Transcript GIS and Remote Sensing in Water Resources Management

WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful Islam
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
WFM 6202: Remote Sensing and GIS in Water Management © Dr. 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).
WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful Islam
Plane Orthogonal Cartesian
Coordinates
WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful Islam
Polar coordinates
WFM 6202: Remote Sensing and GIS in Water Management © Dr. 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).
WFM 6202: Remote Sensing and GIS in Water Management © Dr. 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).
WFM 6202: Remote Sensing and GIS in Water Management © Dr. 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 ]
WFM 6202: Remote Sensing and GIS in Water Management © Dr. 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
WFM 6202: Remote Sensing and GIS in Water Management © Dr. 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.
– 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.
– 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 ]
WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful Islam
Perspective Projection
• Perspective projections are classified based on the
projection center or viewpoint.
WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful Islam
Conical Projection
• Conical projections are classified by the aspect as well
as the cone size
WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful Islam
Conic projection
Conic (tangent)
Conic (secant)
WFM 6202: Remote Sensing and GIS in Water Management © Dr. 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).
WFM 6202: Remote Sensing and GIS in Water Management © Dr. 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.
WFM 6202: Remote Sensing and GIS in Water Management © Dr. 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
WFM 6202: Remote Sensing and GIS in Water Management © Dr. 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.
WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful Islam
Major Transformation
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)
WFM 6202: Remote Sensing and GIS in Water Management © Dr. 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|
•
WFM 6202: Remote Sensing and GIS in Water Management © Dr. 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
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
WFM 6202: Remote Sensing and GIS in Water Management © Dr. 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.
WFM 6202: Remote Sensing and GIS in Water Management © Dr. 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.
WFM 6202: Remote Sensing and GIS in Water Management © Dr. Akm Saiful Islam
Relationship between scale, accuracy and
resolution