1 Spatial Modelling of the Terrestrial Environment - Georeferencial

116 Spatial Modelling of the Terrestrial Environment
assign surveyed elevations to the nearest DEM elevation, provided the point was within
a given search radius. The larger the search radius used, the more check data points are
assigned DEM elevations. However, this reduces confidence in the resulting height discrepancies,
as the average lateral distance between DEM and survey point is increased. In
this study, the search radius was set to 0.5 m (to give a search diameter of 1 m), thereby
matching the DEM grid spacing.
6.3 The Meaning of Error and the Treatment of Error in Digital
Elevation Models
6.3.1 The Definition and Quantification of Error
Perhaps one of the most important aspects of error is a widespread variation in how it is
defined and managed in the measurement of surface topography. By far the most common
reference to surface quality is in terms of its accuracy (e.g. Davison, 1994; Neill, 1994;
Gooch et al., 1999). However, in engineering surveying (e.g. Cooper, 1987; Cooper and
Cross, 1988), it is very common to consider error more generically, in terms of the quality of
topographic data, with accuracy describing one subset of data quality. There are then three
types of error: systematic error, blunders and random errors (e.g. Cooper and Cross, 1988;
Lane et al., 1994), and these are thought to control data accuracy, reliability and precision,
respectively. Systematic errors occur when a measurement is used with an incorrect functional
model (Cooper and Cross, 1988). Cooper and Cross give the example of how the use
of the basic collinearity equations derived from the special case of a perspective projection
(e.g. Ghosh, 1988) will result in systematic error as the functional model (the collinearity
equations) does not include those effects that cause deviation from the perspective projection
(e.g. sensor distortions). The functional model provides an inaccurate description
and leads to systematic errors. Cooper and Cross (1988) note that there did not appear to
be a widely accepted term to describe the quality of a dataset with respect to systematic
errors and recommend the term accuracy. Blunders or gross errors arise from an incorrect
measuring or recording procedure. Cooper and Cross noted that when measurements were
made manually, it was relatively easy to identify and rectify gross errors through independent
checks on measured data. However, with automation of the measurement process,
this is more difficult, but still needs to be undertaken. The quality of a dataset in terms of
blunders is defined in terms of its reliability (Cooper and Cross, 1988). Third, random
errors relate to inconsistencies that are inherent to the measurement process, and cannot be
refined by either development of the functional model or through the detection of blunders.
The quality of a dataset in terms of random errors is defined as its precision.
Whilst these definitions largely relate to the engineering surveying approach to data
quality, there is some difference in terms of the definitions used in statistical analysis.
Everitt (1998) defines: (1) accuracy as the degree of conformity to some recognized standard
value; (2) precision as the likely spread of estimates of a parameter in a statistical model;
and introduces (3), bias, as the deviation of results or inferences from the truth. It is clear
from these definitions that there is some confusion over the meaning of accuracy and of
bias: they appear to be the same thing according to Everitt (1998). This implies that the
distinction between accuracy and bias is a subtle one. Any observation may differ from its
correct value, appearing to be inaccurate, but one observation does not allow us to decide