Geographical Information Systems and Science Longley P A, Goodchild M F, Maguire D J, Rhind D W (2001) John Wiley and Sons Ltd 6. Uncertainty © John Wiley & Sons Ltd

Overview Definition, and relationship to geographic representation Conception, measurement and analysis Vagueness of key GIS attributes ‘Indeterminate’ geographic boundaries Accuracy and measurement error

Introduction Imperfect or uncertain reconciliation [science, practice] [concepts, application] [analytical capability, social context] It is impossible to make a perfect representation of the world, so uncertainty about it is inevitable

Sources of Uncertainty Measurement error: different observers, measuring instruments Specification error: omitted variables Ambiguity, vagueness and the quality of a GIS representation A catch-all for ‘incomplete’ representations or a ‘quality’ measure

U1: Conception Spatial uncertainty Natural geographic units? Bivariate/multivariate extensions? Discrete objects Vagueness Statistical, cartographic, cognitive Ambiguity Values, language

Scale & Geographic Individuals Regions Uniformity Function Relationships typically grow stronger when based on larger geographic units

Scale and Spatial Autocorrelation No. of geographicCorrelation areas

U2: Measurement/representation Representational models filter reality differently Vector Raster

0.9 – – – – 0.1

Other issues Measurements only accurate to a limited extent ‘Continuous’ scales are in practice discrete Discrete isopleth/choropleth map display Choropleth mapping in multivariate cases

Measurement Error Digitizing errors Automated solutions Conflation of adjacent map sheets

Data Integration and Lineage Concatenation E.g. polygon overlay Conflation E.g. rubber sheeting Persistent error indicates shared lineage Errors tend to exhibit strong positive spatial autocorrelation

U3: Analysis Can good spatial analysis develop on uncertain foundations? Can rarely correct source More usually tackle operation (internal validation) Conflation/concatenation allows external validation of zonal averaging effects Aggregation & ecological fallacy

MAUP Scale + aggregation = MAUP can be investigated through simulation of large numbers of alternative zoning schemes

Consolidation Uncertainty is more than error Richer representations create uncertainty! Need for a priori understanding of data and sensitivity analysis