The next step is to identify exactly which distance (d) produces the Maximum Gj*. If the Max Gj* is found at a small distance (d= 1 kernel), then spatial dependence is local and similar values are found within close proximity. If Max Gj* occurs at a greater distance(d>1 kernel), then similar pixel values can still be found when larger distances are considered: the spatial dependence is not local. A single binary image for each SPOT band can be used to visualize the spatial autocorrelation (Figure 5). Interpretation of the images in Figure 5 reveals areas that have shifted from a relatively heterogeneous to a homogeneous surface as well as areas that have shifted from a relatively homogeneous to a heterogeneous surface. Examination of the "distance" images for SPOT band 1 reveals that the shallow coral reef area in the south west quadrant has shifted from a relatively heterogeneous healthy reef to a more homogeneous algae-dominated reef, which is confirmed by our observations during field data collection in 1997 and 2000.

The purpose of such an examination is not to identify the specific substrate, but rather to identify regions that have shifted from a heterogeneous surface to a more homogeneous surface, and vice versa. This type of change detection can be done quickly and without the need for extensive field verification, which enables information to be relayed to appropriate decision makers and resource managers for further examination and appropriate action.

Conclusions
There is little qualitative difference between in situ reflectance values of various substrates collected at depth in a coral reef environment, which indicates that interpretation of remotely sensed imagery may yield inaccurate classification results. Significant mixing of several different substrate types within the relatively large pixels of SPOT HRV images (20x20m) compounds the issue of classification inaccuracy. Other complicating factors include the effects of attenuation and multiple scattering from the overlying water column (Holden and LeDrew, In Press), refraction of light at the air-water interface, scattering and absorption in the atmosphere, and effects of the variable morphology of the substrate with respect to slopes and self-shading.

The interpretation of a derived spatial autocorrelation image based on the Getis Statistic is a simple matter of understanding the series of basic calculations. A measure of spatial autocorrelation, Gj*, is calculated for the central pixel of kernels of increasingly larger size; following this, a single image is compiled whereby for each pixel, for each band, the largest value of Gj* is assigned (Max Gj*). This image reveals the actual value of the Max Gj* for each pixel whereby the magnitude of Gj* provides the interpreter with information regarding the magnitude of reflectance of the particular cluster. The final step in the process is to answer the question: at which distance, or kernel size, is the Max Gj* found? This information allows the interpreter to take the analysis one step further and determine if the spatial dependence is local or spatially extensive. The interpreter can determine the degree of spatial dependence based on the distance at which the Max Gj* is found such that if it is found when the kernel size is small (d= 1) then dependence is local in nature, but if it is found with the kernel is large(d>1), then dependence is not as local and can be considered spatially extensive. This provides the information for the interpreter to infer if the degree of homogeneity or heterogeneity extends over a large or a small area. The main benefits of this approach are that it results in an increased dynamic range of pixel values; it creates an image in which the values are normally statistically distributed; and produces an easily interpretable image to be used as an effective visualization tool.

The case study utilizing readily available satellite imagery based on spatial autocorrelation has produced encouraging results. The next stage will be to operationally use change in spatial autocorrelation to evaluate management decisions within Bunaken National Marine Park, North Sulawesi, Indonesia. For example, zones of limited use have been defined for the park such as "No Take" and "Recreational Use" and it would be useful to know the extent to which these zones are aiding reef recovery or resulting in reef degradation. This approach to image analysis is appropriate for change detection such that the interpreter can determine (1) the degree of spatial autocorrelation (whether homogeneous or heterogeneous), and (2) the area affected (whether spatially extensive, or local in nature). This approach is superior to change detection based on magnitude of reflectance alone because of the value added information of spatial autocorrelation.

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