when spatial data were scaled up, coefficients of correlation between variables varied
greatly depending on the number and size of area units. This implies that any results
and conclusions from studies are dependent on the spatial resolutions that are used and
can be described by the widely known modifiable area unit problem (MAUP)
(Openshaw and Taylor, 1979). The MAUP means that different results can be
obtained when data are aggregated from a finer spatial resolution to a coarser one.
Given a spatial resolution to create the output maps, different upscaling methods can
also lead to different results. Spatial patterns of forest carbon are related to the used
spatial resolutions and upscaling methods to map it. The spatial patterns may show up
in an optimal spatial resolution but disappear in others (Wang et al., 2008). Given the
optimal spatial resolution, on the other hand, the spatial patterns may be captured by
one upscaling method but missed by others. Thus, developing an accurate upscaling
method for multiple-resolution analysis and spatial data aggregation is becoming very
important to detect the spatial patterns of forest carbon, its dynamics over time, and its
relationships with spatial resolutions (Marceau, 1999; Marceau and Hay, 1999;
Pontius and Cheuk, 2006; Wang et al., 2009; Wu and Qi, 2000).
There are several widely used methods to scale up spatial data of a variable across
scales (Jarvis, 1995; Marceau and Hay, 1999; Moellering and Tobler, 1972; Wu,
1999). The simplest method is the nearest neighbor. If a pixel at a coarser spatial
resolution is regarded as a block that consists of smaller pixels, the nearest-neighbor
method assigns the block with the value of the smaller pixel close to the block center.
Obviously, this method misses the dominant feature determined by a distribution of
values of smaller pixels within a block and may lead to the disappearance of the
dominant pattern and process.
Window or block averaging is also a simple and widely used upscaling method. In
this method, a mean value from the smaller pixels within the window or block is
calculated and assigned to this block. This method is accurate and straightforward to
aggregate spatial data from a finer spatial resolution to a coarser one. But it is assumed
that the values of pixels have a normal distribution and linear relationships of spatial
features exist when the spatial data are scaled up from a finer to a coarser resolution. In
fact, the window averaging is a specific case of window filtering, that is, when the
weight used for all the pixels within the window is the same. On the other hand, a
different weight for each pixel can be used, which leads to various window-weighted
averaging methods.
Wang et al. (2004a) pointed out that the key to accurately infer spatial information
from a finer spatial resolution to a coarser one is to capture dominant spatial features,
patterns, and processes of an interest variable. If equal weights are given to each pixel
within a window, the window averaging method neglects the differences in the spatial
autocorrelation between the pixel values. If normal distribution of data does not hold,
a window average will lead to a misinterpretation of dominant spatial features. A
typical example is that few extremely large values within a window will impede the
window averaging method to capture the dominant feature. In addition, in this method
it is assumed that the values of smaller pixels within each block are available.
Combining forest inventory sample plot data and remotely sensed images to map
forest carbon is not the case.
INTRODUCTION
109
greatly depending on the number and size of area units. This implies that any results
and conclusions from studies are dependent on the spatial resolutions that are used and
can be described by the widely known modifiable area unit problem (MAUP)
(Openshaw and Taylor, 1979). The MAUP means that different results can be
obtained when data are aggregated from a finer spatial resolution to a coarser one.
Given a spatial resolution to create the output maps, different upscaling methods can
also lead to different results. Spatial patterns of forest carbon are related to the used
spatial resolutions and upscaling methods to map it. The spatial patterns may show up
in an optimal spatial resolution but disappear in others (Wang et al., 2008). Given the
optimal spatial resolution, on the other hand, the spatial patterns may be captured by
one upscaling method but missed by others. Thus, developing an accurate upscaling
method for multiple-resolution analysis and spatial data aggregation is becoming very
important to detect the spatial patterns of forest carbon, its dynamics over time, and its
relationships with spatial resolutions (Marceau, 1999; Marceau and Hay, 1999;
Pontius and Cheuk, 2006; Wang et al., 2009; Wu and Qi, 2000).
There are several widely used methods to scale up spatial data of a variable across
scales (Jarvis, 1995; Marceau and Hay, 1999; Moellering and Tobler, 1972; Wu,
1999). The simplest method is the nearest neighbor. If a pixel at a coarser spatial
resolution is regarded as a block that consists of smaller pixels, the nearest-neighbor
method assigns the block with the value of the smaller pixel close to the block center.
Obviously, this method misses the dominant feature determined by a distribution of
values of smaller pixels within a block and may lead to the disappearance of the
dominant pattern and process.
Window or block averaging is also a simple and widely used upscaling method. In
this method, a mean value from the smaller pixels within the window or block is
calculated and assigned to this block. This method is accurate and straightforward to
aggregate spatial data from a finer spatial resolution to a coarser one. But it is assumed
that the values of pixels have a normal distribution and linear relationships of spatial
features exist when the spatial data are scaled up from a finer to a coarser resolution. In
fact, the window averaging is a specific case of window filtering, that is, when the
weight used for all the pixels within the window is the same. On the other hand, a
different weight for each pixel can be used, which leads to various window-weighted
averaging methods.
Wang et al. (2004a) pointed out that the key to accurately infer spatial information
from a finer spatial resolution to a coarser one is to capture dominant spatial features,
patterns, and processes of an interest variable. If equal weights are given to each pixel
within a window, the window averaging method neglects the differences in the spatial
autocorrelation between the pixel values. If normal distribution of data does not hold,
a window average will lead to a misinterpretation of dominant spatial features. A
typical example is that few extremely large values within a window will impede the
window averaging method to capture the dominant feature. In addition, in this method
it is assumed that the values of smaller pixels within each block are available.
Combining forest inventory sample plot data and remotely sensed images to map
forest carbon is not the case.
INTRODUCTION
109