to each other Latitude lines are horizontal (cross longitude at right angles) Spacing increases toward the poles so that the projection is conformal Area is distorted, as is scale Used for marine navigation because straight lines are lines of constant azimuth Used to show large portions of globe, except for the poles

14. 14 Transverse Mercator projection Projection of the globe onto a cylinder tangent to a longitude line Latitude and longitude lines are no longer straight lines Distortion of scale, distance, direction, and area increase away from central longitude

15. 15 Universal Transverse Mercator (UTM) projection Special case of transverse Mercator Widely used for designating rectangular coordinates (in meters) on large-scale maps Earth divided into 60 zones (each 6� of longitude wide) Scale variation within a zone is 1 part in 1,000 Zone origin is equator at central longitude, with x value of 500,000 m and y of 0 m for Northern Hemisphere X increases to east, y to the north

16. 16 Cylindrical Equidistant projection Latitude and longitude lines are parallel, equidistant, straight lines, intersecting at right angles Simple linear scaling of latitude and longitude Also known as simple cylindrical or geographic lat/lon projection (ENVI) Neither equal-area nor conformal

17. 17 Space Oblique Mercator Projection Modified cylindrical projection with map surface defined by satellite orbit Designed for displaying early Landsat images and other similar satellite data Central line of projection is satellite groundtrack Scale is true along groundtrack Used only for narrow band along the groundtrack

18. 18 Conic projections Surface projected onto a cone that intersects planet at one or two latitude lines (known as standard parallels) Scale is true along the standard parallels, but distorted elsewhere Can also be conformal, equal-area, or equidistant in limited portions of the map Used for areas of large east-west extent

19. 19 Lambert Conformal Conic projection Uses two standard parallels Is conformal Latitude lines are arcs of concentric circles with spacing decreasing toward center of map Longitude lines are equally spaced and intersect latitudes at right angles Scale is true along standard parallels

20. 20 Albers equal area projection Uses two standard parallels Is equal-area Latitude lines are arcs of concentric circles with spacing decreasing toward north and south edges of map Longitude lines are equally spaced and intersect latitudes at right angles Scale and shape are true along standard parallels

21. 21 Azimuthal projection Surface projected onto a plane, usually tangent to the planet Direction or azimuth from the center of the projection to every other point on the map is correctly shown For spherical form, great circles passing through the center of the map are shown as straight lines

22. 22 Orthographic projection Projection from a point infinitely far from the planet onto a plane tangent to the planet Makes the planet appear like a globe Latitude and longitude lines can be straight lines, ellipses, or circles Neither conformal or equal-area

23. 23 Stereographic Projection Projection from a point on a planet to a plane tangent to the planet and on the opposite side from the projection point A conformal projection Often used to show polar areas with North or South Pole at the center of the map

24. 24 General perspective projection Projections of a planet onto a plane through a single point Simulates the geometry of a framing camera Neither conformal or equal-area Other azimuthal projections are special cases of this projection

25. 25 Pseudocylindrical projections Resemble cylindrical projections Latitude lines are straight and parallel Longitude lines are curves

26. 26 ENVI map projection header information Map projection information stored in ENVI ASCII header file Map info can be added by editing file No registration is performed by editing the Geographic Corners attribute EM � File � Edit ENVI Header

27. 27 Image display tools Cursor Location/Value IM � Tools � Cursor Location/Value� Grid lines IM � Overlay � Grid Lines� Add grids for pixel, map, or geographic coordinate systems Non-pixel coordinates require georeferenced image

28. 28 Grid line settings Save grid settings to file for later use

29. 29 Map coordinate converter EM � Map � Map Coordinate Converter Change projections and datums to desired settings Enter known coordinate Calculate in forward or reverse direction

30. 30 ASCII coordinate converter EM � Map� ASCII Coordinate Conversion Convert one or more files of coordinates or GCPs (ground control points)

31. 31 Resampling and warp methods Pixel resampling methods Nearest neighbor uses the nearest pixel without any interpolation Bilinear is a linear interpolation using 4 neighboring pixels Cubic convolution uses 16 pixels to approximate the sine function using cubic polynomials; significantly slower than other methods Warp methods RST (rotation, scaling and translation), requires at least four GCPs Polynomial, sometimes called �rubbersheeting� Degree of polynomial is dependent upon number of GCPs selected: #GCPs > (degree + 1)^2 Delaunay triangulation fits triangles to the irregularly spaced GCPs and interpolates values to the output grid.

32. 32 Projection conversion: reverse mapping Projection conversion employs reverse mapping to derive output Example: take an input grid and convert to a different projection

33. 33 Projection conversion: bilinear interpolation Bilinear interpolation resampling is used to better approximate output Example:

34. 34 Projection converstion: bilinear interpolation

35. 35 Changing map projections and datums EM � Map � Convert Map Projection Select file and target projection Optionally save warp points to GCP file Set warping and resampling parameters

36. 36 Ground control points A set of image coordinates for an unregistered image corresponding to a known set of locations Sources of known locations may vary Registered images Maps DLGs (digital line graphs) GPS field readings Unregistered images (special case) GCPs saved in ASCII format

37. 37 Georeferencing�GCP collection GCPs required to register image to a map projection Warp (unregistered) image must be displayed to collect GCPs �Image to Map� for registering to DLGs or field readings EM � Map � Registration � Select GCPs: Image to Map Destination projection, datum, and pixel size are specified �Image to Image� for registering to another image EM � Map � Registration � Select GCPs: Image to Image

38. 38 Georeferencing�GCP collection GCPs are entered and managed through GCP selection dialog

39. 39 Georeferencing�GCP collection Collected GCPs are displayed on warp image Map locations may be entered by hand, or automatically entered from vector window or existing registered image ENVI will predict warp image location given map location after four GCPs have been entered GCPs may be updated or deleted to minimize error For best results RMS error < 1.5 Save GCPs to file for later use

40. 40 Georeferencing�image warping Register image from GCP selection dialog Options � Warp Displayed Band� or Options � Warp File� or from ENVI menu EM � Map � Registration � Warp from GCPs: Image to Map or EM � Map � Registration � Warp from GCPs: Image to Image

41. 41 Help Help viewing this document This document was generated using PowerPoint in the multipurpose roll of course handouts, in-class presentation, and on-line reference. As a result, some features of the document deviate from standard practice for a given purpose. For example: Page titles are oriented primarily for use in handouts, but also serve well for presentations. Hyperlinks are underlined, but in black rather than blue to make the in-class presentation more readable. Page margins are great at the top to allow for use in a three-ring binder. Help with this class Help is available from several sources. The first line of defense is the course web page at wufs.wustl.edu/courses/407. Here you will find notes, references, and information on contacting the course instructors. Help on using the EPRSL computers is available from wufs.wustl.edu/computers.