Methods
Measures of spatial autocorrelation indicate the strength of the relationship between values of the same variables, and may be either global or local in nature (Goodchild, 1986). Global measures provide a single value that indicates the level of spatial autocorrelation within the variable distribution, while local measures provide a value for each location within the variable distribution. Local indicators of spatial autocorrelation, such as the Getis statistic used here, are therefore able to identify discrete spatial patterns that may not otherwise be apparent by quantifying the spatial dependence between each pixel and a surrounding kernel of defined pixel dimensions (Wulder and Boots, 1998). The Getis Statistic was first developed for application to point data, and has proven appropriate for identifying spatial "hotspots" (Getis and Ord, 1992). One form of the Getis statistic, Gi * , has been modified and successfully applied to analysis of remotely sensed data at a range of spatial scales (Wulder and Boots, 1998; Derksen et al., 1998). The calculation of G I * using predefined window sizes surrounding a central pixel make it suitable for investigating the distance at which maximum spatial autocorrelation occurs. For its first application to remotely sensed imagery, Wulder and Boots (1998) provide a thorough description of G I * , and conclude that its ability to assess the strength of inter-pixel relationships, as well as the magnitude of spatial autocorrelation is valuable for digital image analysis. The equation for G I * is:



where ?j wij(d)xj is the sum of the variates within distance d of observation i (including i), W*I is the count of the pixels within distance d of pixel i, x is the mean, s is the global standard deviation, and n is the total number of observations. The output values from the above equation can be interpreted similar to standardized Z scores. The largest Gj* value for all distances (d) considered represents the maximum spatial autocorrelation. If the maximum Gj* occurs when the window size is small (i.e. 3x3 pixels), then maximum autocorrelation covers a small area, but if maximum Gj* corresponds to a large window size (i.e. 9x9pixels), then maximum autocorrelation extends to a larger area. A cluster of high pixel values isrepresented by a large positive Gj* value, while a cluster of low pixel values is indicated by a lower Gj* value.

SPOT HRV imagery (August 1997 and July 2000) of Bunaken National Marine Park, North Sulawesi, Indonesia is used for the case study based on spatial autocorrelation. A common subset of a coral reef within the park was selected from the atmospherically corrected and georeferenced image for the case study corresponding to a region in which extensive fieldwork was performed. For each SPOT band, four distances were considered in the calculation of Gj*: d=1, d=2, d=3, and d=4, representing increasingly larger kernels or windows. These distances refer to window sizes of 3x3, 5x5, 7x7, and 9x9 respectively. The resultant Gj* values for each pixel are compared and the largest value retained to Compile a Max Gj* image: the larges Gj* value for all distances represents the maximum spatial autocorrelation. A general overview of the spatial dependence characteristics of the data is provided by this Max Gj* image, which illustrates clusters of high and low digital numbers. Next, for each pixel, the distance at which the Max Gj* occurs is identified; for pixels where Max Gj*occurs at d= 1, spatial dependence is local and the region can be considered heterogeneous, and for pixels where Max Gj* occurs atd>1, spatial dependence is not local therefore the region can be considered homogeneous.

Results
Because identification of specific substrate type may not be the most appropriate and reliable use of available coarse spatial and spectral resolution satellite images, an alternative approach is needed to address the immediate problem of rapidly changing coral reef ecosystems worldwide to aid management of resources. The approach that is tested here is one based on spatial autocorrelation. The hypothesis is that a healthy reef will display relatively great spatial heterogeneity due to the diverse bottom types and benthic habitats, but an unhealthy coral reef will display spatial homogeneity if it is bleached or colonized by macroalgae. This indirect approach to evaluating the overall well being of coral reef ecosystems has the strength of allowing quick and straight forward change detection based on increasing or decreasing diversity/heterogeneity of bottom cover and is not reliant upon substrate identification.

For each band of the SPOT imagery, a series of calculations must be performed to use the Getis statistic to investigate the spatial autocorrelation within the region of interest. The first examination will be of the derived Max Gj* value, which is determined by finding the largest Gj* value among those calculated for the four distances (d=1, d=2, d=3, and d=4) for each pixel. This derived image is found by comparing Gj* for all kernels and assigning the largest value of Gj* to the central pixel of the kernel. A high Max Gj* magnitude indicates a cluster of high digital number values, while a low Max Gj* magnitude indicates a cluster of low digital number values. Max Gj* results for SPOT bands 1 and 2 of the 1997 and 2000 imagery of Bunaken Marine Park are shown in Figure 4 (SPOT band 3 is excluded due to its comparative inability to penetrate the water). The land is masked out of the subscene (shown in black in Figure 4) and not included in the calculations.

The largest Gj* value (i.e. Max Gj*) for all distances represents the maximum spatial autocorrelation such that a cluster of large positive Gj* values reveals high pixel values while a cluster of lower Gj* values reveals low pixel values. For both years, there is great homogeneity observed over the deep-water areas indicated by the extensive Gi* values of zero. There are observable clusters of relatively high Gj* values (Gj* > 37) indicating a conglomeration of high digital number pixel values; this area corresponds to a shallow water zone, which is often exposed at low tide and consists of highly reflective sand and dead coral debris. Surrounding the land mass is a zone of moderate Gj* values (20 < Gj* < 37) revealing areas of maximum spatial autocorrelation between midrange digital numbers; this zone contains healthy coral and a great diversity of benthic habitats.