The Globe and Coordinate Systems

1. The Globe and Coordinate Systems Intro to Mapping & GIS

2. Georeferencing • Is essential in GIS, since all information must be linked to the Earth’s surface • The method of georeferencing must be: • Unique, linking information to exactly one location • Shared, so different users understand the meaning of a georeference • Persistent through time, so today’s georeferences are still meaningful tomorrow

3. Uniqueness • A georeference may be unique only within a defined domain, not globally • There are many instances of Springfield • The meaning of a reference to London may depend on context, since there are smaller Londons in several parts of the world

4. Georeferences as Measurements • Some georeferences are metric • They define location using measures of distance from fixed places • E.g., distance from the Equator or from the Greenwich Meridian • Others are based on ordering • E.g. street addresses in most parts of the world order houses along streets • Others are only nominal • Placenames do not involve ordering or measuring

5. Placenames • The earliest form of georeferencing • And the most commonly used in everyday activities • Many names of geographic features are universally recognized • Others may be understood only by locals • Names work at many different scales • From continents to small villages and neighborhoods • Names may pass out of use in time • Where was Camelot?

6. Postal Addresses and Postcodes • Every dwelling and office is a potential destination for mail • Dwellings and offices are arrayed along streets, and numbered accordingly • Streets have names that are unique within local areas • Local areas have names that are unique within larger regions • If these assumptions are true, then a postal address is a useful georeference

7. Linear Referencing • A system for georeferencing positions on a road, street, rail, or river network • Combines the name of the link with an offset distance along the link from a fixed point, most often an intersection • Regularly spaced addresses, mile markers

8. Where Do Postal Addresses Fail as Georeferences? • In rural areas • Urban-style addresses have been extended recently to many rural areas • For natural features • Lakes, mountains, and rivers cannot be located using postal addresses • When numbering on streets is not sequential • E.g. in Japan

9. Postcodes as Georeferences • Defined in many countries • E.g. ZIP codes in the US • Hierarchically structured • The first few characters define large areas • Subsequent characters designate smaller areas • Coarser spatial resolution than postal address • Useful for mapping

10. ZIP code boundaries are a convenient way to summarize data in the US. The dots on the left have been summarized as a density per square mile on the right

11. Latitude and Longitude • The most comprehensive and powerful method of georeferencing • Metric, standard, stable, unique • Uses a well-defined and fixed reference frame • Based on the Earth’s rotation and center of mass, and the Greenwich Meridian

12. Defining Location on a Spherea Global Coordinate System Defining a location using Latitude and Longitude is perhaps the most common georeferencing system. Let's explore Latitude and Longitude, as well as take a look at other coordinate systems.

13. North Pole Equator Greenwich Definition of longitude. The Earth is seen at left from above the North Pole, looking along the Axis, with the Equator forming the outer circle. The location of Greenwich defines the Prime Meridian. At right, the longitude of the point at the center of the red cross is determined by drawing a plane through it and the axis, and measuring the angle between this plane and the Prime Meridian.

14. Basis of Global Coordinate System • Earth’s rotation gives poles and axis as two natural points of reference on the sphere. • Equator: locus of points on sphere’s surface that are equidistant from the poles. • Great Circle: • Pass a plane through a sphere’s center. • Connect the points along which plane intersects sphere’s surface. • Line defined by the points is a great circle. • Equator is only great circle perpendicular to axis of rotation.

15. Terms to Specify Position on Globe • Latitude: degrees north and south of equator. • Longitude: degrees east and west of Greenwich, England. • Meridian: line of constant longitude. • Parallel: line of constant latitude • Great circle: circle inscribed on surface by a plane passing through earth’s center. • Small circle: circle inscribed on surface by a plane that passes through earth, but misses the center.

17. Arctic Circle Polar Axis Northern Limit Tropic of Cancer Prime Meridian Southern Limit Tropic of Capricorn Equator

18. Global Coordinate System All meridians aregreat circle arcs. All parallels, exceptfor the equator, are small circles.

19. Units of Measure • Traditional Angular Measure: • Degrees: 360 per circle. • Minutes: 60 per degree. • Seconds: 60 per minute.

20. Units of Measure • Angular Measure: • Degrees:360 per circle. • Minutes:60 per degree. • Seconds:60 per minute. • Great Circle Degree Distances: • Degree = 69 miles. • Minute = 1.15 miles. • Second= .02 miles • One tenth second = 10.12 feet • One hundredth second = 1.012 feet.

21. Decimal Degrees • Based on decimal fraction of a degree • Easier to work with • Can express angles to any precision - to hundredths of a degree, to thousandths of a degree, and so on • Better for digital mapping • Decimal Degree Conversion: • Multiply minutes by 60 • Add seconds to results of minutes multiplied by 60. • Divide total by 3,600 • Add result to degrees

22. Example of Decimal Conversion Traditional Measure: 45° 20’ 30” 1200” * 60 = Convert minutes to seconds: Add seconds to converted minutes: = 1230” + Convert seconds to degree fraction: / 3600 = .3416667 Add whole degree to fraction: .3416667 ° 45

23. Global Grid Properties • All meridians equal length • All meridians converge at poles (true north orientation) • All lines of latitude are parallel to the equator • All parallels maintain the same spacing • Meridians and parallels intersect at right angles • The scale on a globe is the same everywhere (unlike a map)

24. Coordinate Systems Cartesian • Numerical systems that specify location in space. • Types of coordinate systems: • Plane coordinates(i.e. FLAT Surface) • Cartesian • Angular/polar • Global or spherical coordinates Polar

25. Cartesian Coordinates Y II I • Origin • Abscissa or X Axis • Ordinate or Y Axis • Position X,Y • Quadrants I through IV • Point Locations:Point X Y 1 x1 y12 x2 y2 • Used for most projections. P1 y1 P2 y2 X x2 x1 III IV

26. (X1 – X2)2 + (Y1 – Y2)2 Distance Calculation for Points Measured in Cartesian Coordinates Y I • Point Locations:Point X Y 1 x1 y12 x2 y2 • Distance Formula: • Distance from Point 1 to Point 2: P1 y1 y1 - y2 P2 y2 x1 - x2 X x2 x1

27. Most Flat Maps Utilize a Cartesian Coordinate System NORTH – SOUTH AXIS EAST – WEST AXIS Ancient Plan of Jerusalem

28. State Plane Coordinates • Defined in the US by each state • Some states use multiple zones • Several different types of projections are used by the system • Provides less distortion than UTM • Preferred for applications needing very high accuracy, such as surveying

30. False Origin What does this point in the middle of the Chesapeake Bay have to do with New Jersey? It's New Jersey's false origin point.

31. NJ State Plane Pros: • Measurable in feet. • No negative values. • All of NJ happens to fit in 1Mx1M ft square. Cons: • NJ Specific • Requires translation.

32. The Universal Transverse Mercator (UTM) Projection • A type of cylindrical projection • Implemented as an internationally standard coordinate system • Initially devised as a military standard • Uses a system of 60 zones • Maximum distortion is 0.04% • Transverse Mercator because the cylinder is wrapped around the Poles, not the Equator

33. Zones are each six degrees of longitude, numbered as shown at the top, from W to E

34. UTM Coordinates • In the Northern Hemisphere define the Equator as 0 mN • The central meridian of the zone is given a false Easting of 500,000 mE • Eastings and northings are both in meters allowing easy estimation of distance on the projection • A UTM georeference consists of a zone number, a six-digit easting and a seven-digit northing • E.g., 14, 468324E, 5362789N

35. Implications of the Zone System • Each zone defines a different projection • Two maps of adjacent zones will not fit along their common border • Jurisdictions that span two zones must make special arrangements • Use only one of the two projections, and accept the greater-than-normal distortions in the other zone • Use a third projection spanning the jurisdiction • E.g. Italy is spans UTM zones 32 and 33

36. The National Grid is a system of metric georeferencing used in Great Britain. It is administered by the Ordnance Survey of Great Britain, and provides a unique georeference for every point in England, Scotland, and Wales. The first designating letter defines a 500 km square, and the second defines a 100 km square (see Box 5.1). Within each square, two measurements, called easting and northing, define a location with respect to the lower left corner of the square. The number of digits defines the precision—three digits for easting and three for northing (a total of 6) define location to the nearest 100 m. Northing 852 100 km Easting 624 SK624852

37. GPS Positioning • Benchmarks or landmarks are not necessary to locate a position on the Earth • GPS (Navstar, GLONASS, Galileo) systems beam information that can be measured to determine location and elevation • Accuracy can be improved using DGPS • Like everything else: Quality Control!

38. Converting Georeferences • GIS applications often require conversion of projections and ellipsoids • These are standard functions in popular GIS packages • Street addresses must be converted to coordinates for mapping and analysis • Using geocoding functions • Placenames can be converted to coordinates using gazetteers