blocks from the sample and image data of finer spatial resolution. In both methods, it
is assumed that an interest variable is a random process, its values at any locations are
realizations of the variable, and they can be obtained by calculating conditional
distributions and generating random numbers from the distributions. The first method
developed by Wang et al. (2004b) creates the conditional distributions and estimates
of the variable at a finer spatial resolution that is consistent with those of the used
sample plot and image data, and the estimates at a coarser spatial resolution are then
calculated using the window averaging method. The second method by Wang et al.
(2004b) directly generates conditional distributions and estimates of this variable at
blocks, a coarser spatial resolution, using the sample plot and image data at a finer
spatial resolution. The former is called point simple cokriging point cosimulation
(PSCPS), while the latter is called point simple cokriging block cosimulation
(PSCBS).
Both simulation-based upscaling methods overcome the gaps mentioned previously. Wang et al. (2004b) pointed out that the methods worked very well for multiple
continuous variables that had any distribution and how to choose them depends on
the users’ emphasis on accuracy of estimates and variances and computational time.
The objective of this study is to further assess and compare these two methods to
create maps of above-ground forest carbon at a spatial resolution of 990 m ´ 990 m
using forest inventory sample plot data and TM images at a spatial resolution of
30 m ´ 30 m. This selected coarser spatial resolution is desirable partly because it is
close to 1 km ´ 1 km, a widely used map unit size for mapping forest carbon at
regional, national, and global scales, and partly because it is a window of 33 ´ 33
pixels of the original spatial resolution 30 m ´ 30 m and can be easily obtained. The
above-ground forest carbon is the carbon equivalent of the above-ground tree
biomass, including standing trees and deadwoods, but not stumps and ground
vegetation. It is expected that this study can provide some suggestions and guidelines
on how to use national forest inventory plot data collected at smaller permanent
sample plots to generate forest carbon maps at any coarser spatial resolutions for large
regions, nations, and even the whole world.
6.2 METHODS
Wang et al. (2004b) introduced both PSCPS and PSCBS upscaling methods in detail.
In this study, they were briefly described. The first part of PSCPS deals with the
generation of forest carbon pixel values using a sequential Gaussian cosimulation
algorithm in which the sample plot data and remotely sensed images have consistent
spatial resolution with the output forest carbon maps. Because of this, the pixels to be
predicted are regarded as points. First of all, the cosimulation divides a study area into
square cells or pixels and follows a random path to visit the pixels. The random path is
determined using a random-number generator. At each pixel, a neighborhood is set up
based on the maximum distance of the spatial autocorrelation of above-ground forest
carbon that is modeled by a variogram model. A collocated simple cokriging unbiased
estimator is employed to create a conditional mean and a conditional variance of the
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UPSCALING WITH CONDITIONAL COSIMULATION FOR MAPPING
is assumed that an interest variable is a random process, its values at any locations are
realizations of the variable, and they can be obtained by calculating conditional
distributions and generating random numbers from the distributions. The first method
developed by Wang et al. (2004b) creates the conditional distributions and estimates
of the variable at a finer spatial resolution that is consistent with those of the used
sample plot and image data, and the estimates at a coarser spatial resolution are then
calculated using the window averaging method. The second method by Wang et al.
(2004b) directly generates conditional distributions and estimates of this variable at
blocks, a coarser spatial resolution, using the sample plot and image data at a finer
spatial resolution. The former is called point simple cokriging point cosimulation
(PSCPS), while the latter is called point simple cokriging block cosimulation
(PSCBS).
Both simulation-based upscaling methods overcome the gaps mentioned previously. Wang et al. (2004b) pointed out that the methods worked very well for multiple
continuous variables that had any distribution and how to choose them depends on
the users’ emphasis on accuracy of estimates and variances and computational time.
The objective of this study is to further assess and compare these two methods to
create maps of above-ground forest carbon at a spatial resolution of 990 m ´ 990 m
using forest inventory sample plot data and TM images at a spatial resolution of
30 m ´ 30 m. This selected coarser spatial resolution is desirable partly because it is
close to 1 km ´ 1 km, a widely used map unit size for mapping forest carbon at
regional, national, and global scales, and partly because it is a window of 33 ´ 33
pixels of the original spatial resolution 30 m ´ 30 m and can be easily obtained. The
above-ground forest carbon is the carbon equivalent of the above-ground tree
biomass, including standing trees and deadwoods, but not stumps and ground
vegetation. It is expected that this study can provide some suggestions and guidelines
on how to use national forest inventory plot data collected at smaller permanent
sample plots to generate forest carbon maps at any coarser spatial resolutions for large
regions, nations, and even the whole world.
6.2 METHODS
Wang et al. (2004b) introduced both PSCPS and PSCBS upscaling methods in detail.
In this study, they were briefly described. The first part of PSCPS deals with the
generation of forest carbon pixel values using a sequential Gaussian cosimulation
algorithm in which the sample plot data and remotely sensed images have consistent
spatial resolution with the output forest carbon maps. Because of this, the pixels to be
predicted are regarded as points. First of all, the cosimulation divides a study area into
square cells or pixels and follows a random path to visit the pixels. The random path is
determined using a random-number generator. At each pixel, a neighborhood is set up
based on the maximum distance of the spatial autocorrelation of above-ground forest
carbon that is modeled by a variogram model. A collocated simple cokriging unbiased
estimator is employed to create a conditional mean and a conditional variance of the
112
UPSCALING WITH CONDITIONAL COSIMULATION FOR MAPPING