GIS September 27, 2005

Announcements Next lecture is on October 18th (read chapters 9 and 10) Next lecture is on October 18th (read chapters 9 and 10)

Uncertainty …

Error (differences between observers or between measuring instruments) Error (differences between observers or between measuring instruments) Accuracy (difference between reality and our representation of reality) Accuracy (difference between reality and our representation of reality) Precision (the repeatability of measurements) Precision (the repeatability of measurements) Quality (attribute accuracy, positional accuracy, logical consistency, completelness, and lineage) Quality (attribute accuracy, positional accuracy, logical consistency, completelness, and lineage)

U1: Conception Spatial uncertainty Spatial uncertainty –Do Natural geographic units exist? –Scales for bivariate/multivariate analyses? –Discrete objects more reliant on “natural units” Vagueness (in boundaries, membership) Vagueness (in boundaries, membership) –Statistical, cartographic, cognitive Ambiguity Ambiguity –Different labels by different national or cultural groups, language (GIS is not value-neutral!!)

Indicators Direct - clear correspondence with mapped phenomenon) Direct - clear correspondence with mapped phenomenon) Indirect (or proxy) – best available measure Indirect (or proxy) – best available measure Selection of indicators is subjective Selection of indicators is subjective Differences in definitions are a major impediment to integration of geographic data over wide areas Differences in definitions are a major impediment to integration of geographic data over wide areas

Fuzzy Approaches to Uncertainty In fuzzy set theory, it is possible to have partial membership in a set In fuzzy set theory, it is possible to have partial membership in a set –membership can vary, e.g. from 0 to 1 –this adds a third option to classification: yes, no, and maybe Fuzzy approaches have been applied to the mapping of soils, vegetation cover, land use, and vulnerability Fuzzy approaches have been applied to the mapping of soils, vegetation cover, land use, and vulnerability

Scale & Geographic Individuals Regions Regions –Uniformity (internal homogeneity) –Functional zones (boundaries as breakpoints) Relationships typically grow stronger when based on larger geographic units 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 Representational models filter reality differently –Vector (requires a priori conceptualization of geographic features as discrete objects) –Raster (boundaries seldom resemble natural features, but convenient and efficient…)

0.9 – – – – 0.1

Other issues Measurements only accurate to a limited extent Measurements only accurate to a limited extent ‘Continuous’ scales are in practice discrete ‘Continuous’ scales are in practice discrete –Discrete isopleth/choropleth map display –Choropleth mapping in multivariate cases –Box 4.3 explains the difference!

Spatially Intensive versus Extensive Variables Choropleth maps use values describing properties of non-overlapping areas (municipalities, states, countries) Choropleth maps use values describing properties of non-overlapping areas (municipalities, states, countries) Extensive variables: values true for the entire area are the same color: E.g. Total population Extensive variables: values true for the entire area are the same color: E.g. Total population Intensive variables: values could potentially be true for every part of the area (an average). E.g. Population density. Intensive variables: values could potentially be true for every part of the area (an average). E.g. Population density.

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

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

U3: Analysis Can good spatial analysis develop on uncertain foundations? 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 Error propagation measures impacts of uncertainty in data on the results Error propagation measures impacts of uncertainty in data on the results

Ecological Fallacy Inappropriate inference from aggregate data about the characteristics of individuals Inappropriate inference from aggregate data about the characteristics of individuals Fundamental difference between geography and other scientific disciplines is that definitions of objects of study is almost always ambiguous. Fundamental difference between geography and other scientific disciplines is that definitions of objects of study is almost always ambiguous.

Modifiable Areal Unit Problem (MAUP) Scale + aggregation = MAUP Scale + aggregation = MAUP –can be investigated through simulation of large numbers of alternative zoning schemes –Apparent spatial distributions which are unrepresentative of the scale and configuration of real-world geographic phenomena (example: urban density)

Summary Uncertainty is more than error Uncertainty is more than error Richer representations can create uncertainty! Richer representations can create uncertainty! Need for a priori understanding of data and sensitivity analysis Need for a priori understanding of data and sensitivity analysis Spatial analysis is often context-sensitive (you need to know your data and place!) Spatial analysis is often context-sensitive (you need to know your data and place!)

Living with Uncertainty Acknowledge that uncertainty is inevitable Acknowledge that uncertainty is inevitable Data should never be taken as truth (assess whether it is suitable) Data should never be taken as truth (assess whether it is suitable) Uncertainties in outputs may exceed uncertainties in inputs because many GIS processes are highly non-linear Uncertainties in outputs may exceed uncertainties in inputs because many GIS processes are highly non-linear Rely on multiple sources of data Rely on multiple sources of data Be honest and informative in reporting the results of GIS analysis. Be honest and informative in reporting the results of GIS analysis.