Methodology

A major objective of this analysis was to provide a gridded data set from supplied point data. Todd Redding requested that (i) final output would take tabular form (Microsoft Excel format .xls), and (ii) spline would be used as the chief method of interpolation. Although Todd Redding requested splining, a literary review and research carried out previous to our analysis, determined that inverse distance weighted interpolation was found to be a more suitable alternative.

	Example IDW Comparisons

(i) The import and export of data acquired from our analysis into tabular form, was found to perform most accurately, and with most precision through the use of ER Mapper 6.0 software. Therefore, a table had to be created for each variable, which included location (x-coordinate, y-coordinate) and the variable's corresponding value (z-value). This table was created within Microsoft Excel and saved as a "Formatted Text" (space-delimited) file (.prn) so data could be imported into ER Mapper.

Once data was interpolated in ER Mapper, the splined image was exported into Microsoft Excel using the Export Raster, XYZ ASCII grid, and function in ER Mapper. This produced a tabular data set of location and value (x, y, z-values) for each variable.

(ii) Splining in ER Mapper involves the use of the Gridding Wizard. Within this wizard, the user is offered the option of tensioning for spline interpolation. Since the objective of this analysis was to enhance and detect edges, most of the original data contained great variation. Tensioning was crucial towards accurately applying a spline function, since most spline functions are not suitable for and do not preserve great variations in data (i.e. ArcView GIS 3.2).

Performing a boundary analysis of the study area is a significant part of this study. Therefore, filters were passed through the splined images to enhance and detect edges. The filters we used were a slope filter, used to enhance and detect rate of change within each variable, and an edge enhancement filter which exaggerates edges.

A Laplacian edge detector filter was not incorporated into this analysis because of the distribution of the original point data. Instead of showing linear boundary lines, points appeared instead that mirrored the location of our data points. This is because the splining method forced the surface of the new DEM to the data points, even if it was noise. The rest of the surface curved away from the points. Linear edges would visually seem to appear where there were more data points, however, because the forest/clear-cut boundary was sampled heavier this led to wrong impressions. The original data was sampled with greater density at the edges, and therefore, any edges detected by the filter would be a result of the distribution of points (Craig Coburn, March 15, 2001).

Laplacian Filters

The edge enhancement filter exaggerates the differences within the data set. We created a 3x3 kernel with 0's in the corners, a 5 in the center and -1's around the side. This filter is supposed to be more mathematically correct than having a filter with just -1's and a 9 (Coburn, 2001). The actual distance from the center pixel to the edge is one unit, however, the distance from the center to the corner is root two units. This filter helps us visualize the boundaries more clearly within the data layers.

Due to the small size of the study area, 3x3 filters were used. A larger filter would be inappropriate because we are working with only five transects. Because this is a small area, a larger filter would have lost too much data along the edges of the data set. Furthermore, the standard ER Mapper slope filter is calculated from a 3x3 region, however, this can be increased by modifying the slope filter.

It would not be possible to use a Laplacian Edge Detection filter on this data because of the aforementioned problems, as well, the edges can not be found on the smooth slopes that the splining created. Therefore, a slope filter was used instead. The algorithm of the use of the Slope filter calculates the slope, or gradient, for a DTM. The numbers output from the Slope_Degrees filter range from 0 to 90. 0 indicates a flat area, with no slope; 90 indicates a vertical slope (ER Mapper, Help File). Layers that showed up the same colour had slopes that were similar throughout the entire data set. This is due to the fact that this algorithm works as an IF/THEN method. For example, If the slope for the entire data set is less than 5 degrees, the algorithm returns a value of 1. All the layers that returned blue had slope values less than 5 degrees across the entire data set.

To determine if any relationships between tree cover and the variables existed, overlays were produced using DIFN. The DIFN layer most accurately shows the forest/clear-cut boundary. Therefore, in order to find the relationships between this boundary and the boundaries within the other variables, the other variables were overlain on top of DIFN. To graphically show the DIFN boundary as being crisp, we thresh-hold sliced its spectral histogram. This spectral histogram distinctly showed a bimodal distribution, which clearly separated areas of high canopy openness and low canopy openness. We sliced the bimodal curve into two, creating graphically a red area with a high open canopy, and black area with a low open canopy.

		Level Slicing Diagram

With the other variables, we level sliced the spectral histogram to generalize and discretize the data. In this step we had to remove a lot of the noise because it became hard to visualize the data at later steps. We sliced the data into approximately five groups depending on the distribution of the variable's data values. The slices were where we saw natural breaks in the data's distribution. The end result was a map with distinct boundaries in green.

Overlaying DIFN with the other variables allowed us to see the fuzzy nature of the soil property's boundaries. Even though we discretized the data, once we overlaid the layers with DIFN, we are able to witness the complexity of the boundaries. Some of the layers showed a definite boundary corresponding to the DIFN layer, with other variables, the correlation was less, and with a few variables, there seemed to be no relationship at all.

The correlation between the tree cover and the other variables is seen through the differences in colour across the overlain layer. Since the DIFN layer has a constant red colour representing the high open canopy area and a black colour representing a low degree of openness. The other layers all used values of green to represent their Y values. These values range from a low represented by black and a high representing a high intensity green. The number of values of green within this range corresponds directly to the number of levels that were sliced within the layer.

Once these layers were overlain we could infer about the boundaries. To infer about these boundaries, additive colour theory must be known. Equal amounts of Red and Green = Yellow. A lesser amount of green gives brown and even less green gives orange. A greater amount of green gives bright yellow.

With this colour theory knowledge, boundary analysis can be performed. An example of this process is to view the overlain layer to see how the colour changes around the DIFN boundary. If the areas relating to the forested areas are shown as black or darker green while the deforested areas show in the yellow range, there is likely a relationship between the boundaries of the DIFN and the other variable. Alternatively, if the edges are green and the deforested area is red or blackish-red, there is likely to be some relationship between the boundaries of the two layers. In layers where the deforested areas are blackish-red and the forested area is dark green, or if the deforested areas are yellow and the forested areas are of high intensity green, there is less of a likelihood that there is a relationship between the DIFN boundary and the other variable. If we noticed a change between the forested and deforested but not directly in conjunction with the sharp boundaries of the canopy cover, it could be inferred that there was more of a fuzzy boundary associated with these two variables. At times, we noticed that there was absolutely no relationship at all.