【正文】 s (about 10%, 40%, 60%, and 90%) and two levels of spatial autocorrelation (low with Moran39。s I and high with Moran39。s I ). The Moran39。s I correlogram for the four simulated map is shown in Fig. 2.Fig. 1. Simulated spatially auto correlated reference maps:(a) high spatial autocorrelation and high class proportion difference (H91)。 (b) high spatial autocorrelation and low class proportion difference (H46)。 (c) low spatial autocorrelation and high class proportion difference (L91)。(d) low spatial autocorrelation and low class proportion difference (L46).Class 1 in dark and Class 2 in white.Table 1Parameters of simulated reference mapsSimulated mapautocorrelation (Moran39。s I)Class 1Class 2H91H46L91L460..42The reason simulated images were used instead of real images is that a series of classified and reference images with controlled levels of spatial autocorrelation and class proportion are difficult to obtain, especially the reference maps. In real images, it is hard to control the spatial autocorrelation and error percentage, which will make systematic analysis difficult. Through simulated images, we can control the level of spatial autocorrelation and produce constant errors across all images. In this way, any differences in the output are due to only the changes in the controlled factors.. Injection of classification errorsPrevious studies stated that erroneous allocations made by a classification are not randomly distributed over thematic maps (Bian and Butler, 1999。 Congalton, 1988b). Often there is a distinct pattern to the spatial distribution of thematic errors arising from the sensor39。s properties (Foody, 2002。 Plourde and Congalton, 2003), and/or ground conditions with the errors spatially correlated at the class boundaries (Congalton, 1988b。 Edwards and Lowell, 1996。 Powell et al., 2004。 Steele et al., 1998). Most errors occurring at the boundaries are associated with mis registration of the data sets and mixed pixels. Based on the above considerations, errors were injected into areas near the class boundaries on the simulated maps used in this study using a frequency distribution model. On each map, about 20% of errors were injected as classification errors, which can often occur in supervised and unsupervised image classifications. The injected error patterns on different maps are shown in Fig. 3. The maps with injected errors were treated as classified maps and the original maps without injected errors were treated as reference maps. The detailed classification errors and accuracy measures for each classified map are listed in Table 2, where Class 12 and Class 21 represent injected errors of class 1 to class 2 and class 2 to class 1, respectively, while correctly classified class 1 and class 2 are expressed as Class 11 and Class 22.Fig. 2. Correlogram of four simulated reference maps (xaxis: lag distance, unit with pixels。 yaxis: spatial autocorrelation level measured with Moran39。s I). (H46: high autocorrelation and low class proportion difference。 H91: high autocorrelation and high class proportion difference。 L46: low autocorrelation and low class proportion difference。 and L91: low autocorrelation and high class proportion difference.)Table 2Parameters of simulated maps with injected errorsSimulated mapClass 11proportionClass 22proportionClass 12proportionClass 21proportionOverallaccuracyKappacoefficientH91H46L91H96(Class 11: correctly classified class 1。 Class 22: correctly classified class 2。 Class12: injected errors of class 1 to class 2。 and Class 21: injected errors of class 2 to class 1。 H91: map with high autocorrelation and high class proportion difference。 H46: map with high autocorrelation and low class proportion difference。 L91: map with low autocorrelation and high class proportion difference。 L46: map with low autocorrelation and low class proportion difference.)Fig. 3. Injected classification error (shown in white) patterns in different maps: (a) high spatial autocorrelation and high class proportion difference (H91)。 (b) high spatial autocorrelation and low class proportion difference (H46)。 (c) low spatial autocorrelation and high class proportion difference (L91)。 and (d) low spatial autocorrelation and low class proportion difference (L46).. SamplingAfter the classified maps and reference maps were simulated, three sampling methods (simple random sampling (SRS), systematic sampling (SYS), and stratified random sampling (StrRS)) were implemented within the ArcGIS environment. The individual pixel, the mon sampling unit for maps generated from remote sensing, was used. Each of the three sampling methods was simulated 100 times for each map using eleven different sample sizes ranging from a minimum of 25 to a maximum of other words, the simulation was repeated 100 times to examine the stability of accuracy measures. The number of simulations was chosen as a tradeoff between statistical stability and putation cost. From a statistical point of view, 30 simulations should be sufficient to provide statistical confidence (Bian and Butler, 1999。 Openshaw and Alvanides, 1999). It should be noted that the maximum sample size used here was only about % of the total pixels, which is much smaller than the maximum percentage of the population sampled in the studies of Congalton (1988b) and Stehman (2000).Simple random sampling (SRS) selected each sampling pixel independently and randomly without replacement (Congalton, 1988b). In SRS sampling, every pixel had the same probability of being selected. In systematic sampling (SYS), only the first sampling pixel was randomly chosen and all other sampling pixels were selected at fixed intervals from the initial pixel (Congalton, 1988b). The interval used in the SYS was a function of the sample size. SYS distributes samples evenly in space. In the stratifi