Thursday, July 16, 2015

Characteristics of maps and map projections

Characteristics of maps:
  1. Maps are always concerned with TWO elements of reality:
        1. Location (spatial data) and 
        2. Attributes (aspatial or non-spatial data)
  2. Maps are reductions of true surfaces. They are two dimensional representations of the earths surface drawn to scale.
  3. Maps are usually outdated representations
  4. Maps are ALWAYS STATIC VERSIONS
  5. Maps cannot be updated. Updation requires preparation of a new map.
A map is a traditional method for storing, analysing and presenting spatial data

Topology is based on the geometric relationship of objects in a map

The purpose of a map is to turn data into information that will be communicated to the user.

Scale is defined as the ratio of a distance on the map to the corresponding distance on the ground. The units for distance should be the same.

THREE BASIC SYMBOL TYPES used are point, line and areas. They are used to represent real world features. The method used to represent a spatial feature DEPENDS ON THE SCALE USED

The relationship between scale and detail is called SCALE RELATED GENERALIZATION.

PROJECTION
-The Earth appears flat at close range
-The Earth is roughly SPHERICAL (as displayed in satellite images)
-Cartographers developed a set of techniques called "MAP PROJECTIONS" to depict the spherical earth in two dimensions with reasonable accuracy.

Imagine a football (inflated) with the image of the Earth on it = 3D representation of Earth
Now deflate the football = 2D representation of Earth

Projection is the process of placing a light bulb in transparent globe on which OPAQUE Earth features are placed and projecting the feature outlines on a 2D surdace surrounding the globe. The globe could be projected on:
-a flat piece of paper
-surrounding the globe in a cylindrical fashion or
-surrounding the globe in a cone

Each of the above three projections form a projection family called:
-Planar projection
-Cylindrical projection
-Conical projection and
-Azimuthal projection

-Projections are not absolute accurate representations of geographical space. The characteristic of maps that must be retained for accurate analytical operations dictate which projections must be used.

-IT IS IMPOSSIBLE TO PRESERVE ALL PROPERTIES AT THE SAME TIME WHEN PERFORMING A MAP PROJECTION.

When performing a map projection, selection of a map projection will be based on what property needs to be preserved. The properties that need to be considered are:
-angles
-shapes
-distances
-directions and
-areal sizes

Angular conformity / Conformal / Orthomorphic projection MAINTAINS correct angular correspondence. This leads to:
-Distortion of areas
-Incorrect measurement

-Equal area / Equivalent projections preserve areas

-Equidistant projections preserve distances

There is NO IDEAL MAP PROJECTION

A map projection can be defined as representation of meridians and parallels portraying the curved surface of the datum surface on a two dimensional plane.
The two surfaces should have a one to one correspondence with each other.
Origin is generally chosen as the intersection of CENTRAL MERIDIAN with CENTRAL PARALLEL.
  1. Map projections transfer the spherical earth onto a two dimensional surface thereby approximating the true shape of the earth. This introduces errors into spatial data.
  2. A projection is a method by which the curved surface of the earth is represented on a flat surface by using mathematical transformations between location of places on earth and their projected locations on the plane.
  3. When curved surface of the earth is shown on a plane, DISTORTION IS INEVITABLE
  4. Distortion is LEAST when the map shows SMALL AREAS and MAXIMUM when the map shows ENTIRE SURFACE OF THE EARTH.
Projections are broadly classified into:
  1. EQUAL AREA PROJECTIONS (display correct area)
  2. CONFORMAL PROJECTIONS (display correct shape/directions) and
  3. EQUIDISTANT PROJECTIONS (display correct distance)
Equal Area Projections (EAP) are used for estimating resource, forest coverage, etc in a region.
Conformal Projections (CP) are used in navigation purposes requiring accurate directions.
CP are also called orthomorphic projections
Ex: Lambert Conformal Conic and Transverse Mercator
Universal Transverse Mercator (UTM) is a special case of transverse mercator

Examples of Non-Conformal Projections are:
  1. Polyconic
  2. Cassini
  3. Alberts Equal area, etc
Important projections for mapping in India:
  1. Polyconic projection
  2. Lambert Conformal Conic projection
  3. Transverse mercator projection
  4. Universal Transverse Mercator projection and
  5. Cassini projection
All geographic surfaces are in TWO tangible formats:
-Discrete: They occupy a given point in space and time (Trees, Houses, etc)
They have zero dimensionality BUT some spatial dimension

-Continuous: They possess infinite number of possible height values distributed without interruption across the surface (Cliff,trenches, ridges, hills, etc)
They are described by:
-Citing their locations
-The area occupied by the feature and
-Their orientation with the addition of the third dimension

-Topographic map shows BOTH DISCRETE and CONTINUOUS information

-Elevation is shown as a series of contour lines

-Man-made features are shown by a lines and shapes

-Different kinds of information that is stored in various ways is called THEME

-DATUM PLANE is the reference surface from which all altitudes are measured. Usually, Datum plane = Mean Sea Level (MSL)

-ELEVATION or ALTITUDE is the vertical distance between GIVEN POINT and DATUM PLANE.

-Height is defined as the vertical difference between an object and its surroundings.

-Difference in elevation of an area between tops of hills and bottoms of valleys is known as relief of the terrain.

-A point of known elevation and position is indicated on a map by the letters B.M (Bench Mark) with the altitude given to the nearest foot.

-A map line connecting points representing places on the Earth's surface that have the same elevation is called CONTOUR LINE.

-Contours represent the THIRD DIMENSION on a map

-The difference in elevation represented by adjacent contours is called CONTOUR INTERVAL.

-Maps are an important for of input to a GIS and a common means to portray the results of analysis from a GIS

-The TWO FUNDAMENTAL ASPECTS OF REALITY that maps and GIS are connected with:
-LOCATIONS and
-ATTRIBUTES
using these, several TOPOLOGICAL and METRIC properties of a relationship can be defined. Eg:
-Distance
-Direction
-Connectivity
-Proximity, etc

SYMBOLOGY:
-Artificial works shown in BLACK
-Water features (streams, swamps and glaciers) shown in BLUE
-Relief shown by contours in BROWN
-Major highways shown in RED
-Areas of woods, orchards, vineyards and scrub shown in GREEN.

-SRS SPATIAL REFERENCING SYSTEM
-GCS GEOGRAPHIC COORDINATE SYSTEM
-RCS RECTANGULAR COORDINATE SYSTEM
-NCS NON-COORDINATE SYSTEM
-SGS SPHERICAL GRID SYSTEM
-CRS COORDINATE REFERENCING SYSTEM

Longitudes = Meridians (Drawn pole to pole)
Longitudes start at GREENWICH (England) also called PRIME MERIDIAN 
(Numbered East to West)
Corresponding meridian on the opposite side of the globe is called: 
INTERNATIONAL DATE LINE
Latitudes lie at RIGHT ANGLES to lines of longitudes and run parallel to each other.
Latitudes = Parallels

Transformation of 3D space to 2D map distorts atleast one of the following:
-SHAPE
-AREA
-DISTANCE or
-DIRECTION

Angular conformity / Conformal / Orthomorphic projections MAINTAIN correct angular correspondence
This leads to:
-Distortion of areas
-Incorrect measurement

Equal area / Equidistant projections PRESERVE AREAS

Equidistant projections PRESERVE DISTANCES

The three projections mentioned above are MUTUALLY EXCLUSIVE

THERE IS NO IDEAL MAP PROJECTION

To transfer the image of the Earth with its irregularities on to a plane surface of a map, THREE factors are involved are:
-GEOID
-ELLIPSOID or ELLIPSOID WITH DATUM
-PROJECTION

The geographical relationships of the Earth in three dimensional form is transferred into two dimensional plane of a map by a process known as "MAP PROJECTION"

-ALL projections developed, fall into one of the following categories:
-CONIC PROJECTION
-CYLINDRICAL PROJECTION and
-PLANAR PROJECTION

-Every flat map MISREPRESENTS the Earth in some way. NO MAP CAN TRULY REPRESENT THE SURFACE OF THE ENTIRE EARTH.

A map or parts of a map can show one or more, but NEVER ALL of the following:
-True shapes
-True direction
-True distance
-True areas

A combination of any two of the above projections forms a hybrid projection

-CONIC PROJECTIONS are suited to map areas having EAST-WEST extent. Ex: USA, Canada, Peoples Republic of China

If a sheet of paper is laid tangentential to a point on the globe and the geographical features of the globe are transferred on it, the projection obtained is called, AZIMUTHAL PROJECTION. In this projection, straight lines intersect the designated center point and parallels appear as concentric circles around the center point.

ADLER has named FIVE BASIC CRITERIA for CLASSIFICATION OF MAP PROJECTIONS.
-Nature of projection surface as defined by geometry
-Contact of projection surface with DATUM surface
-Alignment of projection surface with relation to the datum surface
-Cartographic requirements and
-Mode of generation of DATUM SURFACE and coordinate system

TO MAINTAIN ACCURACY:
-The Earth is a SPHERE for small scale maps and
-The Earth is a SPHEROID for large scale maps

In an ellipsoid or sphere, the latitude and longitude are mentioned in degrees, minutes and seconds of arc.
The plane system of rectangular X and Y coordinates is referred to as EASTING and NORTHING respectively

Commonly used map projections are:
-MERCATOR
-TRANSVERSE MERCATOR
-OBLIQUE MERCATOR
-POLYCONIC PROJECTION
-LAMBERT CONICAL ORTHOMORPHIC PROJECTION
-GRID SYETEMS
-LAMBERT GRID SYSTEM FOR INDIA
-UNIVERSAL TRANSVERSE MERCATOR (UTM) GRID