J 
  
age 
relevance 
scale 
format 
coverage 
accessibility 
| 
  
  
  
  
  
natural variation 
  
observation density 
operator bias 
generalization 
| 
  
  
  
  
(existing data) 
  
INHERITED UNCERTAINT Y | 
  
  
  
  
COMPUTER OPERATION 
  
interpolation 
  
(new data) 
INTRINSIC UNCERTAINTY | 
  
  
  
| 
  
  
  
classification DATA OUTPUT 
DATA INPUT 
  
  
topological logic 
  
  
  
algorithm logic data transfer 
numerical computation VDU resolution encoding error 
data transformation plotter resolution typing error 
digitising error 
digitiser resolution 
  
  
  
  
L 
J 
  
  
OPERATIONAL UNCERTAINTY | 
  
  
  
  
? position ? 
    
  
2identification? 
  
? crisp ? 
  
  
  
? fuzzy ? | 
?homogeneous? 
  
?heterogeneous? 
  
  
  
  
  
Figure 1: Sources of Uncertainty in GIS 
MEASURING, MODELLING AND MANAGING UNCERTAINTY 
The general treatment of uncertainty in GIS to date 
reflects the conceptual closeness of digital maps 
to their analog roots. Whilst Chrisman may assert 
that "no map can be picked apart into completely 
independent pellets of information” (Chrisman, 
1991), any graphic output from a GIS can be 
disaggregated into individually encoded entities. 
These entities can be subjected to an assessment of 
their quality, either individually or in sets. 
Concern with uncertainty in spatial data has 
concentrated on reducing and modelling error. A 
recent overview is given by Chrisman (1991) whilst 
a detailed treatment is provided by Veregin (1989). 
Measurement. 
The main focus has been on establishing the extent 
to which locational and/or attribute errors are 
present within a dataset and, in the recognition 
that these can never be entirely eliminated, how to 
characterize these errors as a metric or statistic. 
Adopted wholesale from the mapping sciences has 
been the testing of geometrical aecuracy based on 
well-defined points having no attribute ambiguity 
(Bureau of Budget, 1947; ASCE, 1983; ASPRS, 1985). 
Testing is carried out by reference to a survey of 
a Resolution 
      
  
  
  
  
  
higher order. Whilst horizontal and vertical 
accuracy can be treated individually, measures such 
as Koppe's formula recognize the link between 
horizontal and vertical accuracy. The logical 
expectation that well-defined points of no 
attribute ambiguity are more likely to be 
accurately surveyed in the first place would 
certainly bias any outcomes, but nevertheless these 
accuracy tests are widely accepted. How often these 
tests are actually carried out is another matter! 
In the context of GIS, the main consideration is 
that much spatial data do not contain well-defined 
points. 
Appropriate testing of attribute accuracy depends 
on the measurement class used. Thus continuous data 
such as digital elevation models (DEM) can be 
tested for horizontal and vertical accuracy as 
above either through interpolating contours or by 
interpolating to known points. An alternative is 
statistical analysis of expected and observed 
values. This type of treatment can be viewed as 
overlooking certain important issues. For DEMs, 
consideration should be given to the limitations of 
source documents (quality of maps or vegetation on 
aerial photographs), the sampling interval and 
orientation of sampling (if in lines or on a grid) 
which will need to be adjusted depending on terrain 
and proposed use of the data (Theobald, 1988). 
Characterization of Spatial Entity 
  
  
  
Exact Inexact 
© Locational Exact No uncertainty Uncertain character 
: Definition 
of Spatial Inexact Uncertain location| Uncertain character 
Entity Uncertain location 
  
  
  
  
  
    
  
Table 1: Contingency table for positional and characterization errors 
(modified from Robinson & Frank, 1985). 
760 
(ZI 
unt 
ae: 
art