Geoscience Reference
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exactly?), followed by reporting results for the full reference data as well as subsets of the data
defined by the location confidence rating. Readers may then judge the potential effect of positional
error by comparing accuracy at various levels of location confidence. A related approach would be
to report accuracy results separately for edge and interior pixels. An alternative approach is to
define agreement based on more information than comparing a single map pixel to a single reference
pixel. In the NLCD assessment, one definition of agreement used was to compare the reference
label of the sample pixel with a mode class determined from the map labels of the 3
3 block of
pixels centered on the nominal sample pixel (Yang et al., 2001). This definition recognizes the
possibility that the actual location used to determine the reference label could be offset by one
pixel from the location identified on the map.
Another important feature of a pixel-based assessment is to account for the minimum mapping
unit (MMU) of the map. When assigning the reference label, the observer should choose the LC
class keeping in mind the MMU established. That is, the observer should not apply tunnel vision
restricted only to the area covered by the pixel being assessed, but rather should evaluate the pixel
taking into account the surrounding spatial context. In the 1990 NLCD, the MMU was a single
pixel. It is expected that NLCD users may choose to define a different MMU depending on their
particular application, but the NLCD accuracy assessment was pixel-based because the base product
made available was not aggregated to a larger MMU.
The problems associated with positional error are largely specific to the response or measurement
component of the accuracy assessment (Stehman and Czaplewski, 1998). However, a few points
related to sampling design should be recognized. Although the MMU is a relevant feature of a map
to consider when determining the response design protocol, it is important to recognize that a MMU
does not define a sampling unit. A pixel, a polygon, or a 3
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3 block of pixels, for example, are all
legitimate sampling units, but a “1.0-ha MMU” lacks the necessary specificity to define a sampling
unit. The MMU does not create the unambiguous definition required of a sampling unit because it
permits various shapes of the unit, it does not include specification of how the unit is accounted
for when the polygon is larger than the MMU, and it does not lead directly to a partitioning of the
region into sampling units. While it may be possible to construct the necessary sampling unit
partition based on a MMU, this approach has never been explicitly articulated. When sampling
polygons, the basic methods available are simple random, systematic, and stratified (by LC class)
random sampling from a list frame of polygons. Less obvious is how to incorporate clustering and
spatial sampling methods for polygon assessment units. Polygons may vary greatly in size, so a
decision is required whether to stratify by size so as not to have the sample dominated by numerous
small polygons. A design protocol of locating sample points systematically or completely at random
and including those polygons touched by these sample point locations creates a design in which
the probability of including a polygon is proportional to its area. This structure must be accounted
for in the analysis and is a characteristic of polygon sampling that has yet to be discussed explicitly
by proponents of such designs. Most of the comparative studies of accuracy assessment sampling
designs are pixel-based assessments (Fitzpatrick-Lins, 1981; Congalton, 1988a; Stehman, 1992,
1997), and analyses of potential factors influencing design choice (e.g., spatial correlation of error)
are also pixel-based investigations (Congalton, 1988b; Pugh and Congalton, 2001).
Problems associated with positional error in accuracy assessment merit further investigation
and discussion. Although it is easy to dismiss pixel-based assessments with a “you-can't-find-a-
pixel” proclamation, a less superficial treatment of the issue is called for. Edges are a real charac-
teristic of all LC maps, and the accuracy reported for a map should account for this reality. Whether
the assessment is based on a pixel or a larger spatial unit, the accuracy assessment should confront
the edge feature directly. Although there is no perfect solution to the problem, options exist to
specify the analysis or response design protocol in such a way that the effect of positional error
on accuracy is addressed. Sampling in a manner that permits evaluating the effect of positional
error seems preferable to sampling in a way that obscures the problem (e.g., limiting the sample
to homogeneous LC regions)
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