1. 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

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

3. 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

4. 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

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

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

9. Scale and Spatial Autocorrelation No. of geographicCorrelation areas 48.2189 24.2963 12.5757 6.7649 3.9902

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

11. 0.9 – 1.0 0.5 – 0.9 0.1 – 0.5 0.0 – 0.1

12. 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

13. Measurement Error Digitizing errors Automated solutions Conflation of adjacent map sheets

17. 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

20. 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

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

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