Geoscience Reference
In-Depth Information
Sources of errors range from those evidenced in the previous paragraphs to
those inherent to nonspatial or text data that are also part of a
GIS
model. For
instance, nonspatial data include knowledge or rules used by expert systems
(Skidmore 1989b). All these errors contribute to error accumulation when
overlaying
GIS
data layers.
Composite overlaying is the simplest overlaying technique. Two or more
layers are combined, and the raster locations (or polygons formed) describe the
union of the classes on the layers. The composite overlay is in effect a univer-
sal Boolean
and
operation over the whole map. That is, for a two-layer data set
comprising layer X and layer Y, we note
X
i
=1,
n
>
Y
j
=1,
m
(i.e., the intersection of
X and Y for the
n
classes in map X and the
m
classes in map Y) at all points over
the map.
Arithmetic and mathematical operators that may be applied to two or
more layers include addition, subtraction, multiplication, division, maximum,
minimum, average, and exponent.
The method by which error is accumulated during the overlaying process
is important for modeling error in the final map products. The first necessity
for modeling map error accumulation is to quantify the error in the individual
layers being overlaid. As discussed earlier, a lot of work has been done on this
problem, with some tangible results.
Newcomer and Szajgin (1984) used probability theory to calculate error
accumulation through two map layers. They assumed that the two map layers
were dependent; that is, if we select a cell that is in error in layer 1 then that act
reduces the probability of selecting an erroneous cell from layer 2. If the data
layers are independent, then an erroneous cell selected from layer 1 does not
reduce the probability of selecting an incorrect cell from layer 2.
Using the statistics of Parratt (1961) with empirical data, Burrough (1986)
concluded that with two layers of continuous data, the addition operation is
unimportant in terms of error accumulation. The amount of error accumu-
lated by the division and multiplication operations is much larger. The largest
error accumulation occurs during subtraction operations. Correlated variables
may have higher error accumulation rates than noncorrelated data because
erroneous regions tend to coincide and concentrate error rates there.
The use of Bayesian logic for
GIS
overlaying is explained in Skidmore
(1989b). As with Boolean, arithmetic, and composite overlaying, there is
inherent error in the individual data layers when overlaying using Bayesian
logic. In addition, Bayesian overlaying uses rules to link the evidence to the
hypotheses; the rules have an associated uncertainty and are an additional
source of error.
