The Application of the Getis Statistic to High Resolution Imagery to Detect Change in Tropical Corals Ellsworth F. LeDrew, Alan Lim Faculty of Environmental Studies University of Waterloo

Healthy Coral and Sun Anemones

Coral Reefs = Rainforests of the Sea

Coral Bleaching % Permanently Damaged

Research Issues  Remote Sensing corrections for water - minus –Refraction at surface in and out –Attenuation of signal with depth –Variation of Attenuation with Wavelength –Effect of Bottom Material  Explore Change Detection Procedure that Overrides these concerns - for the same window, the spatial pattern of depth is constant

Research Strategy  Use a Statistic of Spatial Homogeneity - the Getis Statistic is One of Many  If There is No Change Between Image Dates, There will be No Change in Spatial Homogeneity  If There is an Increase in Stress, It is Probable that Spatial Homogeneity will Increase (e.g. massive bleaching or algae invasion)  A Change in the Getis Statistic Between Image Dates will Indicate the Degree of Change in Spatial Homogeneity

The Getis Statistic  The Getis statistic (G i *) provides the strength of pixel association within a region of spatial dependence.  Computation of G i * generates values which relate to variations within patterns of spatial dependence.  large positive G i * values denote a cluster of high DN values; large negative G i * values denote a cluster of low DN values.  Similar G i * values indicate a region of similar underlying spectral conditions

Getis Statistic Computation  G i * is computed as follows:  Where: –w ij (d) is a spatial weight matrix W i * is the sum of the weights matrix x is the mean of the entire image s is the standard deviation of the entire image n is the number of image pixels

The Getis Calculations  Getis statistic calculated at four distances: d=1 (3 X 3), d=2 (5 X 5), d=3 (7 X 7), d=4 (9 X 9)  Maximum Getis for all windows is retrieved, as well as distance ‘d’  Plot Maximum Getis to view spatial patterns of spatial dependence: subtract two dates to determine change in spatial dependence  Calculate change in distance between two dates to test homogeneity vs heterogeneity hypothesis: –if Maximum Getis Distance (MGD) increases over time, homogeneity increases, –if MGD decreases over time, heterogeneity increases.

Case Studies  Savusavu, Fiji, Spot imagery for 1994 and 1996 –Open Water- no change benchmark –Two Major Cyanide damaged reefs –Not anniversary dates: June and October  Bunaken and Siladen, Indonesia –Spot Imagery for 1990, 1994, 1997, 2000 –Ikonos Imagery for 2001 –All anniversary dates in July –Siladen: only native use –Bunaken: Tourism  Palau, 0.6 m Aerial Photography, 1992, 1997, 2002 –Damsel Fish manicured algae farms

Bunaken Region Spot Image, July 31, 1994 MARINE RAPID ASSESSMENT PROGRAM IN THE BUNAKEN NATIONAL MARINE PARK, NORTH SULAWESI Roeroe, Allard,Yusuf 2000 Red= Science Pink= Water Support Green= Native Use Blue= Tourist

July 14 SPOT 2000 Max GetisJuly 27 SPOT 1990 Max Getis West Bunaken

The Change in Maximum Getis Distance for Fiji

The Change in Maximum Getis Distance for Bunaken

July 14 SPOT 2000 Max Getis June 29 Ikonos 2001 Max Getis West Bunaken

DIFFERENCES IN REAL AND SYNTHETIC SPATIAL RESOLUTION : Siladen

Palau

High spatial resolution (0.6m) digital aerial imagery of the Damsel Fish Farm on a coral reef in Palau for 1992, 1997, Arrow points towards Damsel Fish Manicured Algae Turf for 92 and 97 and lack of Algae for 2002

The Change in Maximum Getis Distance for Palau Damsel Fish Site

The Kolmogorov-Smirnov Statistics for the Shape Difference in Cummulative Histograms of the Temporal Difference in the Getis Statistic. The Critical Value at 0.99 is For example, Damaged Reef A is NOT significantly different from Damaged Reef B Between 1994 and 1996, but the Difference between 1992 to 1997 of the Ngedarrach Reef IS Significantly Different from the difference from 1997 to All are Significantly Different from the Null Case of Open Water Between 1994 and 1996.

Summary of Getis Results  Majority of change during past decade in Maximum Distance :MGD is positive = increase in homogeneity  This is an easily applied image structure measure that reflects changes in coral reef cover. It can be applied quickly to sequential images to identify ‘flash points’ of change that require in situ followup  The spatial structures may be useful in management zonation since they do reflect reef heterogeneity

Summary of Getis Results  Ikonos data provides richer spatial detail than resampled SPOT, as expected, but aggregated statistics are consistent for the two image sets.

West Bunaken Siladen East Bunaken Maximum Getis from SPOT Imagery Examples of Spatial Patterns

The Change in Maximum Getis Distance for Bunaken Marine Park, Indonesia, and Savusavu Bay, Fiji

Siladen, 1990 Siladen, 2000 SPOT enhanced Maximum Getis Statistic

July 14 SPOT 2000 Max Getis June 29 Ikonos 2001 Max Getis Siladen

Kolmogorov-Smirnov Test  Non-Parametric  Test for Significance in Difference of Cumulative Histogram

Siladen, Maximum Getis Statistic Siladen, Difference of Maximum Getis Distance: