4. the nature of geographic data

Geographic Information Systems and ScienceSECOND EDITIONPaul A. Longley, Michael F. Goodchild, David J. Maguire, David W. Rhind© 2005 John Wiley and Sons, Ltd

4. The Nature of Geographic Data

© John Wiley & Sons Ltd

© 2005 John Wiley & Sons, Ltd

Overview: Spatial is SpecialThe 'true' nature of geographic dataThe special tools needed to work with themHow we sample and interpolate (gaps)What is spatial autocorrelation, and how can it be measured?Fractals and geographic representation


Why GIS?Small things can be intricateGIS can:

Identify structure at all scalesShow how spatial and temporal context affects what we do

Allows generalization and accommodates errorAccommodates spatial heterogeneity


Building RepresentationsTemporal and spatial autocorrelationUnderstanding scale and spatial structure

How to sample How to interpolate between observations

Object dimensionsNatural vs. artificial units


Spatial AutocorrelationSpatial autocorrelation is determined both by similarities in position, and by similarities in attributes

Sampling intervalSelf-similarity


Spatial SamplingSample framesProbability of selectionAll geographic representations are samplesGeographic data are only as good as the sampling scheme used to create them


Sample DesignsTypes of samples

Random samplesStratified samplesClustered samples

Weighting of observations


Spatial InterpolationSpecifying the likely distance decay

linear: wij = -b dij

negative power: wij = dij-b

negative exponential: wij = e-bdij

Isotropic and regular – relevance to all geographic phenomena?

Inductive vs. deductive approaches


Spatial Autocorrelation MeasuresSpatial autocorrelation measures:

Moran; nature of observations

Establishing dependence in space: regression analysis

Y = f (X1, X2 , X3 , . . . , XK)Y = f (X1, X2 , X3 , . . . , XK) + εYi = f (Xi1, Xi2 , Xi3 , . . . , XiK) + εi

Yi = b0 + b1 Xi1 + b2 Xi2 + b3 Xi3 + . . . bK XiK + εi


Functional formThe assumptions of inference

Tobler’s LawMulticollinearity


Discontinuous VariationFractal geometry

Self-similarityScale dependent measurementRegression analysis of scale relations


ConsolidationInduction and deductionRepresentations build on our understanding of spatial and temporal structuresSpatial is special, and geographic data have a unique nature

4. the nature of geographic data

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