3. Representing Geography

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3. Representing Geography
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Prince Henry the Navigator, 
Originator of the Age of Discovery in the Fifteenth Century, and promoter of a systematic approach to the acquisition, compilation, and dissemination of geographic knowledge.
Prince Henry the Navigator
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
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Admiral Zheng He
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Overview
Concept of representation, or the construction of a digital model of some aspect of the Earth’s surface. 
The geographic world is extremely complex, so it is necessary to make choices, about what to represent, at what level of detail, and over what time period. 
Generalization methods are used to remove detail that is unnecessary for an application, in order to reduce data volume and speed up operations.
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Learning Objectives
To understand:
The importance of understanding representation in GI databases
The concepts of fields and objects and their fundamental significance
What raster and vector representation entails and how these data structures affect many principles, techniques, and applications of GI
The paper map and its role as a product and data source
The importance of generalization methods and the concept of representational scale
The art and science of representing real-world phenomena in GIS databases
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Outline
Introduction
Digital representation
Representation of what and for whom?
The fundamental problem
Discrete objects and continuous fields
Rasters and vectors
The paper map
Generalization
Conclusion
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Schematic representation of weekend activities of three children in Cheshunt, UK. 
(Reproduced with permission of Yi Gong: base image Courtesy www.openstreetmap.org)
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Representations
Are needed to convey information
Fit information into a standard form or model
In the diagram the colored trajectories consist only of a few straight lines connecting points
If we looked closer we would reveal more information
Almost always simplify the truth that is being represented
There is no information in the representation about daily journeys to work and shop, or vacation trips out of town
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
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Digital Representation
Digital & Binary (1s and 0s)
short (16-bit) and long (32-bit) storage, ASCII, floating point numbers, and BLOBs (binary large object)
The basis of almost all modern human communication
can be handled in ways that are independent of meaning; easy to copy and transmit; stored at high density; easy to transform, process, and analyze
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
The Fundamental Problem Revisited
Geographic data are built up from atomic elements, or facts about the geographic world. 
At its most primitive, an atom of geographic data (strictly, a datum) links a place, often a time, and some descriptive property. 
The fundamental problem is “the world is infinitely complex, but computer systems are finite”.
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Spatial Resolution
Courtesy: NOAA: Liam Gumley, MODIS Atmosphere Group, University of Wisconsin-Madison
This image shows Manhattan at a spatial resolution of 250 m, detailed enough to pick out the shape of the island and Central Park
The image is from NASA’s Terra satellite showing a large plume of smoke streaming southward from the remnants of the burning World Trade Towers in downtown Manhattan on September 11, 2001. 
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Discrete Objects and Continuous Fields
In the discrete object view, the world is empty, except where it is occupied by objects with well-defined boundaries that are instances of generally recognized categories.
Objects can be counted
Objects have dimensionality: 0-dimension (points), 1-dimension (lines), 2-dimensions (areas)
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Discrete Objects and Continuous Fields
The continuous field view represents the real world as a finite number of variables, each one defined at every possible position.
Continuous fields can be distinguished by what varies, and how smoothly.
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Bears are easily conceived as discrete objects, maintaining their identity as objects through time and surrounded by empty space. 
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
(B) A simulated image derived from the Shuttle Radar Topography Mission. The image shows the Carrizo Plain area of Southern California, with a simulated sky and with land cover obtained from other satellite sources. 
(A) Image of part of the Dead Sea in the Middle East. The lightness of the image at any point measures the amount of radiation captured by the satellite’s imaging system. 
Examples of field-like phenomena 
A
B
(Courtesy NASA/JPL–Caltech)
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
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Lakes are difficult to conceptualize as discrete objects because it is often difficult to tell where a lake begins and ends, or to distinguish a wide river from a lake. 
(Oliviero Olivieri/Getty Images, Inc.)
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Rasters and Vectors
Two methods that are used to reduce geographic phenomena to forms that can be coded in computer databases
In principle, each can be used to code both fields and discrete objects, but in practice there is a strong association between raster and fields, and between vector and discrete objects.
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Rasters and Vectors
In a raster representation geographic space is divided into an array of cells, each of which is usually square, but sometimes rectangular.
All geographic variation is then expressed by assigning properties or attributes to these cells. 
The cells are sometimes called pixels (short for picture elements).
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Raster Representation
Each color represents a different value of a nominal-scale variable denoting land-cover class
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Effect of a raster representation using: 
the largest share rule(B) the central point rule
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Rasters and Vectors
Usually, in a vector representation, all lines are captured as points connected by precisely straight lines (some GI software also allows curves).
Features are captured as a series of points or vertices connected by straight lines
areas are often called polygons
lines are sometimes called polylines
the choice between raster and vector is often complex
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
An area (purple line) 
and 
its approximation by a polygon (dashed blue line)
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Regularly spaced sample points
 
(B) Irregularly spaced sample points
 (C) Rectangular cells
 (D) Irregularly shaped polygons
 (E) Irregular network of triangles, with linear variation over each triangle (the triangulated irregular network or TIN model; the bounding box is shown dashed in this case because the unshown portions of complete triangles extend outside it)
 
(F) Polylines representing contours
The six approximate representations of a field used in GI databases. 
(Courtesy U.S. Geological Survey)
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Part of a Digital Raster Graphic,
 a scan of a U.S Geological Survey 1:24000 
topographic map 
(Courtesy USGS)
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
The Paper Map
Has a scale or representative fraction
The ratio of distance on the map to distance on the ground
E.g. 1:24 000 – reduces everything on earth surface to 24,000th its real size
Is a major source of data for GI technologies
Obtained by digitizing or scanning the map and registering it to the Earth’s surface
Digital representations are much more powerful than their paper equivalents
But a GI database is much more than a container of conventional maps: e.g., 3-D, Earth’s curvature
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
25
Generalization
Ways of simplifying the view of the world include:
describe entire areas, attributing uniform characteristics to them, even when areas are not strictly uniform; 
identify features on the ground and describe their characteristics, again assuming them to be uniform;
limit our descriptions to what exists at a finite number of sample points, hoping that these samples will be adequately representative of the whole.
some degree of generalization is almost inevitable in all geographic data.
A map’s specification defines how real features on the ground are selected for inclusion on the map.
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
26
The original feature is shown at its original level of detail, and below it at 50% coarser scale. 
Each generalization technique resolves a specific problem of display at coarser scale and results in the acceptable version shown in the lower right.
Illustrations from McMaster and Shea of their 10 forms of generalization
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
The Douglas–Poiker algorithm 
is designed to simplify complex objects like this shoreline by reducing the number of points in its polyline representation. 
(© iStockphoto)
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind
Conclusions
From paper maps to digital representation 
The fundamental problem
Discrete objects and continuous fields 
Two fundamental ways of representing geography 
Raster and vector
two methods of representing geographic data in digital computers
Representation, or more broadly ontology, is a fundamental issue in GI
Geographic Information Science and Systems (Fourth Edition) | Paul A. Longley | Michael F. Goodchild | David J. Maguire | David W. Rhind