Where am I?

1. Where am I? Lecture 3 CONS 340

2. Learning Objectives • Explain map scale • Define geodesy • Compare geographic and projected coordinate systems • Define spheroids and datums • Datum transformations

3. Map Scale • Linear (also called graphic) • Verbal • 20cm = 4.8km • Representative fraction • 1:24,000 • Conversion Example 20cm = 4.8km (original verbal scale) 20cm = 480,000cm (convert all units to a common metric) 1cm = 24,000cm (make the left side equal to one by dividing) 1 / 24,000 or 1:24,000 (remove the unit designation)

4. Large vs. small scale maps • Because it is a ratio, scale is unitless and large and small scale varies according to project • 1:1 is the largest scale • 1:24,000 is large scale for Conservation • 1:500,000 is a small scale for Conservation • Scale is inversely proportional to area given the same size map (display)

5. Map Scale and You • You will want to pay attention to map scale, because there are always questions on the exams dealing with scale. • For example: Which of these is the larger scale? 1:24,000 or 1:100,000

6. What is Geodesy? • Geodesy is the study of: • The size, shape and motion of the earth • The measurement of the position and motion of points on the earth's surface, and • The study of the earth's gravity field and its temporal variations • Types of Geodesy • terrestrial or classical geodesy • space geodesy • theoretical geodesy

7. Basic Geodesy Facts • Geographic/true directions determined by the orientation of the graticule on the earths' surface

8. Basic Geodesy Facts • Magnetic directions must take into account the compass variation (magnetic declination)

9. Basic Geodesy Facts • Great circle – arc formed by the intersection of the earth with a plane passing through any two surface points and the center of the earth

10. Basic Geodesy Facts Conic projection • Rhumb line, loxodrome or constant azimuth – line which makes a fixed angle with all meridians; spirals to pole Mercator projection

11. The Earth is Not Round • First the earth was flat • 500 BC Pythagoras declared it was a sphere • In the late 1600’s Sir Issac Newton hypothesized that the true shape of the earth was really closer to an ellipse • More precisely an Oblate Ellipsoid (squashed at the poles and fat around the equator) • And he was right!

12. Geoid, Ellipsoid & Sphere • Geoid- estimates the earth's surface using mean sea level of the ocean with all continents are removed • It is an equipotential surface - potential gravity is the same at every point on its surface • Ellipsoid - It is a mathematical approximation of the Geoid • Authalic Sphere - a sphere that has the same surface area as a particular oblate ellipsoid of revolution representing the figure of the Earth

13. Shape of the Earth • Earth as sphere • simplifies math • small- scale maps (less than 1: 5,000,000) • Earth as spheroid • maintains accuracy for larger- scale maps (greater than 1: 1,000,000)

14. Spheroid or Ellipsoid? • What is a Spheroid anyway? • An ellipsoid that approximates the shape of a sphere • Although the earth is an ellipsoid, its major and minor axes do not vary greatly. • In fact, its shape is so close to a sphere that it is often called a spheroid rather than an ellipsoid. • ESRI calls it a spheroid but the two can be used interchangeably • For most spheroids, the difference between its semi-major axis and its semi-minor axis is less than 0.34 percent.

15. How About a Few Ellipsoids

16. Why Do We Need More Than One Spheroid (Ellipsoid)? • The earth's surface is not perfectly symmetrical • the semi-major and semi-minor axes that fit one geographical region do not necessarily fit another one.

17. What is the best Ellipsoid for you? After James R. Smith, page 98

18. Shape of the Earth

19. Relation of Geoid to Ellipsoid From James R. Smith, page 34

20. Vertical Deflection • Important to surveyors • Deflection of the Vertical = difference between the vertical and the ellipsoidal normal • Described by the component tilts in the northerly and easterly directions.

21. Measuring Height • Traditionally measured as height above sea level (Geoid) but is changing due to GPS • The distance between the geoid and the spheroid is referred to as the geoid-spheroid separation or geoidal undulation • Can convert but it is mathematically complex

22. Coordinate Systems

23. Cartesian Coordinate System • Used for locating positions on a flat map • Coordinates tell you how far away from the origin of the axes you are • Referenced as (X,Y) pairs • In cartography and surveying, the X axis coordinates are known as Eastings, and the Y axis coordinates as Northings. • False easting and northings are typically added to coordinate values to keep coordinates in the upper right hand quadrant of the ‘graph’ – positive values

24. 3D Cartesian Coordinates • Cartesian Coordinates can define a point in space, that is, in three dimensions. • To do this, the Z axis must be introduced. • This axis will represent a height above above or below the surface defined by the x and y axes.

25. Local 3D Cartesian Coordinates • This diagram shows the earth with two local coordinate systems defined on either side of the earth. • The Z axis points directly up into the sky. • Instead of (X,Y) it is (X,Y,Z)

26. Geographic Coordinate System • The Equator and Prime Meridian are the reference points • Latitude/ longitude measure angles • Latitude (parallels) 0º - 90º • Longitude (meridians) 0º - 180º • Defines locations on 3- D surface • Units are degrees (or grads) • Not a map projection!

27. City Meridian Athens, Greece 23° 42' 58.815" E Bern, Switzerland 7° 26' 22".5 E Bogota, Colombia 74° 04' 51".3 W Brussels, Belgium 4° 22' 04".71 E Ferro (El Hierro) 17° 40' 00" W Jakarta, Indonesia 106° 48' 27".79 E Lisbon, Portugal 9° 07' 54".862 W Madrid, Spain 3° 41' 16".58 W Paris, France 2° 20' 14".025 E Rome, Italy 12° 27' 08".4 E Stockholm, Sweden 18° 03' 29".8 E Prime Meridians • Origin of Longitude lines • Usually Greenwich, England • Others include Paris, Bogota, Ferro

28. Latitude/ Longitude • Not uniform units of measure • Meridians converge near Poles • 1° longitude at Equator = 111 km at 60° lat. = 55.8 km at 90° lat. = 0 km

29. Decimal Degrees (DD) • Decimal degrees are similar to degrees/minutes/seconds (DMS) except that minutes and seconds are expressed as decimal values. • Decimal degrees make digital storage of coordinates easier and computations faster.

30. Conversion from DMS to DD: • Example coordinate is 37° 36' 30" (DMS) • Divide each value by the number of minutes or seconds in a degree: • 36 minutes = .60 degrees (36/60) • 30 seconds = .00833 degrees (30/3600) • Add up the degrees to get the answer: • 37° + .60° + .00833° = 37.60833 DD

31. Datums

32. Datums (simplified) • Reference frame for locating points on Earth’s surface • Defines origin & orientation of latitude/ longitude lines • Defined by spheroid and spheroid’s position relative to Earth’s center

33. Creating a Datum • Pick a spheroid • Pick a point on the Earth’s surface • All other control points are located relative to the origin point • The datum’s center may not coincide with the Earth’s center

34. Datums, cont. 2 types of datums • Earth- centered • (WGS84, NAD83) • Local • (NAD27, ED50)

36. Why so many datums? • Many estimates of Earth’s size and shape • Improved accuracy • Designed for local regions

37. North American Datums • NAD27 • Clarke 1866 spheroid • Meades Ranch, KS • 1880’s • NAD83 • GRS80 spheroid • Earth- centered datum • GPS- compatible

38. GPS • Uses WGS84 datum • Other datums are transformed and not as accurate • Know what transformation method is being used

39. Relationship between 2 datums

40. Transformation method accuracies • NADCON • HARN/ HPGN • CNT (NTv1) • Seven parameter • Three parameter 15 cm 5 cm 10 cm 1- 2 m 4- 5 m

41. International datums • Defined for countries, regions, or the world • World: WGS84, WGS72 • Regional: • ED50 (European Datum 1950) • Arc 1950 (Africa) • Countries: • GDA 1994 (Australia) • Tokyo