Thinking Spatially with Maps
DeMers: Chapter 3
The map is the fundamental device
by which we abstract our
environment’s space, and within
which the GIS will operate to analyze
it.
Overview
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Maps
Shift in Cartography
Scales
Projections
Grid systems for mapping
The cartographic process
Symbols
Some problems related to specific thematic
maps
Important considerations:
• The cartographic method
– How do we depict spatial features and their
relationships?
– How do we portray a 3D world in 2D?
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
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
Fig. 3.1 - State Park
4. Illustrating scale
• Scale: The ratio of distance on the map to the
same distance as it appears on the earth
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
5. Map Projections
• 3D Earth -> -> 2D surface?
• Families of projections
• Distortions (shape, distance, direction,
area)
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
Classes of map projections
 Cylindrical:Result 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.
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
Historically - light source projected
features on a transparent globe
Three families of map projections
(a) Flat surfaces (b) Cylinders (c) Cones
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
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)
“No flat map can be both equivalent and conformal.”
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.
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.
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
A cartesian coordinate system (X,Y) (N,E)
Digitizers are based on cartesian coordinate system
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).
UTM principles
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
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 classificationoriented manipulation of data prior to map
production (Class interval selection-see Chap9)
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 smoothing:rivers-roads)
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
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 imagery:Geometry and
manipulation (resolution,enhancement,classification)
• Vegetation maps: Sampling and classifications
• Historical maps: Use for spatiotemporal analysis,
different tools for data collection and classification,
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
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.