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Map Projections and Remote Sensing

Map Projections and Remote Sensing. Choosing and Using Map Projections. Why Map Projections?. We need consistent coordinate systems The earth is round and maps are flat We use maps to determine Distances between objects Areas occupied by objects Directions between objects Scale.

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Map Projections and Remote Sensing

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  1. Map Projections and Remote Sensing Choosing and Using Map Projections

  2. Why Map Projections? • We need consistent coordinate systems • The earth is round and maps are flat • We use maps to determine • Distances between objects • Areas occupied by objects • Directions between objects • Scale

  3. Round Earth vs. Flat Map

  4. Map Projection - Definition “Map projections are attempts to portray the surface of the earth or a portion of the earth on a flat surface.” (http://www.colorado.edu/geography/gcraft/notes/mapproj/mapproj_f.html)

  5. Challenges that Map Projections Must Overcome • Distortions • Conformality (Shape) • Area • Direction • Scale • Distance • Many of these things are related to one another

  6. Conformality (Conformal Projections) • Map scale stays the same in any direction • e.g. Lambert Conformal Conic • Preserves the shape of objects • Universal over whole map, but only within small areas (not across large extents like continents)

  7. Lambert Conformal Conic

  8. Area (Equal Area Projections) • An “equal area” projection creates maps where the area on the map is proportional to the area on the ground wherever you are on the map. • e.g. Albers Equal Area • Can be universal—applied to whole map • But…shapes distorted to make areas work

  9. Albers Equal Area

  10. Direction (Equal Azimuthal Projections) • Azimuths (angle from a point on a line to any other point) are correct in all directions • Impossible to do over entire map—typically try to optimize over area of interest or along certain lines

  11. Scale and Distance (Equidistant Projections) • Distance is accurate when measured from one or a few points to all other points • Cannot be universal—never works for measuring distance from all points to all other points

  12. Azimuthal Equidistant

  13. Distortion Trade-offs

  14. Summary – Map Distortions • Can preserve characteristics of interest (e.g. distance, shape) but always at the expense of other characteristics • Must think about what you are using a map or image for when you choose a projection

  15. Projection Strategies – Surfaces and “Light Sources” • Projections can be thought of as shining a light through the globe and projecting (like with a projector) map features onto a surface • Can choose different surfaces • Can orient the surfaces in different ways • Can put the light source in different places

  16. Projection Surfaces • Planes • Planar Projections • Cylinders • Cylindrical Projections • Cones • Conic Projections

  17. Surface Orientations • Case • Tangent • Secant • Aspect • Normal • Transverse • Oblique

  18. Tangent vs. Secant

  19. Normal vs. Transverse

  20. Oblique

  21. Light Sources • Gnomic or Azimuthal – Light shines from center of globe • Stereographic – Light shines from opposite side of globe • Orthographic – Light shines from infinitely far away

  22. Other Problems • Earth is not round • Slightly squashed sphere (called “oblate spheroid”)

  23. Spheroids and Ellipsoids • Mathematical descriptions of the shape of the whole earth • Clarke 1866 • GRS1980 • GRS1984 • Many, many others • MUST BE CONSISTENT WHEN USING MULTIPLE SPATIAL DATASETS!!

  24. Ellipsoid Parameters

  25. Datums • Datums are reference systems based on particular spheroids • NAD27 • NAD83 • WGS84 • Many, many others • MUST BE CONSISTENT WHEN USING MULTIPLE SPATIAL DATASETS!!

  26. Datum Shifts

  27. Geoids • There are undulations at local scales on the earth caused by mountains, rock density differences etc. • Models of the local surface differences are called Geoids • Typically built into the coordinate system (projection) that you are using.

  28. Geoid Heights

  29. Map Projections -- Summary • Allow depiction of curved earth on flat maps • Accurate depiction of one property (e.g. area) usually creates distortion of another (e.g. shape) • Should be considered carefully at outset of any remote sensing (or GIS) project • MUST BE CONSISTENT WHEN USING MULTIPLE SPATIAL DATA LAYERS!

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