Representations / Models
Longley et al., chs. 1-3
Zeiler, chs. 2-3
Why Representations or
Models?
• 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
Knowing the World
• Everything else via communication
– Speech
– Text
– Photographs
– Radio, TV
– Maps
– Internet
– Databases
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!
Communicated Information
• decide where to go as tourists,
shoppers
• choose study areas for research
• manage parks, reserves
• choose where to live
• address urban congestion
• All such information must use a
representation (space and time)
Jonathan Raper’s Week in 2-D
1km
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
Earthvision
(http://www.dgi.com/)
Courtesy Jonathan Raper of City University London, GISci 2002 Keynote
More Representations in
Space/Time
Representation in Space/Time
• What would more
detail show?
• Infinite complexity
Simplification
– must reduce to
manageable volume
Where do Representations occur?
• the human mind, in memory and
reasoning
• speech
• written text
• photographs
• digital databases
• GIS !
Representations are crucial...
• for communication (metaphors,
expressions)
• going beyond the space-time limits of
our senses
• dealing with an infinitely complex world
DIGITAL Representation
• how to express knowledge
exclusively in 0s and 1s?
• how to describe complexity of
world in 0s and 1s?
• the fundamental question of data
modeling for GIS
Communication via a channel
Communication via a channel
• How efficient is the
channel?
• Is there information that
can't be expressed?
• Text omits gesture,
pronunciation, voice
inflection
• GIS as a communication
channel?
• What information about a
place can't be expressed in
GIS?
Communication via a channel
• What if the sender and receiver can't
understand each other?
– different language
– different alphabet
– different GIS
– interoperability
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”
Describing LOCATION
Time ok, Attributes Not Always
• “chilly” is subjective
and relative
• 60°F generally
understood
• did Hugh Grant
climb a hill or a
mountain?
Ontology
• Ontology: the study of the basic elements of
description
• "what we tell about"
• semantics, “semantic interoperability”
• discrete objects and fields are two different
ontologies
www.ucgis.org
Research Challenge in Ontology
A Coastal “Geo-Ontology”
Courtesy Jonathan Raper of City University London, GISci 2002 Keynote
A Complete Representation
•
•
•
•
DIGITAL and GEOGRAPHIC
complete representation of the planet
past, present, and future
“Digital Earth”
– a “camera” pointed at a sunlit Earth
– a virtual, immersive world
Simulated image from NASA’s
SRTM, Carrizo Plain, S. Calif.
The Fading of Digital Earth, v. 1.0
Longley et al., p. 463
• No effective interoperability between
datasets
• No common vision of cooperation
• Low awareness by the public, inaccessibility
• Many stand in the gap now but challenges
remain
–
–
–
–
–
Google Earth
http://topex.ucsd.edu/marine_topo/globe.html
http://www.virtualocean.org
NASA World Wind - http://worldwind.arc.nasa.gov/
ArcGIS Explorer powered by ArcGIS Server
“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)
www.ccsf.caltech.edu/~roy/dataquan/
• 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
options
• Most important option is how we
choose to think about the world
Objects and Fields
How many students at
OSU?
Clouds in sky?
Fish in the sea?
Atmospheric highs in N.
hemisphere today?
Objects
• Well-defined
boundaries in empty
space
• “Desktop littered w/
objects”
• World littered w/ cars,
houses, etc.
• Counts
• 49 houses in a
subdivision
Fields:
care to count every peak, valley,
ridge, slope???
What constitutes a “mountain?”
• 1000 ft was magic
number but how?
Fields
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.
Fields
• each variable has one
value everywhere
• variable is a function of
location
• field = a way of conceiving of
geography as a set of
variables, each having one
value at every location on the
planet
• zf = f (x,y,z,t)
Fields and Objects
• Objects are intuitive, part of everyday
life
– May overlap
• Fields worth measuring at every point
– Often associated with scientific
measurements
– surfaces, fronts, highs, lows
• Both objects and fields can be
represented either in raster or in vector
form
One Variable as Pt (grid or sample), TIN
Raster, Poly, Contours
What changes? Representation or phenomenon?
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.