Datum & Projection Workshop

1. Datum & Projection Workshop GIP-West ASPRS certification preparation Presented by: Eric Zehnbauer

2. What is a datum? • A datum, simply put, is a reference point, line, or surface from which measurements are made. In mapping the Earth, a geodetic datum is a model of the earth from which measurements of positions are made. The various geodetic datums are defined based on various ellipsoids, which are models which closely approximate the geoid (usually an oblate spheroid in shape, as the Earth is not spherical). The geoid is defined as “that equipotential surface which would coincide exactly with the mean ocean surface of the Earth, if the oceans were in equilibrium, at rest, and extended through the continents…” • Ellipsoids are commonly defined by several parameters: • Semimajor axis (a) • Semiminor axis (b) • Coefficient of flattening (1/f) • Other parameters sometimes referred to include aspect ratio, i.e. the semiminor axis/semimajor axis (b/a); and the eccentricity, most often expressed as its squared value - e²

3. What is an ellipsoid? • The Earth’s (and that of most planets) reference ellipsoid is defined as an oblate spheroid due to its rotation, which tends to “squash” the otherwise spherical body flat about its axis of rotation An oblate spheroid type of ellipsoid

4. What is a datum? • A datum will be defined according to the ellipsoid on which it is based, and an origin point. The WGS-84 datum and some other modern datums are termed geocentric because they use the Earth’s center of mass as the origin point. Many other popular datums have other unique origin points.

5. Other horizontal datums: • North American Datum of 1927 (NAD27): Ellipsoid – Clarke 1866; Origin Point – Meades Ranch, Kansas • Provisional South American Datum 1956: Ellipsoid – International 1924; Origin Point – La Canoa, Venezuela • Pulkovo 1942 Datum: Ellipsoid – Krassovsky 1940; Origin Point – Pulkovo Astronomical Observatory (near St. Petersburg, Russia) • Ordnance Survey of Great Britain 1936: Ellipsoid – Airy 1830; Origin Point – Royal Greenwich Observatory

6. What is a projection? • A projection is a method of representing a 3-dimensional surface (such as a sphere) in 2 dimensions (such as a flat map). By their nature, all map projections will distort the three dimensional surface to some extent. Different projections will have lesser distortion in some parameters (scale, area, direction, etc.) but possibly greater distortion in others. Peter H. Dana, The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder.

7. Types of projections The type of distortions which occur will be predictable depending on the type of projection. Different projections are used to minimize distortions in distance, area, azimuth, etc. • Major types of projections include: • Conic – the spherical surface is projected onto a cone • Cylindrical – the spherical surface is projected onto a cylinder • Azimuthal – the spherical surface is projected onto a plane • Projections may be either: • Tangent – the sphere touches the projection surface at one point (azimuthal projections) or along one circular arc (conic, cylindrical) • Secant – projection surface cuts through the sphere, intersecting the sphere along one circular arc (azimuthal) or two arcs (conic, cylindrical)

8. Tangent projections Peter H. Dana, The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder.

9. Secant projections Peter H. Dana, The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder.

10. Cylindrical projections A cylindrical projection may have several different types of orientation: Normal Oblique Transverse The Mercator projection and Transverse Mercator projection are widely-used cylindrical projections. In the case of the Transverse Mercator projection, the cylinder is tangent to the sphere along a central meridian Peter H. Dana, The Geographer's Craft Project, Department of Geography, The University of Colorado at Boulder.

11. The Mercator Projection The Mercator projection and Transverse Mercator projection are widely-used cylindrical projections. In the case of the Mercator projection, the cylinder is either tangent to the sphere at the Equator, or intersects the sphere along two standard parallels. Scale is true along the standard parallels but nowhere else. The Mercator projection, as with all normal cylindrical projections, is characterized by equidistant meridians which are all straight lines, intersecting at right angles parallels which are also straight lines but which are not equidistant. Spacing between parallels (and thus, distortion) increases with distance away from the Equator. Although the Mercator projection introduces great amounts of areal distortion, it has remained a widely used projection due to its usefulness in maritime navigation. This is due to the fact that all routes of constant azimuth (i.e., rhumb lines) are straight lines on a Mercator projection map. Thus, a mariner can draw a straight line between any two points and determine the heading necessary to reach the destination.

12. The Mercator Projection NGA and National Ocean Survey (NOS) nautical charts are still produced on the Mercator Projection to this day. graphic from: Wikipedia

13. Conic Projections • Albers equal-area projection – maintains accuracy of areas, but distorts scale and distance. graphic from: Wikipedia

14. Conic Projections • Lambert Conformal Conic – maintains true scale along the standard parallels (arcs where cone intersects sphere); by having the cone secant to the sphere, this minimizes distortion of the 3-D surface. The map is conformal, i.e. it preserves angles. On a map with Lambert Conformal Conic projection, the cone normally intersects the sphere such that the latitudinal extent between the standard parallels is exactly twice that of the extent above and below the standard parallels; e.g. a TPC, produced on a 4° latitude band, will have standard parallels each 40 min. in from the upper and lower limits. graphic from: Wikipedia

15. Azimuthal Projections • Gnomonic – an azimuthal equidistant projection; all straight lines emanating from the center point are great circle routes, distances are preserved. graphic from: Wikipedia

16. Azimuthal Projections • Stereographic projection – a conformal projection (preserves angles); not equal area or equidistant. Polar Stereographic projection is commonly used in mapping Polar areas. graphic from: Wikipedia

17. Miscellaneous Projections • Pseudocylindrical projections, such as the Mollweide Projection,resemble cylindrical projections, with straight and parallel latitude lines and equally spaced meridians, but the other meridians are curves.The Eckert, Sinusoidal, and Mollweide projections are all pseudocylindrical and equal-area. Mollweide Projection graphic from: Wikipedia

18. Miscellaneous Projections Sinusoidal Projection graphic from: Wikipedia

19. A Unique Projection The Craig Retroazimuthal projection (a.k.a. Qibla or Mecca projection) was developed by British cartographer James Craig to help Muslims find their qibla. Craig Retroazimuthal Projection graphic from: Wikipedia

20. Useful links: • http://www.ngs.noaa.gov/PUBS_LIB/Geodesy4Layman/TR80003B.HTM • http://en.wikipedia.org/wiki/Cartographic_projections • http://en.wikipedia.org/wiki/Geodetic_datum • http://en.wikipedia.org/wiki/Reference_ellipsoid • http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html • http://www.posc.org/Epicentre.2_2/DataModel/ExamplesofUsage/eu_cs34c.html • http://www1.nga.mil/ProductsServices/GeodesyGeophysics/Pages/default.aspx/tm83581/toc.htm • http://www.dmap.co.uk/ll2tm.htm

21. Questions?