WFM 6202: Remote Sensing and GIS in Water Management

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WFM 6202 Remote Sensing and GIS in Water
Management
Part-B Geographic Information System (GIS)
Lecture-5 Coordinate System and Map Projection

• Akm Saiful Islam

Institute of Water and Flood Management
(IWFM) Bangladesh University of Engineering and
Technology (BUET)
December, 2009
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Coordinate Systems

• Geospatial data should be geographically
  referenced ( called georeferenced or geocoded) in
  a common coordinate system.
• Plane Orthogonal CoordinatesOne of the most
  convenient way of locating points is to use plane
  orthogonal coordinates with x (horizontal) and y
  (vertical) axis.
• Polar CoordinatesA 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 CoordinatesThree dimensional (3D)
  orthogonal coordinates are also used to locate
  points with the plane coordinates (x, y) and
  height or depth (z).

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Plane Orthogonal Cartesian Coordinates
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Polar coordinates
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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).

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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).

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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/handou
ts/geodeticgeocentric.doc
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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

?
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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/co
urses/FOR503/Part4.htm
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Perspective Projection

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

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Conical Projection

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

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Conic projection
Conic (tangent)
Conic (secant)
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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).

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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.

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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

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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.

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Major Transformation

• Helmert 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)

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Distance

• Distance is one of the important elements in
  measuring spatial objects in GIS. Several
  different concepts of distance are defined as
  follows.
• Euclidean DistanceEuclidean 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 DistanceManhattan distance D is
  defined as the rectilinear rout measured along
  parallels to X and Y axes
• D x1 - x2 y1-y2

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Distances (Contd..)

• Great Circle DistanceGreat 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

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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.

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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.

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Relationship between scale, accuracy and
resolution