TEACHING GEOG 385.02/GTECH 785.02  GIS APPLICATIONS IN SOCIAL GEOGRAPHY Back to MP home page

### MASTERY EXERCISE 4. COST-DISTANCE OPERATORS

The Exercise:

This is the fourth mastery exercise and it will focus on tools for distance analysis, both simple linear distance and cost distance. The problem in this exercise is to assess the accessiblity of a new road to two villages located in a coastal area of Vietnam. The new road is the only paved road in the area and villagers are interested to find the least cost path between their villages and the new road.

The exercise should be done in five stages.

Stage 1: Exploring the Data

The data provided includes the following:

VINHDEM            A digital elevation model for the study area.
VINH345              A satellite image for the study area.

VILLAGE1           A vector file with the location of village #1.
VILLAGE2           A vector file with the locaiton of village #2.

PATHPTS             A point symbol file.

Examine the elevation data using a quantitative palette. Examine the satellite data using the color composit palette. Add the vector layers to the satellite image to view their relative locations in the landscape. Note the resolution of the data from the document files.

Stage 2: Calculating Distances from the Road

Assume that villagers do not want to walk for more than 1 hour to get to the new paved road. If travel time is more than 1 hour, it is unlikely that they will use the road on a regular basis. On average, the villagers can walk 3 kilometers within 1 hour.

Would the villagers in both villages use the road on a regular basis? We can find out by simply calculating distance from the road to all other locations (including the villages). In Idrisi distance must be calculated from some feature represented as non-zero cells in a raster image. Before distances from the road can be calculated, it must first be made into a raster image. Do this and then calculate distances (calculating distance could take a few minutes).

1. How far is village #1 from the road? Village # 2? What important information does the program (Idrisi) use to calculate distances?

2. How long would it take to travel from village #1 to the road? From village #2? (Hints: It takes 1 hour to travel 3 kilometers, 1 kilometer equals 1000 meters). You can give your answers in terms of hours where any location less than 3 kilometers would be a fraction of an hour from the road.

Stage 3: Re-examining the Data

Distance from the road to the locations of the villages was calculated above in terms of simple linear distance.

3. Given only the simple distance information calculated above, what would the least cost pathways from each village to the road look like? (Hint: You don not need to calculate the least cost pathways to answer this question).

Examine the data for this study area a second time. Use ORTHO to view the elevation data (with the satellite data as the drape image and composite palette) in orthograpic perspective. Also, produce an analytically hillshaded image of the study area. Add the vector layers for the road and the two villages to the hillshaded image.

4. From your re-examination of the data, what characteristic of the landscape do you think would greatly affect travel time from each village to the road? What context operator gives a measure of that characteristic?

Stage 4: Accounting for Mountains

Travel times will obviously be affected by the hills that are found in some parts of the study area. Rather than simple linear distance, it would be more realistic to calculate a cost distance where steep slopes would cost more to travel across in terms of time. On average, the steepness of slopes will affect travel times regardless of the direction of slope (note: a more nuanced analysis might try to account for slope directions). Calculate slope values for all locations using a familiar context operator.

Slopes that are 0 to just less than 5 degrees will provide the easiest and, hence, fastest terrain to travel across; slopes that are from 5 to just less than 10 degrees will take twice as long to cross as the easiest slopes; slopes from 10 degrees to just less than 30 degrees will take 5 times as long to cross as the easiest slopes; and any slope 30 degrees or higher will present an absolute barrier to regular travel.

Given this information about the relative time (based on slope values) to travel across different locations, an image of slopes can be turned into an image of relative friction values. The result would be an image where each location has a friction value representing the relative cost (in terms of time) to travel through that location. Create that image and give a friction value of 1 to the locations that are the quickest to travel across, a friction value of 2 to those locations that would take twice as long to cross, etc.

After creating an image containing relative frictions (or absolute barriers) for all locations in the study area, calculate the cost distance from the road. Recall that you must CONVERT the friction image such that it is a real binary file. Also, with this data set, the cost calculation can take 10 minutes.

5. What algorithm is best for calculating cost distance in this example? Why?

6. What is the cost to travel from the road to each of the villages?

In this example, the base friction value of 1 meant that locations (cells) with that friction value can be crossed using 1 unit of cost. Because our friction values were based on relative time to travel across terrain with different slope values, cost is in terms of time. Knowing that 3 kilometers can be crossed in 1 hour (where friction values are 1) and knowing the resolution of each cell, the units of cost (in terms of time) can be calculated.

7. In this example, what are the units of cost (e.g. what does a cost value of 178 mean)? How far are the two villages from the road in terms of time?

Stage 5: Least Cost Pathways

Finally, we can use the results of the cost distance calculation to find the least cost pathways from the road to each of the villages. The villages would be the targets to which the least cost path is calculated from the road. The least cost pathways need to be calculated one at a time for each village.

Using the cost distance image created in stage 4 above, calculate the least cost path from the road to village #1 (Hint: The village is the target to which a least cost path is calculated. Also, the target must be input into the least cost path calculation as a raster image).

Do the same for village #2 and display your results using the QUAL256  palette.

To better view the least cost pathways in the context of your data, convert each pathway into a vector line file using RASTERVECTOR conversion in Reformat menu. This module transforms individual (non-zero) raster cells into vector points, lines, or polygons that can then be added as a layer to a raster display. Select raster to line conversion.

Display again the hillshaded image of the study area using the GREY256 palette. Add layers such that the villages, the new paved road, and the two pathways are seen.

8. Clearly the least cost pathways are not strait lines. Why?

Extra Credit (1 pt):

Assume there are many other villages in this study area and you want to know which are within 1 hour travel time of the new road (accounting for slopes). In this case, it would be very helpful to have a simple Boolean image that shows all locations that are within 1 hour travel time of the new road. Create this image and print it for extra credit.