1. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam WFM 6202: Remote Sensing and GIS in Water Management Akm Saiful Islam Institute of Water and Flood Management (IWFM) Bangladesh University of Engineering and Technology (BUET) [Part-B: Geographic Information System (GIS)] Lecture-5: Coordinate System and Map Projection December, 2009

2. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Coordinate Systems Geospatial data should be geographically referenced ( called georeferenced or geocoded) in a common coordinate system.  Plane Orthogonal Coordinates One of the most convenient way of locating points is to use plane orthogonal coordinates with x (horizontal) and y (vertical) axis.  Polar Coordinates A polar coordinate system with the angle (q ) measured from the polar axis (x axis) and distance (r) from the pole is used in some cases.  3D Orthogonal Coordinates Three dimensional (3D) orthogonal coordinates are also used to locate points with the plane coordinates (x, y) and height or depth (z).

3. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Plane Orthogonal Cartesian Coordinates

4. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Polar coordinates

5. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam 3D Coordinate System In case of locating points on the Earth on the assumption of a sphere, latitude (  ), the angle measured between the equatorial plane and the point along the meridian and longitude ( ), the angle measured on the equatorial plane between the meridian of the point and the Greenwich meridian (or called the central meridian) are used as shown in Figure 1.3 (c). Longitude has values ranging from 0° ( Greenwich, U.K. ) to + 180° (eastly) and from 0° to -180° (westly).Figure 1.3 (c)

6. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam The Shape of the Earth The shape of the Earth can be represented by an ellipsoid of rotation (or called a spheroid) with the lengths of the major semi-axis (a) and the minor semi-axis (b).

7. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Geodetic and Geocentric Latitude Geocentric Latitude – The acute angle measured perpendicular to the equatorial plane and a line joining the center of the earth and a point on the surface of the reference ellipsoid. Geodetic Latitude – The acute angle between the equator and a line drawn perpendicular to the tangent of the reference ellipsoid. Map coordinates are given as longitude and geodetic latitude. [Source : http://ccar.colorado.edu/ASEN5070/handouts/geodeticgeocentric.doc ]http://ccar.colorado.edu/ASEN5070/handouts/geodeticgeocentric.doc

8. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Map Projection A map projection is a process of transforming location on the curved surface of the Earth with the geodetic coordinates (, ) to planar map coordinates (x, y). More than 400 difference map projections have been proposed. The map projections are classified by the following parameters. –projection plane: perspective, conical, cylindrical –aspect: normal, transverse, oblique –property: conformality, equivalence, equidistance –size: inside, tangent, secant 

9. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Projection property 1.Conformality is the characteristic of true shape, wherein a projection preserves the shape of any small geographical area. This is accomplished by exact transformation of angles around points. navigation –The property of conformality is important in maps which are used for analyzing, guiding, or recording motion, as in navigation. 2.Equivalence is the characteristic of equal area. Preservation of equivalence involves an inexact transformation of angles around points and thus, is mutually exclusive with conformality except along one or two selected lines. populations –The property of equivalence is important in maps which are used for comparing density and distribution data, as in populations. 3.Equidistance is the characteristic of true distance measuring. The scale of distance is constant over the entire map. –Equidistance is important in maps which are used for analyzing velocity, e.g. ocean currents. Typically, reference lines such as the equator or a meridian are chosen to have equidistance and are termed standard parallels or standard meridians. [ Source: http://www.forestry.umt.edu/academics/courses/FOR503/Part4.htm ]http://www.forestry.umt.edu/academics/courses/FOR503/Part4.htm

10. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Perspective Projection Perspective projections are classified based on the projection center or viewpoint.

11. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Conical Projection Conical projections are classified by the aspect as well as the cone size

12. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Conic projection Conic (tangent) Conic (secant)

13. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Cylindrical Projections Cylindrical projections are classified as in case of conical projections. One of the most popular cylindrical projections is the Universal Transverse Mercator (UTM) with a transverse axis, secant cylinder and conformality (equal angle).

14. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam UTM Projection Universal Transverse Mercator (UTM) with a transverse axis, secant cylinder and conformality (equal angle). UTM is commonly used for topographic maps of the world, devided into 60 zones with a width of 6 degree longitude.

15. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Coordinate Transformation Coordinate transformation is to transform a coordinate system (x, y) to another coordinate system (u, v). The transformation is needed in the following cases: 1.to transform different map projections of many GIS data sources to an unified map projection in a GIS database, 2.to adjust errors which occur at map digitization due to shrinkage or distortion of the map measured, and 3.to produce geo-coded image by so called geometric correction of remote sensing imagery with geometric errors and distortions

16. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Reference for Coordinate Transformation Coordinate transformation is executed by a selected transformation model (or mathematical equation), with a set of reference points (or control points), that are selected as tic masks at the corner points, rescau or ground control points.

17. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam a)Helmert Transformation scale, rotation and shift b)Affine Transformation skew, scale of x and y,and shift c)Pseudo Affine Transformation bi-linear distortion d)Quadratic Transformation parabolic distortion e)Perspective Projection rectification of aerial photo f)Cubic Transformation cubic and distortion) Major Transformation

18. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Distance Distance is one of the important elements in measuring spatial objects in GIS. Several different concepts of distance are defined as follows. Euclidean Distance Euclidean distance D is the defined as the distance measured along a straight line from point (x1, y1 ) to point (x2, y2 ) in Cartesian coordinate system. D2 = ( x1 - x2 ) 2 + ( y1- y2 ) 2 Manhattan Distance Manhattan distance D is defined as the rectilinear rout measured along parallels to X and Y axes D = | x1 - x2| + | y1-y2|

19. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Distances (Contd..) Great Circle Distance Great circle distance D is defined as distance along the great circle of the spherical Earth surface from a point (  1, 1; latitude and longitude) to another point (  2, 2) where R is the radius of the Earth (R = 6370.3 km) on the assumption that the Earth is a sphere. Mahalanobis Distance X 0 Mahalanobis distance D is a normalized distance in the normal distribution from the center (X 0 ) to a point (X) in case of n dimensional normal distribution. Mahalanobis distance is used in the maximum likelihood method for the classification of multi-spectral satellite images. where S: variance-covariance matrix

20. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Distances (Contd..) Time Distance Time distance is defined as the time required to move from point B to point A by using specific transportation means.

21. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Scale, Accuracy and Resolution Scale of map refers to the ratio of distance on a map over the corresponding distance on the ground. The scale is represented as 1: M or 1/M, where M is called the scale denominator. The larger the scale, the more the detail described by the map and with higher accuracy. Accuracy is generally represented by standard deviation of errors, that is difference between measurements and the true value.

22. WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful IslamDr. Akm Saiful Islam Relationship between scale, accuracy and resolution