Geoscience Reference
In-Depth Information
Table 14.1
Accuracy Ranks Assigned to the Reference Data of the AZ-GAP Land-Cover Map
Rank
Answer
Description
1
Wrong
The reference and map types did not correspond, and there was no ecological
reason for the noncorrespondence.
2
Understandable
but Wrong
The reference and map types did not correspond, but the reason for non-
correspondence was understood
a
.
3
Reasonable or
Acceptable
The reference and map types were all the same life form (i.e.,
formation types
b
).
4
Good
The reference and map types were characterized by the same species at the
dominant species level.
5
Absolutely
Right
The reference and map types were exactly the same.
a
These reasons include vegetation types that are ecotonal and/or vegetation types that can occur as inclusions
within other vegetation types.
b
Tundra, Coniferous Forest, Evergreen Woodland, Chaparral, Grasslands, Desert Scrub, Riparian Broadleaf
Woodland/Forest, Riparian Leguminous Woodland/Forest, Riparian Scrub, Wetlands, Water, and Developed.
Increase (R - M)
=
difference between the Right and Max functions
The Max (M) function calculated the same information as user's accuracy in a binary assess-
ment. The Right (R) function allowed reasonable and better answers to be counted. For this study,
the R function calculated the accuracy of the LC map to the life form level or better. The Increase
(R - M) function reflected the improvement in accuracy associated with using the R function instead
of the M function. Since the Gopal-Woodcock (1994) fuzzy set assessment was altered to save
time in the field, certain data for calculating membership, difference, ambiguity, and confusion
statistics were not collected.
14.3.4
Spatial Analysis
The nature of the accuracy ranks were explored by calculating the mean, median, and mode,
and a histogram was plotted. The points were mapped to display the accuracy rank and location of
the data. Interpolating the accuracy ranks produces a continuous map of thematic accuracy. Kriging
was data driven and exploited the spatial autocorrelation exhibited by the data. An ordinary kriging
regression technique for estimating the best linear unbiased estimate of variables at an unsampled
location was applied to reduce the local variability by calculating a moving spatial average.
The kriging interpolation produces continuous values even though the accuracy ranks are
ordinal. However, a value between two of the ranks is meaningful, and this suggests that the kriged
results are also meaningful. For example, a value between “reasonable or acceptable” and “good”
can be characterized as “reasonably good.”
The first step in the kriging process was to calculate the empirical variogram, or an analogous
measure of the spatial autocorrelation present in the data. The variogram is one of the most common
measures of spatial autocorrelation used in geostatistics. It is calculated as 0.5 the average difference
squared of all data values separated by a specified distance (lag):
1
Â
2
(14.1)
g ()
h
=
(
zz
i
-
)
j
2
|
Nh
()|
Nh
()
where
h
= distance measure with magnitude only,
N(h)
= set of all pair-wise Euclidean distances
i
-
j = h
,
|N(h)|
= number of distinct pairs in
N(h)
, and
z
and
z
= fuzzy set ranks at spatial locations
i
j
.
For the accuracy ranks in this study, we chose to use a modified version of the variogram to
calculate the empirical variogram, as follows (Cressie and Hawkins, 1980):
i
and
j
