WFM 6202: Remote Sensing and GIS in Water Management Geographic Information System (GIS) Lecture 5 Coordinate System and Map Projection Dr. A.K.M. Saiful Islam Institute of Water and Flood Management (IWFM) Bangladesh University of Engineering and Technology (BUET) January, 2016

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).

Plane Orthogonal Cartesian Coordinates

Polar coordinates

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).

Lat / Long Coordinate System Latitude GPS for Ologists Summer 2005 Lat / Long Coordinate System Latitude Parallels of latitude 0° latitude north latitude south 90°N equator National Park Service - Pacific Islands GIS Field Technical Support Center

Lat / Long Coordinate System Longitude Grenwich, England West Longitude Meridians of longitude 0° longitude Prime Meridian East longitude

Coordinates Lat/long system measures angles on spherical surfaces 60º east of PM 55º north of equator

The earth is a spheroid The best model of the earth is a globe

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).

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 ]

Maps are flat easy to carry good for measurement scaleable

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  

Projection property 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. The property of conformality is important in maps which are used for analyzing, guiding, or recording motion, as in navigation. 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. The property of equivalence is important in maps which are used for comparing density and distribution data, as in populations. 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 ]

1. Equal Angle Projection

2. Equal Area Projection

3. Equidistance Projection

Map Projection: Plane as developable surface

Perspective Projection Perspective projections are classified based on the projection center or viewpoint.

Conical Projection Conical projections are classified by the aspect as well as the cone size

Conic projection Conic (tangent) Conic (secant)

Lambert Coniformal Conic (LCC) Projection Projection: Lambert Conformal Conic False Easting: 2743185.699 Meters False Northing: 914395.233 Meters Central Meridian: 90.0 (DD) First Standard Parallel: 23.15 (DD) Second Standard Parallel: 28.80 (DD) Latitude of Origin: 26.00 (DD) Linear Unit: Meter Datum: Everest_1830 or D_Everest_Bangladesh Spheroid: Everest_1830 or Everest_Adj_1937

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).

an imaginary light is “projected” onto a “developable surface” a variety of different projection models exist

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.

Coordinate systems Universal Transverse Mercator (UTM) Based on the Transverse Mercator projection 60 zones (each 6° wide) false eastings Y-0 set at south pole or equator Exclude North poles (< 80 °)

UTM Zone Numbers GPS for Ologists Summer 2005 Seque, Because both lat/long and UTM have their axis at an abstract location in space, both are relative to the shape of the Earth, which is represented in a datum. In mapping, datums represent the point or line of reference that is used as a starting location for measurement. As our understanding of the shape of the Earth has changed, the frame of reference (i.e. datum) for mapping has changed, and the “starting point” from which we measure has changed as well. National Park Service - Pacific Islands GIS Field Technical Support Center

Bangladesh Transverse Mercator (BTM) projection Bangladesh falls into two different UTM zones (45N and 46N). To overcome this issue, Flood Action Plan (FAP 19) introduced a new projection system as BTM in 1992. Projection: Transverse Mercator False Easting: 500000.0 False Northing: -2000000.0 Central Meridian: 90.0 Scale Factor: 0.9996 Latitude of Origin: 0.0 Linear Unit: Meter Datum: Everest_1830 or D_Everest_Bangladesh or D_Gulshan_303 Spheroid: Everest_1830 or Everest_Adj_1937

False Easting and False Northing

Scale Factor

“Shape” of the Earth (e.g., GRS-80, WGS-84) Best-fit ellipsoid GPS for Ologists “Shape” of the Earth Summer 2005 Best-fit ellipsoid (e.g., GRS-80, WGS-84) The Figure of the earth: The globe is kinda squished, Its lumpy and irregular in shape but we have to assign something simple to define this squished shape. We call this an ellipsoid. Both LAT/Long and UTM are relative to the shape of the Earth, which is represented by a datum. National Park Service - Pacific Islands GIS Field Technical Support Center

Datums A system that allows us to place a coordinate system on the earth’s surface A reference datum is a known and constant surface which can be used to describe the location of unknown points. On Earth, the normal reference datum is sea level. On other planets, such as the Moon or Mars, the datum is the average radius of the planet.

Datum and Ellipsoids Datum - represented by ellipsoid Reference ellipsoid examples: Clarke 1866 GRS 80 WGS 84 Common geographical datum: North American Datum of 1927 (NAD27) NAD83 World Geodetic System of 1984 (WGS84)

NAD27: Clarke 1866 ellipsoid origin in Kansas GPS for Ologists NAD27: Clarke 1866 ellipsoid origin in Kansas Summer 2005 Datum Origin on Surface of Earth As I see it, NAD27’s biggest problem is that the datum origin is on the surface of the earth and it’s second biggest problem is that the Clark 1866 ellipsoid just doesn’t work as you leave the vicinity of Meades Ranch. Be careful, the diagram looks like you’re saying NAD27 is ECEF. Ellipsoid Model based on less precise surveys National Park Service - Pacific Islands GIS Field Technical Support Center

GPS Datum: WGS 84 Origin is at the Earth’s center of mass (geocentric) GPS for Ologists Summer 2005 GPS Datum: WGS 84 Origin is at the Earth’s center of mass (geocentric) This is the datum used for the NAVSTAR GPS satellites National Park Service - Pacific Islands GIS Field Technical Support Center

WGS84: WGS84 ellipsoid origin center of earth GPS for Ologists Summer 2005 WGS84: WGS84 ellipsoid origin center of earth The origins of the WGS84 and NAD83 ellipsoids are at the center of the earth’s mass, which makes them ideal for a GPS datum National Park Service - Pacific Islands GIS Field Technical Support Center

Datum Adjustments Known as Datum Adjustments or Epochs GPS for Ologists Summer 2005 Datum Adjustments Known as Datum Adjustments or Epochs WGS84 (G1150) – most current version “Original” NAD83 = NAD83 (1986) NAD83 (1992) NAD83 (2002) …… Most Current NAD83 NAD83 (CORS96) (Epoch 2003.00) Just when you thought all you had to learn was a Datum name like WGS84… It’s a bit more complicated. As a datum is more precicesly defined or datums become adjusted over time as we learn more about the center of the earths mass. Satellite, gravity measurements all enhance the level of precision that we can measure things. Datums therefore are adjusted or realized using the term epochs. These datum reference frames are noted by a year (1986) or (1992). Whats happened is that the most current realization of NAD83 and WGS84 differ by up to a meter. Errors can be introduced into a map by assuming these are the same National Park Service - Pacific Islands GIS Field Technical Support Center

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: to transform different map projections of many GIS data sources to an unified map projection in a GIS database, to adjust errors which occur at map digitization due to shrinkage or distortion of the map measured, and to produce geo-coded image by so called geometric correction of remote sensing imagery with geometric errors and   distortions

Map projections always introduce error and distortion

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.

Major Transformation Helmert Transformation Affine Transformation scale, rotation and shift Affine Transformation skew, scale of x and y,and shift Pseudo Affine Transformation bi-linear distortion Quadratic Transformation parabolic distortion Perspective Projection rectification of aerial photo Cubic Transformation cubic and distortion)

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|

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 Mahalanobis distance D is a normalized distance in the normal distribution from the center (X0) 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

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.

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.

Relationship between scale, accuracy and resolution