Representations / Models

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

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!

Knowing the World

• Everything else via communication– Speech– Text– Photographs– Radio, TV– Maps– Internet– Databases

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

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 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???

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

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

Field/Raster WorldviewTessellated Ground Plane

Orange County, CA

Courtesy of Russ Michel, Pictometry Intl. Inc.

Object/Vector Worldview

Projected with flat ground plane Projected with tessellated ground plane

Courtesy of Russ Michel, Pictometry Intl. Inc. Orange County Street Centerlines

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?

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

Describing LOCATION

What constitutes a “mountain?”

• 1000 ft was magic number but how?

ICAN Interoperability Prototypeican.ucc.ie

Starts with metadata interoperability

…

Atlas XISO Metadata

&MIDA terminology

FGDC Metadata&

OCA terminology

X Standard&

X terminology

“Coastline”“Shoreline”

“Mapping” of Terms:

MIDA: “Coastline”

is similar to

OCA: “Shoreline”

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.