Representations / Models Longley et al., chs. 1-3 Zeiler, chs. 2-3

Representations / Models
Why Representations or
• How do we know what we know?
• Human sight
– Visible spectrum, horizon at ~10km
visibility 100 km
• Human sound
– 50Hz to 15KHz up to 100 m
• Taste, Touch, Smell
Surface of the Earth?
• 500,000,000 sq km
– on average 100 sq m is sensed directly
p = 100/500,000,000,000,000 m
p = 0.0000000000002 or 2 x 10 -13 spatially
• 5 billion years
– we live through ~70
p = 70/5,000,000,000
p = 0.000000014 or 1.4 x 10 -8 temporally
\ we know almost nothing of the surface
of the Earth via our senses!
Knowing the World
• Everything else via communication
– Speech
– Text
– Photographs
– Radio, TV
– Maps
– Internet
– Databases
Jonathan Raper’s Week in 2-D
Each color= 1 day
Courtesy Jonathan Raper of City University London, GISci 2002 Keynote
Darker= later in the day
Jonathan Raper’s Month in 3-D
X & y axes are
spatial and z is
seconds from
midnight. Points are
from GPS carried on
all journeys with
static time autocompleted. Model
produced by
Courtesy Jonathan Raper of City University London, GISci 2002 Keynote
More Representations in
Representation in Space/Time
• What would more
detail show?
• Infinite complexity
– must reduce to
manageable volume
Geographic Representation
• “Location, location, location!”
– to map, to link based on the same place,
– to measure distances and areas
• Time
– height above sea level (slow?)
– Sea surface temperature (fast)
• Attributes
– physical or environmental
– soci-economic (e.g., population or income)
Geographic Representation
The “atom” of geographic information
< location, time, attribute >
“It’s chilly today in Corvallis”
< Corvallis, today, chilly >
“at 44° N, 123° E at 12 noon PST the
temperature was 60°F”
“Atoms” of Geographic Information
• an infinite number
• two-word description of every sq km on
the planet, 10 Gb
• store one number for every sq m, 1 Pb
(trillion bytes)
• Too much for any system
• How to limit?
Limiting Detail
• aggregate, generalize, approximate
• ignore the water?!
– 2/3 of planet!
• one temperature for all of Corvallis
– one number for an entire polygon
• sample the space
– only measure at weather stations, temp.
varies slowly
• all geographic data miss detail
– all are uncertain to some degree
The Problem of Infinite Complexity
• many ways of limiting detail
• a GIS user must make choices
• GIS developers must allow for many
• Most important option is how we
choose to think about the world
Objects and Fields
How many students at
Clouds in sky?
Fish in the sea?
Atmospheric highs in N.
hemisphere today?
• Well-defined
boundaries in empty
• “Desktop littered w/
• World littered w/ cars,
houses, etc.
• Counts
• 49 houses in a
care to count every peak, valley,
ridge, slope???
what varies continuously and how smoothly
measurable at every point on a surface
• Radiation captured by satellite
• Elevation
• Temperature
• Soil type
• Soil pH
• Rainfall
• Land cover type
• Ownership
An image of part of the lower Colorado River in the southwestern USA. The lightness of the image at any point
measures the amount of radiation captured by the satellite's imaging system. Image derived from a public domain
SPOT image, courtesy of Alexandria Digital Library, University of California, Santa Barbara.
Tessellated Ground Plane
Orange County, CA
Courtesy of Russ Michel, Pictometry Intl. Inc.
Object/Vector Worldview
Projected with flat ground plane
Courtesy of Russ Michel, Pictometry Intl. Inc.
Projected with tessellated ground plane
Orange County Street Centerlines
• each variable has one
value everywhere
• variable is a function of
• field = a way of conceiving of
geography as a set of
variables, each having one
value at every location on the
• zf = f (x,y,z,t)
Fields and Objects
• Objects are intuitive, part of everyday
– May overlap
• Fields worth measuring at every point
– Often associated with scientific
– surfaces, fronts, highs, lows
• Both objects and fields can be
represented either in raster or in vector
One Variable as Pt (grid or sample), TIN
Raster, Poly, Contours
What changes? Representation or phenomenon?
• Ontology: the study of the basic elements of
• "what we tell about"
• semantics, “semantic interoperability”
• discrete objects and fields are two different
Research Challenge in Ontology
A Coastal “Geo-Ontology”
Courtesy Jonathan Raper of City University London, GISci 2002 Keynote
Describing LOCATION
What constitutes a “mountain?”
• 1000 ft was magic
number but how?
ICAN Interoperability Prototype
Starts with metadata interoperability
“Mapping” of Terms:
MIDA: “Coastline”
is similar to
OCA: “Shoreline”
Atlas X
ISO Metadata
MIDA terminology
FGDC Metadata
OCA terminology
X Standard
X terminology
Gateway to the Literature
• Goodchild, M. F., M. Yuan, Cova, T. Towards a general
theory of geographic representation in GIS. Int. J. Geog.
Inf. Sci. 21(3-4): 239-260, 2007.
• Comber, A., P.R. Fisher, J., and R. Wadsworth,
Integrating land-cover data with different ontologies:
Identifying change from inconsistency, Int. J. Geog. Inf.
Sci., 18 (7), 691-708, 2004.
• Golledge, R., The Nature of Geographic Knowledge,
Annals of the AAG, 92(1): 1-14, 2002.
• Kavouras, M., M. Kokla, and E. Tomai, Comparing
categories among geographic ontologies, Comp. Geosci,
31 (2), 145-154, 2005.
• Kuhn, W., Semantic reference systems, Int. J. Geog. Inf.
Sci., 17 (5), 405-409, 2003.

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