Geographic Information Systems

1. Geographic Information Systems Chapter 2 – Map Projections and Coordinate Systems

2. 2.1 Introduction • The locations of map features are based on a plane coordinate system expressed on x- and y- coordinates, whereas the locations of spatial features are based on the geographic coordinate system expressed in longitude خط الطول and latitude خط العرض values. • To bridge the two systems, Projection transforms the spherical surface of the earth to a map projection, which provides the basics for a plane coordinate system.

3. Cont. • A basic principle in GIS is that map layers to be used together must have the same coordinate system. • There are situations of two or more different coordinate systems need to be unified in one coordinate system (so they need to be transformed to one coordinate system). • Projection converts digital maps from longitude and latitude values to plane coordinates, and reprojection converts from one plane coordinate system to another.

4. 2.2 Geographic Coordinate System • The Geographic Coordinate System is the location reference system for spatial features on the Earth’s surface. • The geographic coordinate system consists of meridians خطوط الطول and parallels خطوط العرض. • Meridians are lines of longitude running north and south and used for measuring locations in the E-W direction.

5. Cont. • Using the meridian passing through Greenwich (the prime meridian or 0), one can measure the longitude value of a point on the Earth’s surface or 0 to 180 east or west of the prime meridian. • Parallels are lines of latitude, running east and west, and used for measuring location in the N-S direction. • Using the equator as 0 latitude, one can measure the latitude value of a point as 0 to 90 north or south of the equator.

8. Cont. • The origin of the geographic coordinate system is where the prime meridian meets the equator. • So, longitude values are similar to X values in a coordinate system and latitude values are similar to Y values. • Latitude values are positive of north of the equator and negative of south of the equator. • Longitude values are positive in the eastern hemisphere and negative in the western hemisphere.

9. Cont. • Longitude and latitude values may be measured in the degrees-minutes-seconds (DMS), or decimal degrees (DD). • 1 degree equals 60 minutes, and 1 minute equals 60 seconds. • The conversion between the two systems is easy, for example a latitude value 45o52’30” would be equal to 45.875o (45 + 52/60 +30/3600).

11. 2.3 Map Projections • Projection transforms the spherical Earth’s surface to a two-dimensional or plane surface. • The outcome of this transformation is a map projection: a systematic construction of lines on a plane surface representing the geographic coordinate system. • The transformation from the Earth’s surface to a flat surface always involves distortion and no map projection is perfect.

12. Cont. • A map projection faithfully reproducing all features of the original sphere would be perfectly equidistant; i.e., distances between every two points would keep the same ratio on both map and sphere. Therefore, all shapes would also be preserved. On a flat map this property is simply not possible. • For many mapping applications, a lesser constraint - fidelity إخلاص of shape, or conformality, is the most fundamental requisite: the angle between any two lines on the sphere must be the same between their projected counterparts on the map; in particular, each parallel must cross every meridian at right angles.

13. Cont. • Also, scale at any point must be the same in all directions.

14. Cont. • Every map projection preserves certain spatial properties while sacrificing other properties. • There are several types of projections: • Conformal امتثالي Projection: preserves local angels and shapes (A map projection which is a conformal mapping, i.e., one for which local angles on a sphere are mapped to the same angles in the projection). • Equivalent معادل Projection: represents areas in correct relative size. • Equidistant متساوي البعد Projection: maintains consistency of scale along certain lines. • Azimuthal Projection: retains certain accurate directions.

15. Cont. • Cartographersرسم الخرائط often use a geometric object (like cylender) to illustrate how to construct a map projection. • For example, by placing a cylinder tangent to a lighted globe الكرة الارضية, one can draw a projection by tracing the lines of longitude and latitude onto the cylinder. • The cylinder in this case is the projection surface, and the globe is called the reference globe.

17. Cont. • Other common projection surfaces include a cone and a plane. • A map projection is called a cylindrical projection if it can be constructed using a cylinder, a conic projection is using a cone, and an azimuthal projection if using a plane.

18. Cont. • A common measure of projection distortion is scale, which is defined as the ratio of a distance on a map (or globe) to its corresponding ground distance. • When a map projection is used as the basis of a coordinate system, the center of the map projection, as defined by the central parallel and the central meridian, becomes the origin of the coordinate system and divides the coordinate system into for quadrants.

19. Cont. • The x-, y-coordinates of a point are either positive or negative, depending on where the point is located.

21. Cont. • To avoid having negative coordinates, GIS users can assign x-, y-coordinate values to the origin of the map projection. • The false easting is assigned x-coordinate value and the false northing is the assigned y-coordinate value.

22. 2.3.2 Datum • So far map projections assumed the Earth is a perfect sphere. • The Earth is wider along the equator than between the poles. • To map spatial features more accurately, we need to work with two closely related parameters in projection: Spheroidجسم شبيه بالكرة and Datum.

23. Cont. • A spheroid is a model that approximates the shape and size of the Earth. • A much more accurate model than a sphere, a spheroid has its major axis (a) along the equator and its major axis (b) connecting the poles. • Datum is a mathematical model of the Earth, which serves as the reference or base for calculating the geographic coordinates of a location. • there are a lot of ways to implement datum: Clarke 1866, NAD27 (North American Datum), NAD83, GRS80 (Geodetic Reference System), WGS84 (World Geodetic System).

25. 2.4 Plane Coordinate Systems • Because a plane coordinate system is based on a map projection, the terms of coordinate system and map projection are sometimes used interchangeably. • Plane coordinate systems are designed for detailed calculations and positioning and are typically used in large-scale mapping such as at scale 1:24,000 or larger. • Accuracy in feature’s absolute position and its relative position to other features is more important to a coordinate system than the preserved property of a map projection.

26. Cont. • To maintain the level of accuracy desired for measurements, a coordinate system is often divided into different zones, with each zone having a separate map projection. • Three coordinate systems are commonly used in the United States: • The Universal Transverse Mercator (UTM) grid system. • The Universal Polar Stereographic (UPS) grid system. • The State Plane Coordinate (SPC) system.

27. 2.4.1 The Universal Transverse Mercator (UTM) Grid System • Used worldwide, the UTM grid system divides the earth’s surface between 840 N and 800 S into 60 zones. • Each zone covers 60 of longitude, and is numbered sequentially with zone 1 beginning at 1800 W. • In the northern hemisphere, UTM coordinates are measured from a false origin located at the equator and 500,000 meters west of a UTM zone’s central meridian.

29. Cont. • In the southern hemisphere, UTM coordinates are measured from a false origin located at 10,000,000 meters south of the equator and 500,000 meters west for the UTM zone’s central meridian. • Because UTM coordinates are measured from a false origin, they are often very large numbers. • Shifting is used to get the accurate coordinate in order to preserve data precision for computations with coordinates.

30. Cont. • If x-shift value is set as -500,000 meters and the y-shift value is -5,170,000 meters for a map, the coordinates for its NW corner will be changed to 0 and 7164 meters. • X-shift and y-shift must be documented along with the projection parameters in the metadata (information about data), especially if the map is to be shared with other users.