distribution varies and can be modeled using a beta or normal probability density
function (Hastings and Peacock, 1975), which leads to two upscaling methods called
the beta distribution simulation and the normal distribution simulation.
Using the upscaling methods, Wang et al. (2004a) scaled up Landsat TM images
from a pixel size of 30 m ´ 30 m to a coarser spatial resolution of 90 m ´ 90 m in
which field observations of the interest variables were available. The aggregated
images were then employed to map vegetation cover percentage that had a normal
distribution and infer a soil erosion relevant topographic factor that was characterized
by a reversed J-shape distribution. The results showed that the beta distribution
simulation method was the best regardless of the distributions of the spatial data. The
reason is mainly because the beta distribution simulation method has the strong ability
to accommodate the variable distribution.
All the upscaling methods mentioned previously can be applied to aggregate
spatial data of a map or image from a finer spatial resolution to a coarser one when
spatial data are available everywhere. However, when forest carbon is mapped by
combining forest inventory sample plot data and remotely sensed image, the plot data
only exist at the sample locations and cannot be directly aggregated by simply
calculating a window mean. First, field observations of interest variables are available
only at the sample plots that have finer spatial resolutions. Second, few or no plot data
may exist within a window that corresponds to the desirable coarser spatial resolution.
Third, the plot data have to be combined with remotely sensed images in order to
generate spatially explicit estimates of forest carbon at the unobserved locations, but
the relationships of the plot data with the used images may differ at the finer and
coarser spatial resolution, respectively (Simic et al., 2004; Wang et al., 2004b).
Moreover, when spatial data are scaled from a finer spatial resolution to a coarser one,
the uncertainties of the input data are propagated to the aggregated data. However, the
existing methods neglect modeling the propagation of the uncertainty to the coarser
spatial resolution. In addition, these methods also discard spatial dependency of
neighboring sample locations and image pixels.
Block cokriging in geostatistics can be used to generate spatially explicit estimates
of an interest variable at a coarser spatial resolution by combining sample plot data
and remotely sensed images at a finer spatial resolution. Using this method, Atkinson
and Kelly (1997) aggregated point snow depth data to larger blocks and at the same
time obtained the variances of the block estimates as a measure of uncertainty. This
implies that cokriging, to some extent, can meet some of the aforementioned
challenges. However, the cokriging variances vary depending on only the spatial
configuration of spatial data, not on the data values themselves. That is, the variances
do not really reflect the uncertainties of block estimates.
Wang et al. (2004b) developed and compared two spatial variability based
algorithms for scaling up vegetation cover percentage from a spatial resolution of
30 m ´ 30 m to a pixel size of 90 m ´ 90 m in the aid of TM images as secondary
variables. Both methods are based on a collocated simple cokriging estimator and a
sequential Gaussian cosimulation algorithm and take spatial autocorrelation of
variables into account in the upscaling process of spatial data. This makes it possible
to simultaneously and accurately obtain estimates and estimation variances of larger
INTRODUCTION
111
function (Hastings and Peacock, 1975), which leads to two upscaling methods called
the beta distribution simulation and the normal distribution simulation.
Using the upscaling methods, Wang et al. (2004a) scaled up Landsat TM images
from a pixel size of 30 m ´ 30 m to a coarser spatial resolution of 90 m ´ 90 m in
which field observations of the interest variables were available. The aggregated
images were then employed to map vegetation cover percentage that had a normal
distribution and infer a soil erosion relevant topographic factor that was characterized
by a reversed J-shape distribution. The results showed that the beta distribution
simulation method was the best regardless of the distributions of the spatial data. The
reason is mainly because the beta distribution simulation method has the strong ability
to accommodate the variable distribution.
All the upscaling methods mentioned previously can be applied to aggregate
spatial data of a map or image from a finer spatial resolution to a coarser one when
spatial data are available everywhere. However, when forest carbon is mapped by
combining forest inventory sample plot data and remotely sensed image, the plot data
only exist at the sample locations and cannot be directly aggregated by simply
calculating a window mean. First, field observations of interest variables are available
only at the sample plots that have finer spatial resolutions. Second, few or no plot data
may exist within a window that corresponds to the desirable coarser spatial resolution.
Third, the plot data have to be combined with remotely sensed images in order to
generate spatially explicit estimates of forest carbon at the unobserved locations, but
the relationships of the plot data with the used images may differ at the finer and
coarser spatial resolution, respectively (Simic et al., 2004; Wang et al., 2004b).
Moreover, when spatial data are scaled from a finer spatial resolution to a coarser one,
the uncertainties of the input data are propagated to the aggregated data. However, the
existing methods neglect modeling the propagation of the uncertainty to the coarser
spatial resolution. In addition, these methods also discard spatial dependency of
neighboring sample locations and image pixels.
Block cokriging in geostatistics can be used to generate spatially explicit estimates
of an interest variable at a coarser spatial resolution by combining sample plot data
and remotely sensed images at a finer spatial resolution. Using this method, Atkinson
and Kelly (1997) aggregated point snow depth data to larger blocks and at the same
time obtained the variances of the block estimates as a measure of uncertainty. This
implies that cokriging, to some extent, can meet some of the aforementioned
challenges. However, the cokriging variances vary depending on only the spatial
configuration of spatial data, not on the data values themselves. That is, the variances
do not really reflect the uncertainties of block estimates.
Wang et al. (2004b) developed and compared two spatial variability based
algorithms for scaling up vegetation cover percentage from a spatial resolution of
30 m ´ 30 m to a pixel size of 90 m ´ 90 m in the aid of TM images as secondary
variables. Both methods are based on a collocated simple cokriging estimator and a
sequential Gaussian cosimulation algorithm and take spatial autocorrelation of
variables into account in the upscaling process of spatial data. This makes it possible
to simultaneously and accurately obtain estimates and estimation variances of larger
INTRODUCTION
111