method. The spatial distributions of the block predicted values were similar to those
obtained using the PSCPS upscaling method (Figure 6.4b). But, all the differences of
the aggregated block predicted values by PSCBS from those by PSCPS were positive,
implying the PSCBS smoothed the block values more than the PSCPS, although
differences that ranged from 0 to 12.7 tons/ha with a mean of 4.9 tons/ha were
relatively small (Figure 6.4d). Because of the lack of field observations at the coarser
spatial resolution, this study was not able to verify which upscaling method led to
smaller root mean-square error for the aggregated block values.
Moreover, both upscaling methods PSCPS and PSCBS directly output the variances
of predicted values at the coarser spatial resolution of 990 m ´ 990 m (Figures 6.5a,b).
The spatial distributions of the block variances were similar to that of the block
predicted values (Figure 6.4c). That is, in the areas where the block predicted values
were greater, the variances of the block predicted values were also greater. However,
PSCBS (Figure 6.5b) resulted in smaller variances of the block values compared to
PSCPS (Figure 6.5a). Using the block predicted values and variances (Figure 6.4b vs.
Figure 6.5a, Figure 6.4c vs. Figure 6.5b), the coefficients of variation for the block
predicted values were calculated in Figure 6.5c for PSCPS and Figure 6.5d for PSCBS.
Both upscaling methods led to similar spatial distributions of variation coefficients of
the block values. Compared to the spatial distributions of the block predicted values
and variances, the spatial patterns of the variation coefficients showed up in an opposite
way. In the areas where the block estimates and variances were larger, the coefficients
of variation were smaller and vice versa. In addition, these upscaling methods also
produced the probability values for the block values larger than a given threshold value.
In Figures 6.5e for PSCPS and Figure 6.5f for PSCBS, as examples, the maps of
probability values for the block predicted values larger than the sample mean were
presented. In the areas where there were larger block predicted values, the probability
values for the predicted values larger than the sample mean were also higher.
6.5 CONCLUSIONS AND DISCUSSION
Combining sample plot data and remotely sensed images has been widely used to map
forest carbon stocks through spatial interpolation methods, including regression
modeling, neural network, and K-nearest neighbors. However, these methods lack
the ability to directly aggregate the spatial data and their uncertainties from a finer
spatial resolution to a coarser one when the sizes of forest inventory sample plots (i.e.,
30 m ´ 30 m) are inconsistent with the sizes of map units (i.e., 1 km ´ 1 km) that are
often required to map forest carbon stocks at regional, national, and global scales
(Wang et al., 2004b, 2009, 2011). More important is that these methods neglect the
spatial autocorrelation of variables and the propagation of input spatial uncertainties
across scales. Although various data aggregation methods have been developed, none
of them can be directly used to scale up the sample plot data and remotely sensed
images from a finer spatial resolution to a coarser one because the plot data are
available only at the sampled locations.
In this study, two upscaling methods developed by Wang et al. (2004b), PSCPS
and PSCBS, were demonstrated to map above-ground forest carbon stocks in Lin-An
120
UPSCALING WITH CONDITIONAL COSIMULATION FOR MAPPING
obtained using the PSCPS upscaling method (Figure 6.4b). But, all the differences of
the aggregated block predicted values by PSCBS from those by PSCPS were positive,
implying the PSCBS smoothed the block values more than the PSCPS, although
differences that ranged from 0 to 12.7 tons/ha with a mean of 4.9 tons/ha were
relatively small (Figure 6.4d). Because of the lack of field observations at the coarser
spatial resolution, this study was not able to verify which upscaling method led to
smaller root mean-square error for the aggregated block values.
Moreover, both upscaling methods PSCPS and PSCBS directly output the variances
of predicted values at the coarser spatial resolution of 990 m ´ 990 m (Figures 6.5a,b).
The spatial distributions of the block variances were similar to that of the block
predicted values (Figure 6.4c). That is, in the areas where the block predicted values
were greater, the variances of the block predicted values were also greater. However,
PSCBS (Figure 6.5b) resulted in smaller variances of the block values compared to
PSCPS (Figure 6.5a). Using the block predicted values and variances (Figure 6.4b vs.
Figure 6.5a, Figure 6.4c vs. Figure 6.5b), the coefficients of variation for the block
predicted values were calculated in Figure 6.5c for PSCPS and Figure 6.5d for PSCBS.
Both upscaling methods led to similar spatial distributions of variation coefficients of
the block values. Compared to the spatial distributions of the block predicted values
and variances, the spatial patterns of the variation coefficients showed up in an opposite
way. In the areas where the block estimates and variances were larger, the coefficients
of variation were smaller and vice versa. In addition, these upscaling methods also
produced the probability values for the block values larger than a given threshold value.
In Figures 6.5e for PSCPS and Figure 6.5f for PSCBS, as examples, the maps of
probability values for the block predicted values larger than the sample mean were
presented. In the areas where there were larger block predicted values, the probability
values for the predicted values larger than the sample mean were also higher.
6.5 CONCLUSIONS AND DISCUSSION
Combining sample plot data and remotely sensed images has been widely used to map
forest carbon stocks through spatial interpolation methods, including regression
modeling, neural network, and K-nearest neighbors. However, these methods lack
the ability to directly aggregate the spatial data and their uncertainties from a finer
spatial resolution to a coarser one when the sizes of forest inventory sample plots (i.e.,
30 m ´ 30 m) are inconsistent with the sizes of map units (i.e., 1 km ´ 1 km) that are
often required to map forest carbon stocks at regional, national, and global scales
(Wang et al., 2004b, 2009, 2011). More important is that these methods neglect the
spatial autocorrelation of variables and the propagation of input spatial uncertainties
across scales. Although various data aggregation methods have been developed, none
of them can be directly used to scale up the sample plot data and remotely sensed
images from a finer spatial resolution to a coarser one because the plot data are
available only at the sampled locations.
In this study, two upscaling methods developed by Wang et al. (2004b), PSCPS
and PSCBS, were demonstrated to map above-ground forest carbon stocks in Lin-An
120
UPSCALING WITH CONDITIONAL COSIMULATION FOR MAPPING