Thinking Spatially with Maps DeMers: Chapter 3

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Thinking Spatially with Maps DeMers Chapter 3

• The map is the fundamental device by which we
  abstract our environments space, and within
  which the GIS will operate to analyze it.

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Overview

• Maps
• Shift in Cartography
• Scales
• Projections
• Grid systems for mapping
• The cartographic process
• Symbols
• Some problems related to specific thematic maps

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Important considerations

• The cartographic method
• How do we depict spatial features and their
  relationships?
• How do we portray a 3D world in 2D?

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Maps

• Maps are a graphic form of spatial data
• Map as Model The Abstraction of Reality a map
  is an abstraction of reality not meant to show
  every detail implies selective inclusion/exclusion
  of objects and phenomena (as well as their
  attributes)
• Types
• Reference
• Thematic

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3. Shift in Cartography

• Communication paradigm
• Assumed that the map itself was a final product
  designed to communicate spatial pattern through
  the use of symbols, class limit selection, and so
  on. E.g. Tourism maps
• Map is end result and the user is incapable of
  regrouping the data into forms more useful
• Analytical (holistic) paradigm
• Maintains the raw attribute data inside a
  computer storage and displays data based on user
  needs and classification
• The map allow for both communication and analysis

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Fig. 3.1 - State Park
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4. Illustrating scale

• Scale The ratio of distance on the map to the
  same distance as it appears on the earth

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Effect of scale on accuracy
The rule of thumb It is always better to reduce
a map after analysis than to enlarge it for
analysis
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5. Map Projections

• 3D Earth -gt -gt 2D surface?
• Families of projections
• Distortions (shape, distance, direction, area)

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Definition

• Map projections are attempts to portray the
  surface of the earth or a portion of the earth on
  a flat surface. Some distortions of conformality,
  distance, direction, scale, and area always
  result from this process.
• Some projections minimize distortions in some of
  these properties at the expense of maximizing
  errors in others. Some projection are attempts to
  only moderately distort all of these properties

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Classes of map projections

• CylindricalResult from projecting a spherical
  surface onto a cylinder.When the cylinder is
  tangent to the sphere contact is along a great
  circle (by a plane passing through the center of
  the Earth).
• Conic Result from projecting a spherical surface
  onto a cone. When the cone is tangent to the
  sphere contact is along a small circle.
• Azimuthal Result from projecting a spherical
  surface onto a plane.When the plane is tangent to
  the sphere contact is at a single point on the
  surface of the Earth.

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Classes of map projections-continue

• Miscellaneous projections Include unprojected
  ones such as rectangular latitude and longitude
  grids and other examples of that do not fall into
  the cylindrical, conic, or azimuthal categories

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Historically - light source projected features on
a transparent globe
Three families of map projections (a) Flat
surfaces (b) Cylinders (c) Cones
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Distortions

• When projecting from 3D sphere to 2D globe, there
  will be some distortions in shape, distance,
  direction, area
• Conformal or orthomorphic map projection When
  the scale of a map at any point on the map is the
  same in any direction, the projection is
  conformal. Meridians (lines of longitude) and
  parallels (lines of latitude) intersect at right
  angles. Shape is preserved locally on conformal
  maps.
• It retains the property of angular conformity,
  but results in distortion of areas

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Distortions-continue

• Equal area or equivalent projections Preserves
  areas, but distorted angles, i.e. areas and
  angles cannot be preserved at the same time
• Equidistant projections Preserves distance along
  standard parallels or from one or two points
• Azimuthal projection A map preserves direction
  when azimuths (angles from a point on a line to
  another point) are portrayed correctly in all
  directions (navigation)

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No flat map can be both equivalent and
conformal.
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Selection of a projection

• The first step in choosing a projection is to
  determine Location, Size, and Shape
• These three things determine where the area to be
  mapped falls in relation to the distortion
  pattern of any projection. One "traditional" rule
  says
• A country in the tropics asks for a cylindrical
  projection.
• A country in the temperate zone asks for a
  conical projection.
• A polar area asks for an azimuthal projection.

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Selection of a projection-continue

• Implicit in these rules of thumb is the fact that
  these global zones map into the areas in each
  projection where distortion is lowest
• Cylindricals are true at the equator and
  distortion increases toward the poles.
• Conics are true along some parallel somewhere
  between the equator and a pole and distortion
  increases away from this standard.
• Azimuthals are true only at their center point,
  but generally distortion is worst at the edge of
  the map.

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6. Grid systems for mapping

• Need a grid (coordinate system) for distance and
  direction on the earth.
• Also need grid system that take into account the
  distortions introduced by projecting world onto
  2D map.
• Rectangular coordinates (plane coordinates)
• Basic Cartesian coordinate system (x,y)
• Plane coordinate system are used to represent
  large areas and not small scale maps. For small
  scale maps, adjustment must be made to compensate
  for the distortions.
• The Universal Transverse Mercator (UTM) is the
  most prevalent plane grid system used in GIS
  operations

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A cartesian coordinate system (X,Y) (N,E)
Digitizers are based on cartesian coordinate
system
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The Universal Transverse Mercator (UTM)

• UTM system is used to define horizontal,
  positions world-wide by dividing the surface of
  the Earth into 6 degree zones, each mapped by the
  Transverse Mercator projection with a central
  meridian in the center of the zone. UTM zone
  numbers designate 6 degree longitudinal strips
  extending (60 zones) from 80 degrees South
  latitude to 84 degrees North latitude. The zones
  numbering starts at 180th meridian in east ward
  direction
• Eastings are measured from the central meridian
  (with a 500km false easting to insure positive
  coordinates). Northings are measured from the
  equator (with a 10,000km false northing for
  positions south of the equator).

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UTM principles
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The cartographic process

• The main four general steps in cartographic
  process are
• Data collection Field survey
• Data compilation Development of base map
• Map production Output of a map with all features
• Map reproduction Quantitative production at
  different scales (Magnification, reduction)
• Although the analytical or holistic paradigm may
  not follow the same steps, the process is almost
  similar

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Map symbolism

• Geographic objects (point, line, area, surface)
  are represented by symbols on the map
• Symbol geometry and dimensionality are sometimes
  not a true representation of an object, but are
  often manipulated to achieve a particular visual
  response (e.g. area symbol represent a point
  feature)
• A major difference between communication and
  holistic paradigms is the classification-oriented
  manipulation of data prior to map production
  (Class interval selection-see Chap9)

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Class interval selection methods

• Constant interval Same number of areas/data in
  each category/class (contour interval)
• Variable intervals Isolating certain high or
  low values, for highlighting variations in value
  (Creating a discrete set of point symbols to show
  variation in attribute variable)
• Considerations must be paid, during the input to
  GIS, to symbols, method of classification, and
  graphic simplification (if road, river, and
  railway are very near, they can be displaced from
  their original location to improve visualization)
  (feature elimination (filtering) and
  smoothingrivers-roads)

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Map abstraction and cartographic database

• Cartographic database are collected from existing
  cartographic documents, which may include some
  filtering and smoothing of spatial feature,
  therefore the GIS input will not be accurate
• Geographic database are collected from field
  (surveying, GPS) or remotely sensed data, which
  are more accurate and sometimes the GIS input
  device (scanner, digitizer) may not give the same
  accuracy
• Incompatibility between maps generated from
  different sources or scale may arise in GIS
• The scale of input for a cartographic database
  should be as nearly identical as possible

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Some problems related to specific thematic maps

• Soil maps Provide information for agricultural
  activities. Problems associated with soil maps
  are method of sampling using aerial photographs
  (distortion, relief, projection- Orthophotomaps)
• Zoological maps Provide information about animal
  locations (point or area). Problems associated
  with these maps is the movement of animal,
  therefore time domain must be encounter
• Remote sensing imageryGeometry and manipulation
  (resolution,enhancement,classification)
• Vegetation maps Sampling and classifications
• Historical maps Use for spatiotemporal analysis,
  different tools for data collection and
  classification,

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Questions

• 1. What is the difference between communication
  and holistic paradigms in cartography
• 2. How scale is illustrated on a map and the
  potential problems in analyses when scale is
  changed.
• 3. Briefly discuss the classes of map
  projections.
• 4. What basic properties of the spherical earth
  are affected by using map projection?
• 5. What are the factors that considered in
  selection of a projection

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References

• Anson, R. W., 1996. Basic Cartography for
  Students and Technician. Butterwork.
• Clarke, K. C., 1990. Analytical and Computer
  Cartography, Prentice Hall, New York.
• Maling, D.H. 1992. Co-ordinate Systems and Map
  Projections, 2nd Ed. Pergamon Press. Oxford.
• Muehrcke, Phillip C. 1986. Map use Reading,
  Analysis, Interpretation. Madison, WI JP
  Publications.
• Robinson, A. H., J. L. Morrison, P. C. Muehrcke,
  A. Jon Kimerling, and S. C. Guptil, 1995.
  Elements of Cartography, 6th ed., John Wiley
  Sons, Inc., New York. (Very Important Reference).
• Snyder, John P. 1987. Map Projections a working
  Manual. USGS Professional Paper 1395. Washington,
  DC United States Government Printing Office.