A break between cynical and critical
One of the many rest stops while climbing up the learning curve of ESDA is a review of spatial
autocorrelation. An example from an Indonesian coral reef helps clarify the concept: Healthy coral
reefs support highly heterogeneous species populations. Pollution, typically muddy runoff from
shoreline construction, can clog and kill the coral, turning the damaged reef into a homogeneous
algae farm. Comparing one area of a healthy reef to its neighbors should show little similarity,
whereas any spot in a dead reef will be similar to any other spot — algae everywhere.
Marine conservationists want to track the spread of reef damage in order to apply realistic
management schemes. High spectral resolution data can discriminate between healthy corals,
bleached corals, sea grass and algae-covered surfaces, but sensors capable of this resolution
are not available from a satellite platform. Less-detailed data, such as SPOT (www.spot.com) HRV
or Landsat TM imagery are available, however. So, rather than attempting to detect change in species
mix over time, why not compare change in diversity over time instead? This is where spatial
autocorrelation helps. Although too coarse (at 20- or 30-meter pixel resolution) to reveal specific
species, SPOT and Landsat data pixels will either be similar to their neighbors or different. Such
was the approach Heather Holden (National University of Singapore), Chris Derksen, and Ellsworth
LeDrew (University of Waterloo, Canada) took to detect change in the Bunaken National Marine Park,
North Sulawesi, Indonesia (www.gisdevelopment.net/aars/acrs/2000/ts3/cost006.shtml).
In light of this change detection example, the reef researchers’ definition of spatial
autocorrelation should make sense: “Spatial autocorrelation is…the situation where one variable
(reflectance value of a pixel in this case) is related to another variable located nearby
(surrounding pixels). Spatial autocorrelation is useful since it not only considers the value of
that pixel (magnitude of reflectance), but also the relationship between that pixel and its
surrounding pixels.” Said another way, spatial autocorrelation reveals spatial patterns in which
areas (or points) close together are more similar than areas (or points) that are far apart.
Zero to sixty. This is the basic ESDA concept; now try leaping the gap to explore one of
its details. As CSISS’s Sam Ying points out when recounting the history of spatial autocorrelation
(www.csiss.org/classics/content/61), it is scale
dependent. Ying illustrates his point with two identical datasets, the first divided into
four squares in which the squares adjacent to white squares are always black, displaying no
spatial autocorrelation. The second, though containing identical underlying data, is divided
into 16 grid cells, resulting in positive spatial autocorrelation: the squares in the corners
are surrounded on two sides with squares of the same color (see Figure 2).