Spatial Analysis: Part 1

Once images for the factors and constraints to be considered were generated, spatial analysis was carried out using the Decision Wizard module in IDRISI. In order to best represent the factors influencing the suitability of an area for Bloody Henriques the Englishman and his crew to bury their treasure and to use these in a multi-criteria analysis, distance surfaces had to be converted to standardized fuzzy images. This was done through the Decision Wizard module as follows...

Distance from commercial areas:

A monotonically increasing linear function was used to calculate a fuzzy image of the factor image representing distance from commercially zoned landuse areas (COMMERCIALDIST). This function was chosen because suitability was deemed to constantly increase with distance from commercial areas. People tend to congregate in commercial areas to work, run errands or socialize with friends and family. Ideal locations for burying treasure are designed to protect the treasure from others so that the original looters can return to it at a later date. These areas, therefore, must be out of the view of others. As such, a starting point of 0m and an end point of 8112.34m (the highest value of the distance image) were set. Click on the link below for a full-sized view of the fuzzy image generated...

COMMERCIALFUZZ

Distance from high density areas:

A monotonically increasing linear function was also used to calculate a fuzzy image of the factor image representing distance from areas of high population density (HIGHDENSITYDIST). This function was chosen because the suitability of a certain area for burying 'booty' is directly related to distance from high population density areas. The ideal location, historically, has been remote Caribbean islands situated as far as possible from the prying eyes of fellow 'bilge rats' and colonial trade officials. The starting point was set at 0m and the end point was again set as the highest value of the input distance surface (17490.6m). Click on the link below for a full-sized view of the fuzzy image generated...

HIGHDENSITYFUZZ

Distance from liquor stores:

A symmetrical J-shaped function was used to calculate a fuzzy image of the factor image representing distance from liquor stores (LIQUORDIST). This function was chosen as it was determined that suitability would increase in an exponential fashion with distance from liquor stores to a certain optimal range of distances and would then decrease in an exponential fashion. This is because ideal locations for hiding treasure should be close to liquor stores but not so near as to increase the risk of outsiders finding the loot. In fact, locations in the immediate vicinity are not very suitable at all. The optimal distance range was set as between 1500m and 3000m as these distances were thought to be within a viable walking distance but outside the immediate vicinity of liquor stores. Click on the link below for a full-sized view of the fuzzy image generated...

LIQUORFUZZ

Distance from oceans and navigable rivers:

A symmetrical linear function was used to calculate a fuzzy image of the factor image representing distance from oceans and navigable rivers (OCEANDIST). This function was chosen as it was determined that suitability would increase at a constant rate with distance from oceans and navigable rivers to an optimal range and would then decrease at a constant rate. This is because Bloody Henriques the Englishman and his crew want to protect their treasure from the natural environment but also do not want to carry the heavy chest too far from the shore. An optimal range of between 50m and 300m from oceans and navigable rivers was set. This range was felt to be outside the influence of tidal and river level fluctuations that might serve to expose the buried treasure yet inside a walkable distance for his crew. Click on the link below for a full-sized view of the fuzzy image generated...

OCEANFUZZ

Spatial Analysis: Part 2

The factors were then weighted using an Analytical Hierarchy Process. This process uses the 'weight' module and pairwise comparisons to derive factor weights and, ultimately, to determine how factors will trade off. Factor weights were decided on the basis of the criteria laid out by Bloody Henriques the Englishman. As shown in the chart below, Bloody Henriques felt that the distance from commercial areas (record 1) was equally as important as distance from high population density areas (record 2). Distance from liquor stores (record 3) was deemed strongly less important than these two factors while distance from oceans and navigable rivers (record 4) was deemed strongly more important.

This pairwise comparison generated the following weights and consistency ratio...