1. 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.
Chapter 3: The map as a model of geographic data

2. Overview Maps Shift in Cartography Scales Projections
Grid systems for mapping
The cartographic process
Symbols
Some problems related to specific thematic maps
1. Introduction
The map is the fundamental language of geography - and therefore of automated geography
A graphic form of spatial data abstraction composed of different:
Grid systems
Projections
Symbols
Scales

3. Important considerations:
The cartographic method
How do we depict spatial features and their relationships?
How do we portray a 3D world in 2D?
Important considerations:
1. Need to understand the cartographic method and its implications for correct analysis and interpretation
How do we depict spatial features and their relationships?
Scale
Entities and attributes
How do we portray a 3D world in 2D?
Families of projections
Grid systems - advantages/disadvantages in GIS

4. 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
2. Maps as abstractions of reality
Maps model spatial phenomena, they're not a miniature version of reality - doesn't show every detail
Types:
1. Reference - example: road map of California
2. Thematic - primary form used in GIS - shows distribution

5. 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
The way maps are viewed and used has changed in the past few decades with the computer revolution
Also the way we deal with spatial data in general has changed
Communication paradigm - In the olden days the map was the end result - designed to communicate a spatial pattern through symbols - no raw data for user
Analytical (holistic) paradigm (Tobler, 1959) - raw data maintained for later reclassification - user defined - idea is that a map should allow for both communication and analysis

6. Fig. 3.1 - State Park Fig. 3.1 - State Park example
Figure shows identical area being used for different purposes:
3.1a: communication paradigm creates visual display of spatial relationships for tourists
3.1b: analytical paradigm for rangers to manage the area - need quantitative information about the region - each theme or layer would have different information (veg. type, amt. of dead brush, range of species)

7. 4. Illustrating scale
Scale: The ratio of distance on the map to the same distance as it appears on the earth
4. Scale (fig. 3.2)
We need to remember that maps are a reduction of reality
Scale is the amount of reduction found on a map
It is the ratio of distance on the map to the distance on earth
Verbal scale - could be different units
RF - same units
Graphic scale

8. 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
GIS software can change scale easily - the scale you use for input may differ from the scale you use for display
BEWARE - quality of analysis is affected by scale at which data was inputted originally - Fig. 3.3
Small scale - 1:100,000 (1 mm on map = 100,000 mm on ground)
Large scale - 1:24,000 (1 mm on map = 24,000 mm on ground)
Largest scale map - 1:1 (1 unit on map = 1 unit on ground)
Effect of scale on accuracy - going from small scale to large scale - lines thicker, areas less precise -
Measurement and analysis difficult
General rule of thumb - its better to reduce a map after analysis than to enlarge it for analysis

9. 5. Map Projections 3D Earth -> -> 2D surface?
Families of projections
Distortions (shape, distance, direction, area)
How do we represent a 3D world on a 2D map???
Example: Peel an orange
Need map projections
Distortions - 1. angles or shape, 2. distance, 3. direction and 4. areal size
Conformal Projection (angular conformity) - Retains the property of angular correspondence (N and E are at 90 deg) - distorts area, preserves angles (shapes) - To preserve direction also want conformal
Equal area -preserves area - exmapleAlbers equal area or Lambert’s equal area.
Choosing a projection-depends on the intended use of the map
Equal area vs. True shape
True direction vs. true distance

10. 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

11. 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.

12. 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

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

15. 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

16. 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)

17. “No flat map can be both equivalent and conformal.”

19. 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.

20. 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.

21. 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
6. Grid systems for mapping
We have seen that we need a grid or coordinate system for distance and direction on the earth (chap. 2)
This coordinate system based on lat. and long. Is very useful for locating objects on a sphere.
But we are using 2D maps that are projected from the 3D sphere.
So we need one more coordinate system(s) that correspond to the distortions we just introduced.
Plane coordinates are not used on small scale maps due to the potential for distortion (example: a map of the entire United States).

22. A cartesian coordinate system (X,Y) (N,E)
This is the basic cartesian coordinate system that we all learned.
X and y axis with a 0, 0 origin.
By tradition, when reading maps using a rectangular coordinate system:
the x value is called the easting and they value is the northing.
Most rectangular (plane ) soordinate systems attempt to adjust for conformality by using only conformal projections. (examples, Transverse Mercator, Lamberts’ conformal conic)
Digitizers are based on cartesian coordinate system

23. 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).

25. UTM principles Each zone is 84N - 80 S and 6 degrees wide.
CA is in zones 10 and 11.
Has 2 primary ordinates - equator and 80S
Each zone is divided into rows of 8 degrees latitude
Can get measurements of up to 1 m in accuracy

26. 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

27. 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)

28. 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)

29. 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

30. 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,

31. 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

32. References
Anson, R. W., Basic Cartography for Students and Technician. Butterwork.
Clarke, K. C., Analytical and Computer Cartography, Prentice Hall, New York.
Maling, D.H Co-ordinate Systems and Map Projections, 2nd Ed. Pergamon Press. Oxford.
Muehrcke, Phillip C 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, Elements of Cartography, 6th ed., John Wiley & Sons, Inc., New York. (Very Important Reference).
Snyder, John P Map Projections: a working Manual. USGS Professional Paper Washington, DC: United States Government Printing Office.