PNNL-13501 - Pacific Northwest National Laboratory

Figure 1. Ordinary kriging of 2 m data using 100 samples (upper left), 200 samples (upper right), and 400 samples (lower left).
The original 2 m imagery is shown in the lower right for comparison.
classes. The local mean used for each 2 m airborne pixel
was then determined by the corresponding landscape class
each pixel was situated in. The results of the Gaussian
simulation with locally varying means are shown in
Figure 2, as with the ordinary kriging, the simulations
were performed using 100, 200, and 400 samples.
Summary and Conclusions
The most significant result was our evaluation of three
methods for interpolating biomass data, and an estimation
of the number of samples required. This result is
summarized in Figure 3, which shows the root mean
square error for linear regression (top), Gaussian
simulation with locally varying means (middle), and
ordinary kriging (bottom) plotted as a function of the
number of 2 m samples used. For the 46-ha farmland site
that was evaluated, increasing the number of samples did
little to improve the regression error, but greatly improved
the simulation and kriging errors. Another result was that
the Gaussian simulation with locally varying means did
not provide an improved interpolation over the ordinary
kriging for this test site. We believe that this is a result of
what is referred to as the mixed pixel problem; that is, a
15 m satellite pixel is viewing several 2 m pixels of
222 FY 2000 Laboratory Directed Research and Development Annual Report
possibly differing targets or compositions. The mixed
pixel problem is inherent to almost any application with
spatial analysis applied to imagery at different scales. We
see this as edge effects in the test site. Figure 4 shows the
highest absolute errors for the simulated map occur near
field edges and roads. Boundary conditions such as roads
and field edges may cause different pixel classification in
the 15 m satellite imagery relative to the 2 m airborne
data. Thus, a 2 m pixel representing a road might actually
be categorized as field and assigned the local mean based
on that misclassification. These boundary conditions are
a challenge that could be explored in other datasets.
References
Goovaerts P. 1997. Geostatistics for natural resources
evaluation. Oxford University Press, New York.
Murray CJ, LL Cadwell, JL Downs, and MA Simmons.
1999. “Fusing vegetation data sets to provide a spatial
analysis of Sage Grouse habitat on the Army’s Yakima
Training Center.” In: ED McArthur, WK Ostler, and
CL Wambolt (eds.) Shrubland Ecotones; Proc. RMRS-P-
00. Ogden, Utah: U.S. Department of Agriculture, Forest
Service, Rocky Mountain Research Station.