Introduction to Geographic Information Systems (GIS) September 5, 2006 SGO1910 & SGO4030 Fall...

Introduction to Geographic Information Introduction to Geographic Information Systems Systems

(GIS)(GIS)

September 5, 2006September 5, 2006

SGO1910 & SGO4030SGO1910 & SGO4030

Fall 2006 Fall 2006

Karen O’BrienKaren O’BrienHarriet Holters Hus, Room 215Harriet Holters Hus, Room 215

karen.obrien@sgeo.uio.nokaren.obrien@sgeo.uio.no

AnnouncementsAnnouncements

• Home pages – reviewHome pages – review

• Review lecture: Thursday, September Review lecture: Thursday, September 21, 12.15-14.00, Room 323, HHH21, 12.15-14.00, Room 323, HHH

• Mid-term quiz: September 26 Mid-term quiz: September 26

(chapters 1, 3, 4, 5)(chapters 1, 3, 4, 5)

ReviewReview

• Spatial Data Models Spatial Data Models

• Conceptual and Digital Conceptual and Digital RepresentationsRepresentations

• Discrete Objects and FieldsDiscrete Objects and Fields

• Vector and RasterVector and Raster

Discrete ObjectsDiscrete Objects

• Points, lines, and areasPoints, lines, and areas

• CountableCountable

• Persistent through time, perhaps Persistent through time, perhaps mobilemobile

• Biological organismsBiological organisms– Animals, treesAnimals, trees

• Human-made objectsHuman-made objects– Vehicles, houses, fire hydrantsVehicles, houses, fire hydrants

FieldsFields

• Properties that vary continuously over Properties that vary continuously over spacespace– Value is a function of locationValue is a function of location– Property can be of any attribute type, Property can be of any attribute type,

including directionincluding direction

• Elevation as the archetypeElevation as the archetype– A single value at every point on the Earth’s A single value at every point on the Earth’s

surfacesurface– Any field can have slope, gradient, peaks, pitsAny field can have slope, gradient, peaks, pits

A raster data model uses a gridA raster data model uses a grid

• One grid cell is one unit or holds one attribute. One grid cell is one unit or holds one attribute.

• Every cell has a value, even if it is “missing.” Every cell has a value, even if it is “missing.”

• A cell can hold a number or an index value A cell can hold a number or an index value standing for an attribute.standing for an attribute.

• A cell has a resolution, given as the cell size in A cell has a resolution, given as the cell size in

ground units.ground units.

Generic structure for a grid Generic structure for a grid

Figure 3.1 Generic structure for a grid.

Row

s

Columns

Gridcell

Grid extent

Resolution

Legend

Urban area

Suburban area

Forest (protected)

Water

Raster representation. Each color represents a different value of a nominal-

scale field denoting land use.

Vector DataVector Data

• Used to represent points, lines, and areasUsed to represent points, lines, and areas

• All are represented using coordinatesAll are represented using coordinates– One per pointOne per point– Areas as polygonsAreas as polygons

• Straight lines between points, connecting back to the Straight lines between points, connecting back to the startstart

• Point locations recorded as coordinatesPoint locations recorded as coordinates

– Lines as Lines as polylinespolylines• Straight lines between pointsStraight lines between points

Areas are lines are points are Areas are lines are points are coordinatescoordinates

RepresentationsRepresentations

• Representations can rarely be Representations can rarely be perfectperfect– Details can be irrelevant, or too Details can be irrelevant, or too

expensive and voluminous to recordexpensive and voluminous to record

• It’s important to know what is It’s important to know what is missing in a representationmissing in a representation– Representations can leave us uncertain Representations can leave us uncertain

about the real worldabout the real world

Representation: A fundamental Representation: A fundamental problem in GISproblem in GIS

• Identifying what to leave in and what to Identifying what to leave in and what to take out of digital representations.take out of digital representations.

• The scale or level of detail at which we The scale or level of detail at which we seek to represent reality often seek to represent reality often determines whether spatial and determines whether spatial and temporal phenomena appear regular or temporal phenomena appear regular or irregular. irregular.

• The spatial heterogeneity of data also The spatial heterogeneity of data also influences this regularity or irregularity.influences this regularity or irregularity.

Today’s Topic:Today’s Topic:

The Nature of The Nature of Geographic DataGeographic Data

(Or how phenomena vary across space, and the general nature of geographic variation)

Scale Scale

• Scale refers to the details; fine-scaled data Scale refers to the details; fine-scaled data includes lots of detail, coarse-scaled data includes lots of detail, coarse-scaled data includes less detail.includes less detail.

• Scale refers to the extent. Large-scale project Scale refers to the extent. Large-scale project involves a large extent (e.g. India); small-involves a large extent (e.g. India); small-scale project covers a small area (e.g., scale project covers a small area (e.g., Anantapur, India) Anantapur, India)

• Scale can refer to the level (national vs. local)Scale can refer to the level (national vs. local)• Scale of a map can be large (lots of detail, Scale of a map can be large (lots of detail,

small area covered) or small (little detail, small area covered) or small (little detail, large area covered) (large area covered) (Opposite of other Opposite of other interpretationsinterpretations!!)!!)

Principal objective of GIS Principal objective of GIS analysis:analysis:

• Development of representations of Development of representations of how the world looks and works.how the world looks and works.

• Need to understand the nature of Need to understand the nature of spatial variation:spatial variation:– Proximity effectsProximity effects– Geographic scale and level of detailGeographic scale and level of detail– Co-variance of different measures & Co-variance of different measures &

attributesattributes

• Space and time define the geographic Space and time define the geographic context of our past actions, and set context of our past actions, and set geographic limits of new decisions geographic limits of new decisions (condition what we know, what we (condition what we know, what we perceive to be our options, and how perceive to be our options, and how we choose among them)we choose among them)

• Consider the role of globalization in Consider the role of globalization in defining new patterns of behaviordefining new patterns of behavior

Geographic data:Geographic data:

• Smoothness versus irregularitySmoothness versus irregularity

• Controlled variation: oscillates Controlled variation: oscillates around a steady state patternaround a steady state pattern

• Uncontrolled variation: follows no Uncontrolled variation: follows no patternpattern

(violates Tobler’s Law)(violates Tobler’s Law)

Tobler’s First Law of Tobler’s First Law of GeographyGeography

• Everything is related to everything Everything is related to everything else, but near things are more else, but near things are more related than distant things.related than distant things.

Spatial AutocorrelationSpatial Autocorrelation

• The degree to which near and more The degree to which near and more distant things are interrelated. Measures distant things are interrelated. Measures of spatial autocorrelation attempt to deal of spatial autocorrelation attempt to deal simultaneously with similarities in the simultaneously with similarities in the location of spatial objects and their location of spatial objects and their attributes. (Not to be confused with attributes. (Not to be confused with temporal autocorrelation)temporal autocorrelation)

Example: GDP dataExample: GDP data

Spatial autocorrelation:Spatial autocorrelation:

• Can help to generalize from sample Can help to generalize from sample observations to build spatial observations to build spatial representationsrepresentations

• Can frustrate many conventional Can frustrate many conventional methods and techniques that tell us methods and techniques that tell us about the relatedness of events. about the relatedness of events.

The scale and spatial structure of a particular application suggest ways in which we should sample geographic reality, and the ways in which we should interpolate between sample observations in order to build our representation.

Types of spatial Types of spatial autocorrelationautocorrelation

• PositivePositive (features similar in location (features similar in location are similar in attribute)are similar in attribute)

• NegativeNegative (features similar in (features similar in location are very different)location are very different)

• ZeroZero (attributes are independent of (attributes are independent of location)location)

• The issue of sampling interval is of The issue of sampling interval is of direct importance in the direct importance in the measurement of spatial measurement of spatial autocorrelation, because spatial autocorrelation, because spatial events and occurrences can conform events and occurrences can conform to spatial structure (e.g. Central to spatial structure (e.g. Central Place Theorem).Place Theorem).

Spatial SamplingSpatial Sampling

• Sample frames (“the universe of Sample frames (“the universe of eligible elements of interest”)eligible elements of interest”)

• Probability of selectionProbability of selection

• All geographic representations are All geographic representations are samplessamples

• Geographic data are only as good as Geographic data are only as good as the sampling scheme used to create the sampling scheme used to create themthem

Sample DesignsSample Designs

• Types of samplesTypes of samples– Random samples (based on probability Random samples (based on probability

theory)theory)– Stratified samples (insure evenness of Stratified samples (insure evenness of

coverage)coverage)– Clustered samples (a microcosm of Clustered samples (a microcosm of

surrounding conditions)surrounding conditions)

• Weighting of observations (if spatial Weighting of observations (if spatial structure is known)structure is known)

• Usually, the spatial structure is Usually, the spatial structure is known, thus it is best to devise known, thus it is best to devise application-specific sample designs.application-specific sample designs.– Source data available or easily collectedSource data available or easily collected– Resources available to collect themResources available to collect them– Accessibility of all parts to samplingAccessibility of all parts to sampling

Spatial InterpolationSpatial Interpolation

• Judgment is required to fill in the Judgment is required to fill in the gaps between the observations that gaps between the observations that make up a representation.make up a representation.

• To do this requires an understanding To do this requires an understanding of the effect of increasing distance of the effect of increasing distance between sample observationsbetween sample observations

Spatial InterpolationSpatial Interpolation

• Specifying the Specifying the likely distance decaylikely distance decay– linear: linear: wwij ij == -b d -b dijij

– negative power: negative power: wwij ij == d dijij-b-b

– negative exponential: negative exponential: wwij ij == e e-bdij-bdij

• Isotropic (uniform in every direction) Isotropic (uniform in every direction) and regular – relevance to all and regular – relevance to all geographic phenomena?geographic phenomena?

Key point:Key point:

• An understanding of the spatial An understanding of the spatial structure of geographic phenomena structure of geographic phenomena helps us to choose a good sampling helps us to choose a good sampling strategy, to use the best or most strategy, to use the best or most appropriate means of interpolating appropriate means of interpolating between sampled points, and to build between sampled points, and to build the best spatial representation for a the best spatial representation for a particular purpose.particular purpose.

Spatial AutocorrelationSpatial Autocorrelation

• Induction: reasoning from the data to Induction: reasoning from the data to build an understanding.build an understanding.

• Deduction: begins with a theory or Deduction: begins with a theory or principle. principle.

• Measurement of spatial Measurement of spatial autocorrelation is an inductive autocorrelation is an inductive approach to understanding the approach to understanding the nature of geographic datanature of geographic data

Spatial Autocorrelation Spatial Autocorrelation MeasuresMeasures• Spatial autocorrelation measures: Spatial autocorrelation measures:

– Geary and Moran; nature of observationsGeary and Moran; nature of observations

• Establishing dependence in space: Establishing dependence in space: regression analysisregression analysis– Y = f (XY = f (X11, X, X2 2 , X, X3 3 , . . . , X, . . . , XKK))

– Y = f (XY = f (X11, X, X2 2 , X, X3 3 , . . . , X, . . . , XKK) + ε) + ε

– YYii = f (X = f (Xi1i1, X, Xi2 i2 , X, Xi3 i3 , . . . , X, . . . , XiKiK) + ε) + εii

– YYii = b = b00 + b + b11 X Xi1i1 + b + b22 X Xi2i2 + b + b33 X Xi3 i3 + . . . b + . . . bKK X XiKiK + ε + εii

Y is the dependent variable, X is the independent variable

Y is the response variable, X is the predictor variable

Spatial AutocorrelationSpatial Autocorrelation

• Tells us about the interrelatedness of Tells us about the interrelatedness of phenomena across space, one phenomena across space, one attribute at a time. attribute at a time.

• Identifies the direction and strength Identifies the direction and strength of the relationshipof the relationship

• Examining the residuals (error terms) Examining the residuals (error terms) through Ordinary Least Squares through Ordinary Least Squares regression regression

Discontinuous VariationDiscontinuous Variation

• Fractal geometryFractal geometry– Self-similaritySelf-similarity– Scale dependent measurementScale dependent measurement– Each part has the same nature as the Each part has the same nature as the

wholewhole

• Dimensions of geographic features:Dimensions of geographic features:– Zero, one, two, three… fractalsZero, one, two, three… fractals

ConsolidationConsolidation

• Representations build on our Representations build on our understanding of spatial and understanding of spatial and temporal structurestemporal structures

• Spatial is special, and geographic Spatial is special, and geographic data have a unique naturedata have a unique nature

• This unique natures means that you This unique natures means that you have to know your application and have to know your application and datadata