Geoscience Reference
In-Depth Information
Ordinary kriging was performed on the fuzzy set reference data. The model and parameters
were selected to produce a regularly spaced lattice of points representing accuracy ranks. Kriging
predicted continuous (rather than ordinal) accuracy ranks ranging from one to five. The resulting
tabular file of coordinate locations and predicted accuracy ranks was converted to a grid format,
with predicted accuracy rank as the value of each 1-km
cell. The result is a fuzzy spatial view of
accuracy, a map of predicted accuracy ranks for northern Arizona. The continuous accuracy rank
estimates were rounded into ordinal ranks for ease of interpretation and display. A frequency
histogram was produced from the predicted accuracy ranks.
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14.4 RESULTS
14.4.1
Binary Analysis
User's and producer's accuracies for each cover type and overall accuracy were low (Table
14.2). The highest producer's accuracies were for anthropogenically defined cover types industrial
(60%) and mixed agriculture/urban/industrial (80%). Producer's accuracies for natural cover types
ranged between zero and 50%; the best performers were Encinal mixed oak/mixed chaparral/semi-
desert grassland - mixed scrub (50%) and Mohave blackbush - Yucca scrub (50%). Likewise, the
highest user's accuracies were also for anthropogenically defined cover types urban (91%) and
industrial (86%). Natural cover types ranged between 0 and 48.3%; the best performer was Engel-
mann spruce - mixed conifer (48.3%). The standard error was
<
5% for almost all sampled
vegetation types, and overall map accuracy was 14.8%.
14.4.2
Fuzzy Set Analysis
The Max statistic for the fuzzy set reference data yields the same information as user's accuracy
for the binary accuracy assessment (Table 14.3). However, the R function provided a different view.
Accuracy improves across the table for all cover types because the R function was more inclusive
than the M function. For example, in cover class 18 (ponderosa pine - pinyon - juniper), the M
statistic indicates this type has very low accuracy (5%). The R statistic indicated that when assessed
at the life-form level it was 74% correct. The range for R statistics was large, between 0 and 100%.
However, the cover types were more often correct to the life form (mean 52.7% ± 33.4%) compared
to the M statistic (mean 13.8% ± 18.8%). The mean increase in accuracy when viewed at the life
form level was 38.8% ± 31.5%.
14.4.3
Spatial Analysis
The accuracy ranks had a mean and median near 3.0 with a large standard deviation; however,
the mode did not correspond to the mean and median (Figure 14.2). The distribution had a fairly
broad shape but is mostly symmetrical. The fuzzy set reference data (Figure 14.3) illustrated classic
signs of being positively spatially autocorrelated at shorter distance separations (Figure 14.4 and
Figure 14.5). This was substantiated by the lower variance values at shorter lag distances. Also,
the variance values seem to reach a plateau at a lag distance where they become uncorrelated. The
empirical variogram was best fit with a spherical model (Figure 14.4). The parameters were
iteratively changed to achieve a low residual sum of squares and resulted in a nugget of 0.6638,
sill of 1.4081, and range of 22.6 km.
The spherical model and parameters were used to determine the weights in the kriging equations.
The predicted accuracy ranks produced from kriging do not reach the extremes of “wrong” and
