Understanding Coordinate Systems in GIS

1. Referencing Data to Real Locations Module 3 ESRI Virtual Campus Learning ArcGIS Desktop Training Course ESRI ArcGIS

2. Referencing Data to Real Locations • A GIS represents reality, it is not reality. • A GIS map must accurately represent feature locations. • To determine location of features in real world or on map need a reference system • A set of lines of known location that can be used to determine the locations of features that fall between the lines

3. Referencing Data to Real Locations • Coordinate Systems • Reference systems used to determine feature locations • In this module learn about • different coordinate systems • how they work • how to change the coordinate system of a map. • Understanding coordinate systems  manage your data to increase accuracy

4. Learning Objectives • Name two types of coordinate systems. • Identify components of each type of coordinate system. • Assign coordinate system information to a dataset. • Set display units for a data frame and measure distances on a map. • Explain what a map projection is. • List the major categories of map projections. • List spatial properties that may be distorted when different map projections are applied. • Change the map projection for a data frame and describe its effects.

5. Understanding Coordinate Systems • Two types of coordinate systems • Geographic • Used to locate objects on the curved surface of the earth • Projected • Used to locate objects on a flat surface • a paper map or a digital GIS map displayed on a flat computer screen. • Each attempts to model earth and feature locations accurately • But no system is completely accurate

6. Geographic Coordinate System • Reference system for identifying locations and measuring features on the curved surface of the earth • Consists of a network of intersecting lines called a graticule • Intersecting lines = longitude and latitude

7. Geographic Coordinate System • Graticule • Longitude • Vertical lines • Latitude • Horizontal lines • Because earth is spherical, these lines form circles

8. Geographic Coordinate System • Measurements expressed in • Degrees • 1/360th of a circle. • Can be divided into 60 minutes • Minutes • Can be divided into 60 seconds • Seconds

9. Geographic Coordinate System • Lines of longitude • Called meridians • Measures of longitude begin at the prime meridian • Defines zero value for longitude • Range from 0° to 180° going east • Range from 0° to -180° going west • Lines of latitude • Called parallels. • Measures of latitude begin at the equator • Range from 0° to 90° from the equator to the north pole • Range from 0° to -90° from the equator to the south pole

10. Geographic Coordinate System • Prime meridian • Green line • Starting point for longitude • Has a value of 0 • Equator • Red line • Starting point for latitude • Has a value of 0 • Runs midway between the north and south poles • Dividing earth into northern and southern hemispheres.

11. Geographic Coordinate System • Longitude and latitude actually angles measured from earth's center to point on earth's surface • For example, consider these coordinates: • Longitude: 60 degrees East (60° 00' 00") • Latitude: 55 degrees, 30 minutes North (55° 30' 00") • Longitude coordinate refers to angle formed by two lines • one at the prime meridian • the other extending east along the equator. • Latitude coordinate refers to angle formed by two lines • one on the equator • the other extending north along the 60° meridian.

12. Geographic Coordinate System • Longitude and latitude are angles measured from the earth's center to a point on the earth's surface.

13. Understanding Spheroids • Many models of the earth's shape • Each has its own geographic coordinate system • All based on • degrees of latitude and longitude • Exact latitude-longitude values assigned to individual locations will vary

14. Understanding Spheroids • Two shapes commonly used to model earth • Sphere • Spheroid

15. Sphere vs Spheroid • Assuming the earth is a sphere greatly simplifies mathematical calculations • Works well for small-scale maps • Maps that show large area of the earth • A sphere does not provide enough accuracy for large-scale maps • maps that show smaller area of earth in more detail • For those, it is preferable to use a spheroid • A spheroid is a more accurate model of the earth, but it's not perfect.

16. Understanding Spheroids • Planet Earth • slightly pear-shaped and bumpy • has several dents and undulations • south pole is closer to the equator than north pole • Geoid • Model for complicated of earth • Too mathematically complicated to use for practical purposes, so spheroid is used as a compromise

17. Understanding Spheroids • Different spheroids currently in use • Some spheroids were developed to • Model the entire earth • Model specific regions more accurately • World Geodetic System of 1972 (WGS72) and 1984 (WGS84) • Used to represent the whole world • Clarke 1866 and Geodetic Reference System of 1980 (GRS80) • Most commonly used in North America

18. Understanding Spheroids • Why do you need to know about spheroids? • Because ignoring deviations and using the same spheroid for all locations on the earth could lead to measurement errors of several meters or, in extreme cases, hundreds of meters.

19. Understanding Datums • A spheroid doesn't describe the earth's shape exactly. • A geographic coordinate system needs a way to align the spheroid being used to the surface of the earth for the region being studied. • For this purpose, a geographic coordinate system uses a datum. • A datum specifies which spheroid you are using as your earth model and at which exact location (a single point) you are aligning that spheroid to the earth's surface.

20. Understanding Datums • Red spheroid • Aligned to the earth to preserve accurate measurements for North America • Blue spheroid • Aligned to the earth to preserve accurate measurements for Europe

21. Understanding Datums • Datum • Defines origin of geographic coordinate system • The point where the spheroid matches up perfectly with the surface of the earth and where the latitude-longitude coordinates on the spheroid are true and accurate. • All other points in the system are referenced to the origin. • In this way, a datum determines how your geographic coordinate system assigns latitude-longitude values to feature locations. • There are different datums to help align the spheroid to the surface of the earth in different regions

22. Does Changing Datums Affect Your Data • If you change the datum of the geographic coordinate system, you should know that the coordinate values of your data will also change. • For example, consider a location in Redlands, California, that is based on the North American Datum of 1983 • The coordinate values of this location are: • –117° 12' 57.75961" (longitude)34° 01' 43.77884" (latitude) • Now consider the same point on the North American Datum of 1927 • –117° 12' 54.61539" (longitude)34° 01' 43.72995" (latitude) • The longitude value differs by about three seconds, while the latitude value differs by about 0.05 seconds.

23. Does Changing Datums Affect Your Data • In both NAD 1927 and the NAD 1983 datums • Spheroid matches the earth closely in North America • Is quite a bit off in other areas • Notice that the datums use different spheroids and different origins • NAD 1927 • origin aligns the Clark 1866 spheroid with a point in North America • NAD 1983 • Origin aligns the center of the spheroid with the center of the earth

24. Does Changing Datums Affect Your Data • The most recently developed and widely used datum for locational measurement worldwide is • World Geodetic System of 1984 (WGS 1984)

25. Projected Coordinate Systems • The surface of the earth is curved but maps are flat. • To convert feature locations from the spherical earth to a flat map • Latitude and longitude coordinates from a geographic coordinate system must be converted, or projected, to planar coordinates

26. Projected Coordinate Systems • A map projection uses mathematical formulas to convert geographic coordinates on the spherical globe to planar coordinates on a flat map.

27. Projected Coordinate Systems • Projected coordinate system • A reference system for identifying locations and measuring features on a flat (map) surface • Consists of lines that intersect at right angles, forming a grid • Based on Cartesian coordinates • Have an origin, an x and a y axis, and a unit for measuring distance

28. Projected Coordinate Systems • Based on Cartesian coordinates which use a grid. • Feature locations are measured using x and y coordinate values from the point of origin.

29. Projected Coordinate Systems • The origin of the projected coordinate system • (0,0) • commonly coincides with the center of the map. • This means that x and y coordinate values will be positive only in one quadrant of the map (the upper right). • On published maps, however, it is desirable to have all the coordinate values be positive numbers.

30. Projected Coordinate Systems • To offset this problem • Mapmakers add 2 numbers to each x and y value • Numbers are big enough to ensure that all coordinate values, at least in the area of interest, are positive values. • False easting • Number added to the x coordinate • False northing • Number added to the y coordinate

31. Projected Coordinate Systems • A false easting value of 7,000,000 was added to each x coordinate. • A false northing value of 2,000,000 was added to each y coordinate.

32. Working with Coordinate Systems in ArcGIS • All geographic datasets have a geographic coordinate system (GCS). • Some datasets also have a projected coordinate system (PCS). • When you add a dataset to ArcMap it detects the geographic coordinate system and the projected coordinate system if there is one

33. Working with Coordinate Systems in ArcGIS • If all the data you want to display on a map is stored in the same geographic coordinate system, you can just add it to the map—the layers will overlay properly. • If some of the datasets also have projected coordinate systems, even if they are different, you can also just add them to the map without data alignment worries— • ArcMap will automatically make the layers overlay using a process called "on-the fly projection." • The geographic coordinate system is the common language. • ArcMap can convert the geographic coordinate system to any projected coordinate system and it can convert any projected coordinate system back to the geographic coordinate system.

34. Working with Coordinate Systems in ArcGIS • An issue arises when you want to display datasets that have different geographic coordinate systems on the same map. • The first layer you add to an empty data frame determines the coordinate system for the data frame. • If that layer has a projected coordinate system, the data frame will have that same projected coordinate system. • If you add a layer that has the same geographic coordinate system but a different projected coordinate system (or no projected coordinate system at all), ArcMap will perform an on-the-fly projection and convert the data to the data frame's projected coordinate system. • The layers will overlay properly.

35. Working with Coordinate Systems in ArcGIS • If, however, you try to add a layer that has a different geographic coordinate system, ArcMap will display a warning message telling you that it may not be able to properly align the data. • ArcMap can still project the data on the fly, but it can no longer guarantee perfect alignment. • For perfect data alignment, you need to apply a transformation to make the geographic coordinate systems match

36. Working with Coordinate Systems in ArcGIS • How do you know what coordinate system your data is stored in? • You can view the coordinate system information for a dataset in ArcCatalog™, in its metadata. • If a dataset has no coordinate system information in its metadata (it's missing), you may not be able to display the data in ArcMap. • You may need to do some research to find out the coordinate system, then define the coordinate system using the ArcGIS tools provided.

37. Understanding Map Units and Display Units • Map units • Units in which coordinates for a dataset are stored • Determined by the coordinate system • If data is stored in a geographic coordinate system • Map units are usually decimal degrees • If data is stored in a projected coordinate system • Map units are usually meters or feet • Units can be changed only by changing the data's coordinate system. • Display unit • Independent of map units • Are a property of a data frame • The units in which ArcMap displays coordinate values and reports measurements. • You can set the display units for any data frame and change them at any time.

38. Decimal Degrees • Latitude and longitude are angle measurements • Angles are measured in degrees. • Degrees can be expressed two ways: • degrees, minutes, seconds (DMS) • decimal degrees (DD). • In a GIS, decimal degrees are more efficient because they make digital storage of coordinates easier and computations faster. • Convert from DMS to DD • Latitude of London expressed in DMS • 51° 29' 16" North. • To convert this location to DD, • Divide each value by the number of minutes (60) or seconds (3600) in a degree: • 29 minutes = 29/60 = 0.4833 degrees16 seconds = 16/3600 = 0.0044 degrees • Add up the degrees to get the answer: • 51° + 0.4833 ° + 0.0044 ° = 51.4877 DD

39. Exercise • View and modify coordinate system information

40. Working with Map Projections • Map projection • Used to convert data from a geographic coordinate system to a projected (planar) coordinate system • There are many different map projections • Each preserves the spatial properties of data (shape, area, distance, and direction) differently

41. Work with Map Projections • Maps are always flat, so do you always need a map projection? • Maybe—it depends on what you want to do. • For example, suppose your project doesn't require a high level of locational accuracy—you won't be performing analysis based on location and distance or you just want to make a quick map. In these situations, there is probably no need to convert your data to a projected coordinate system.

42. Work with Map Projections • Use a map projection to convert data to a projected coordinate system • If you need to perform analysis • measure distances, calculate areas and perimeters, determine the shortest route between two points • If you need to show a particular spatial property for features on a map as it really exists on the earth

43. Types of Map Projections • The term "map projection" comes from the concept of projecting a light source through the earth's surface onto a two-dimensional surface (a map).

44. Types of Map Projections • Map projections are created using mathematical formulas • There are three types of surfaces that a map can be projected onto: • Cylinder • Cone • Plane • Each of these surfaces can be laid flat without distortion.

45. Types of Map Projections • Projections based on each surface can be used for mapping particular parts of the world • Cylinder • wrapped around the earth so that it touches the equator • accurate in the equatorial zone • Cone • placed over the earth so it touches midway between the equator and the pole • accurate in the mid-latitude zone • Plane • touches the earth at a pole • accurate in the polar region. • Knowing the surface used helps determine if the map projection is right for purpose

46. Projections Based on a Cylinder • Produce maps with • straight, evenly-spaced meridians • straight parallels that intersect meridians at right angles • Created by • wrapping a cylinder around a globe • projecting a light source through the globe onto the cylinder • cutting along a line of longitude • Being laid flat

47. Projections Based on a Cone • Produce maps with • straight converging longitude lines • concentric circular arcs for latitude lines • Created by • setting a cone over a globe • projecting light from the center of the globe onto the cone • cutting along a longitude line

48. Projections Based on Plane • Produce maps on which • longitude lines converge at the north pole and radiate outward • Latitude lines appear as a series of concentric circles • Created by • passing a light source through the earth onto a flat surface (plane). • In this example, the plane touches the earth at the north pole.

49. Understanding Distortion • Converting locations from a spherical surface to a flat surface causes distortion • Four spatial properties subject to distortion: • Shape • Area • Distance • Direction • Each map projection is good at preserving one or more (but not all)

50. Understanding Distortion • Different map projections preserve different spatial properties and produce different-looking maps.