Overview

1. Datums and Projections:How to fit a globe onto a 2-dimensional surface

2. Overview Ellipsoid Spheroid Geoid Datum Projection Coordinate System

3. Definitions: Ellipsoid Also referred to as Spheroid, although Earth is not a sphere but is bulging at the equator and flattened at the poles Flattening is about 21.5 km difference between polar radius and equatorial radius Ellipsoid model necessary for accurate range and bearing calculation over long distances ? GPS navigation Best models represent shape of the earth over a smoothed surface to within 100 meters

6. Geoid: the true 3-D shape of the earth considered as a mean sea level extended continuously through the continents Approximates mean sea level WGS 84 Geoid defines geoid heights for the entire earth

8. Definition: Datum A mathematical model that describes the shape of the ellipsoid Can be described as a reference mapping surface Defines the size and shape of the earth and the origin and orientation of the coordinate system used. There are datums for different parts of the earth based on different measurements Datums are the basis for coordinate systems Large diversity of datums due to high precision of GPS Assigning the wrong datum to a coordinate system may result in errors of hundreds of meters

9. Commonly used datums

10. Projection Method of representing data located on a curved surface onto a flat plane All projections involve some degree of distortion of: Distance Direction Scale Area Shape Determine which parameter is important Projections can be used with different datums

11. Projections The earth is “projected” from an imaginary light source in its center onto a surface, typically a plate, cone, or cylinder.

12. Other Projections Pseudocylindrical Unprojected or Geographic projection: Latitude/Longitude There are over 250 different projections!

20. Mathematical Relationships Conformality Scale is the same in every direction Parallels and meridians intersect at right angles Shapes and angles are preserved Useful for large scale mapping Examples: Mercator, Lambert Conformal Conic Equivalence Map area proportional to area on the earth Shapes are distorted Ideal for showing regional distribution of geographic phenomena (population density, per capita income) Examples: Albers Conic Equal Area, Lambert Azimuthal Equal Area, Peters, Mollweide)

21. Mathematical Relationships Equidistance Scale is preserved Parallels are equidistantly placed Used for measuring bearings and distances and for representing small areas without scale distortion Little angular distortion Good compromise between conformality and equivalence Used in atlases as base for reference maps of countries Examples: Equidistant Conic, Azimuthal Equidistant Compromise Compromise between conformality, equivalence and equidistance Example: Robinson

23. Projections and Datums Projections and datums are linked The datum forms the reference for the projection, so... Maps in the same projection but different datums will not overlay correctly Tens to hundreds of meters Maps in the same datum but different projections will not overlay correctly Hundreds to thousands of meters.

24. Coordinate System A system that represents points in 2- and 3- dimensional space Needed to measure distance and area on a map Rectangular grid systems were used as early as 270 AD Can be divided into global and local systems

25. Geographic coordinate system Global system Prime meridian and equator are the reference planes to define spherical coordinates measured in latitude and longitude Measured in either degrees, minutes, seconds, or decimal degrees (dd) Often used over large areas of the globe Distance between degrees latitude is fairly constant over the earth 1 degree longitude is 111 km at equator, and 19 km at 80 degrees North

26. Universal Transverse Mercator Global system Mostly used between 80 degrees south to 84 degrees north latitude Divided into UTM zones, which are 6 degrees wide (longitudinal strips) Units are meters

28. State Plane Coordinate System Local system Developed in the ’30s, based on NAD27 Provide local reference systems tied to a national datum Units are feet Some larger states have several zones Projections used vary depending on east-west or north-south extent of state

31. Each of the three coordinate systems (Lat/Long, UTM, and SPCS) have their own set of tick marks on 7½ minute quads: Lat/Long tics are black and extend in from the map collar UTM tic marks are blue and 1000 m apart SPCS tics are black, extend out beyond the map collar, and are 10,000 ft apart

32. Other systems Global systems Military grid reference system (MGRS) World geographic reference system (GEOREF) Local systems Universal polar stereographic (UPS) National grid systems Public land rectangular surveys (township and sections)

33. Determining datum or projection for existing data Metadata Data about data May be missing Header Opened with text editor Software Some allow it, some don’t Comparison Overlay may show discrepancies If locations are approx. 200 m apart N-S and slightly E-W, southern data is in NAD27 and northern in NAD83

34. Selecting Datums and Projections Consider the following: Extent: world, continent, region Location: polar, equatorial Axis: N-S, E-W Select Lambert Conformal Conic for conformal accuracy and Albers Equal Area for areal accuracy for E-W axis in temperate zones Select UTM for conformal accuracy for N-S axis Select Lambert Azimuthal for areal accuracy for areas with equal extent in all directions Often the base layer determines your projections

35. Summary There are very significant differences between datums, coordinate systems and projections, The correct datum, coordinate system and projection is especially crucial when matching one spatial dataset with another spatial dataset.