The SCDF Link

This example illustrates the SCDF ArcView-XGobi link. In this analysis we specifically examine the spatial cumulative distribution function (SCDF) computed on the crown defoliation index (CDI) which is a weighted average of the two variables, crown dieback (CDB) and foliage transparency (FTR).

Crown dieback refers to the percentage of dead branches in the upper sunlight exposed parts of the tree crown. The assumption is that these branches have died from stressors in the environment other than lack of light. It is measured as a percentage in increments of 5 from 0 to 100. Foliage transparency refers to the amount of light penetrating foliated branches. It ignores "holes" in the tree due to bare branches and is measured on the same scale as crown dieback. The CDI= measures tree crown health as a response to stressors and it is computed as follows:

where is the diameter at breast height of tree , and is the number of trees in the sampling site. Notice that high values indicate poor health. Recall that is the region over which the SCDF is computed, which is a subset of the region of study, . The region of the study here is the forested parts od the northeast USA given by the states of Maine, New Hampshire, Vermont, Massachusetts, Rhode Island, and Connecticut.

The SCDF link allows up to 10 regions to be specified by interactively drawing a polygon on the screen. The color of the polygon is used to identify the SCDF for that region. In this example, two areas are delineated for SCDF prediction (above).

In addition, the SCDFs were brushed so that the top 10% of the points (the trees displaying the worst health in each of the two regions) were highlighted (as shown by the rectangular brush in the XGobi plot window). The ArcView window indicates that these sites fall mainly in two clusters (near the coast and near the Canadian border both running across the two states). Although in this data the choice of regions is rather arbitrary this serves to demonstrate how an analyst might examine forest health in different political regions such as states. Here the regions of poor health fall across state boundaries so we could conclude that the problem is likely to be from an environmental stressor rather than due to differing state policies on forest management.

Using a long vertically-oriented brush moved from left to right across the plot would allow the examination of the CDI values. This would be useful, for example, if it had been decided that a CDI value of 15 or more corresponded to a forest in poor health, then the proportion of values above this cutoff could be examined along with their geographical location. In this way regions considered to be in good (nominal), marginal, or poor (sub-nominal) health would be examined.

Another interesting point to note is that in this example we actually used concomitant information from a remotely sensed image, digital elevation data and precipitation to predict the CDI on a finer grid than the original. A method of constrained kriging (Cressie, 1993) was used. The modeling is described in Majure and others (1996B). The Basic link was used to examine the concomitant information but the modeling was conducted outside of the link in S (Becker, Chambers, and Wilks, 1988). It would be desirable to do the modeling within the link environment as well and for this we hope to include a link to S in the future. A more complete description of the data and the spatial CDF is provided in Majure and others (1996A).