Representations / ModelsLongley 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 mp = 0.0000000000002 or 2 x 10 -13

spatially• 5 billion years

– we live through ~70 p = 70/5,000,000,000p = 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

Courtesy Jonathan Raper of City University London, GISci 2002 Keynote

Each color= 1 day Darker= later in the day

1km

Jonathan Raper’s Month in 3-D

Courtesy Jonathan Raper of City University London, GISci 2002 Keynote

X & y axes are spatial and z is seconds from midnight. Points are from GPS carried on all journeys with static time auto-completed. Model produced by Earthvision (http://www.dgi.com/)

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

• Much human communication is now digital (email, fax, voice mail, DVD…)

• sent through a “pipe” consisting of 0s and 1s

• stored on devices that can store only 0s and 1s

• processed as 0s and 1s

Digital (cont.)

• 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. 1.0Longley 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– NASA World Wind - http://worldwind.arc.nasa.gov/

– ArcGIS Explorer powered by ArcGIS Server– http://topex.ucsd.edu/marine_topo/globe.html

“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 FieldsObjects• Well-defined boundaries in empty space

• “Desktop littered w/ objects”

• World littered w/ cars, houses, etc.

• Counts• 49 houses in a subdivision

How many students at OSU?

Clouds in sky?

Fish in the sea?

Atmospheric highs in N. hemisphere today?

Fields:care to count every peak, valley,

ridge, slope???

What constitutes a “mountain?”

• 1000 ft was magic number but how?

Fieldswhat varies continuously and how smoothlymeasurable at every point on a surface

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.

• Radiation captured by satellite• Elevation• Temperature• Soil type • Soil pH• Rainfall• Land cover type• Ownership

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), TINRaster, Poly, ContoursWhat changes? Representation or phenomenon?

Gateway to the Literature

• 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.

• Dobson, J., Geographer questioned at pearly gates, GEOWorld, 15 (9), 26-27, 2002.

• 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.