Idrisi's Spatial Trend of Change Map: An explanation

 

Some of the more complex pieces of output that are produced as part of Idrisi's Land Change Modeler are the Spatial Trends of Change maps. Using the Selva Tutorial Exercise 6-1 data that documents the land cover / use changes from 1985 to 1999 (for the central Massachusetts area--CMA), the figure below was created following the steps presented in Exercise 6-1 step m (i.e., the map provides a generalization of the transition from any previous land cover [All] in 1985 to the Residential (> 2 acre) land cover in 1999; the 'generalization' being used is the default cubic trend surface).

The intention of the Spatial Trend of Change module is to provide a means of generalizing the pattern of change. The numeric values do not have any special significance (in and of themselves), other than to provide an indication of where the change was more intense (higher numbers, redder colours) or less intense (lower numbers, darker green to blue colours). The output from the Spatial Trend of Change module is a smooth surface that represents gradual trends in the surface (the transition in land cover) over the area of interest.

We can see in the image presented above that within the CMA the transition to residential ( > 2 acres) was more intense along a north-south line that runs approximately across the middle of the region, with higher values at the northern and southern edges of the image. The transition intensity was least along the eastern edge of the region, but it was also low in the western portions of the CMA. (Interpreting the reason behind the pattern would require access to additional information, such as where major roads and urban centres are located, etc.--forces that could drive the intensity of the transitions. See the discussion below for an indication of how that process of interpretation could begin.)

Conceptually, the results produced by the Spatial Trend of Change module are like taking a stiff piece of paper and fitting it to the data (but only allowing the paper to have a limited number of 'bends'). The following illustrates a set of sample points of elevation taken on a gently sloping hill and a 1st order surface being applied to model the slope (the piece of paper is magenta and it was not allowed, in this case, to have any bends in it).

In the following illustration a valley is being modeled using a 2nd order surface (the piece of paper is allowed to have one bend in it).

A 3rd order surface--such as the one used by default in the Spatial Trend of Change module--allows the piece of paper to have two bends in it, as illustrated below (note that the one bend forms the dominant hill, while the second bend produces the dip along the top of the hill).

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In order to see if I could determine why the spatial trend of change map showed the pattern it did, I decided to see if the pattern was related to primary (limited access) roads. My reasoning was--people are willing to move into the area if they are able to access a high-speed transportation corridor to get to work. In order to produce the image below took a bit of manipulation: I had to create a raster map showing only the primary limited access roads [this was easily derived from the RoadsCMA layer by right-mouse clicking on the legend entry for Primary--Limited Access roads and selecting Create Boolean for Current Class], I then converted that raster image to a vector map [Reformat / RasterVector], which I then overlaid on the spatial trend of change map. The result, presented below, does lend some support to my hypothesis. The major limited access highway (I495) in that region does run north-south through much of the high-intensity areas of the spatial change map. Access to a highway would not be the only driving factor, of course, but it could be one of several important factors driving the observed changes.