Map Projections and Remote Sensing

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

11. 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

12. 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

13. Azimuthal Equidistant

14. Distortion Trade-offs

15. 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

16. 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

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

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

19. Tangent vs. Secant

20. Normal vs. Transverse

21. Oblique

22. 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

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

24. 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!!

25. Ellipsoid Parameters

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

27. Datum Shifts

28. 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.

29. Geoid Heights

30. 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!