This chapter describes the methodology that will be applied in Chapter 9. While humans have the biological capacity for route optimization and the cultural tools to navigate strategically to places, there is no single, universal variable according to which that humans can be expected to optimize. Instead our complex dual physical and cultural landscape allows for no assumptions about a culture’s preferences in route choice. For this reason, a methodology that can quantitatively assess the significance of any matches between a route model and a preserved route or route system is valuable. It opens up the possibility for researchers to build route models based on both complex cultural and simpler physical hypotheses and test those hypotheses against the archaeological and/or historical records.
This study builds optimal, least cost path route models of single variables and assesses the significance of each individual variable one at a time against preserved hollow way routes in the North Jazira of the fourth and early third millennia B.C. These models represent what the route(s) would look like if a population optimized their travel according to the chosen hypothetical variable. The degree to which the model
matches or overlaps the preserved hollow way routes provides information about the travel motivations of the populations that created and used the hollow way routes.
The construction of an effective optimal, least cost path route model involves not only the conscious selection or development of a function that matches the researcher’s hypothesis, but also consideration of the relevant variables incorporated into the cost surface whose least cost will be calculated. Only then can the route model be
constructed and run. The routes generated by the model are only the expression of the researcher’s hypothesis, they are not reconstructions of movement. The testing of the hypothesis occurs when these models are statistically compared using
quantitative analysis to preserved archaeological routes or known historical routes.
Through the repeated testing and quantifying of different route models against preserved/known routes it is expected that it will eventually be possible to generate formulas that accurately express the travel preferences of specific cultures that can
170 Construction of a Route Model
Figure 7.1 A flow chart depicting the construction of a route model.
Identification of the least cost path (ArcMap least cost path,
GRASS, r.drain)
Apply chosen function to the cost surface layer (Naismith's Rule, Tobler's Hiking Function,
etc.)
Combine costs to create a total cost surface layer (for
example, use terrain coefficients to combine land
cover and slope costs)
Any other cost variables Land Cover Layer
Archaeobotanical Data Soil Maps
Slope Layer
Digital Elevation Model (DEM)
171 be used to fill in gaps or intelligently predict the locations of routes where none are preserved through careful use of analogy between cultures – a sort of calibrated route prediction.
7.1 Common Functions for Generating Optimal, Least Cost, Paths
7.1.1 Energy (Easiest)
All versions of the GIS program ArcMap, since at least 8.9, have a default function for generating least cost paths that will minimize energy consumption; this is called Least Cost Path. The routes generated can drastically increase the length of the route taken between two locations or result in a route that takes much longer than necessary, because distance and time are not considered at all. The route it generates, given only a slope layer, is a least cost energy path only.
ArcMap calculates horizontal and vertical costs difficulty in a pair of tools that can be run simultaneously called Cost Distance and Cost Backlink.32 The user creates a layer to define the source locations; the start and end points of the modelled route. Then, the user adds a cost surface layer containing the data on any variables that may affect ease of movement. In archaeology, the cost layer is often a simple slope layer derived from a digital elevation model (DEM) with the slope value for each cell calculated either in degrees or percentages. (There is, however, no software limitation to the sophistication of the cost layer added here.) Using the cost layer values provided, the tools calculate the cost from each source location to each other source location in the following way. First, the difficulty of travelling to each of the cells around the initial source location is calculated, followed by the next adjacent cells until the other source location(s) are reached. This is repeated for each source location and the path between any given two source locations is calculated in both directions (source A to source B and source B to source A). The smallest possible value a cell can receive from all these calculations is retained as the value of that cell. The four specific formulas used to calculate these values are as follows:
32 The Path Distance and Path Distance Backlink tools are an alternative option that allow users to apply custom functions, including Tobler’s Hiking Function.
172 1. For perpendicular movement: 𝑥1 =(c1+c2)
2 where c1 and c2 are the values of a cell (1) and its adjacent cell (2), and 𝑥1 represents the cost of travelling
between the two cells.
2. For diagonal movement: 𝑥1 = √2(c1+c2 2) where c1 and c2 are the values of a cell (1) and a diagonally adjacent cell (2), and 𝑥1 represents the cost of travelling between the two cells.
3. For each additional cell by perpendicular movement: 𝑥2 = 𝑥1 +(c2+c3)
2 where c2 and c3 are the values of cell (2) and adjacent cell (3), 𝑥1 represents the cost of moving between cell (1) and cell (2), and 𝑥2 represents the total cost of travelling between cell (1) and cell (3).
4. For each additional cell by diagonal movement: 𝑥2 = 𝑥1+ (√2(c2+c2 3)) where c2 and c3 are the values of cell (2) and adjacent cell (3), 𝑥1 represents the cost of moving between cell (1) and cell (2), and 𝑥2 represents the total cost of travelling between cell (1) and cell (3).
This method of calculation, sequentially considering the cost of travel to each
succeeding set of neighbouring cells by adding the least possible cost of travel from all previous cells, uses Dijkstra’s algorithm (Rees 2004, 204). To find the easiest routes, the user then inputs these cost distance and cost backlink layers generated earlier through use of the Cost Distance and Cost Backlink tools into the cost path function.
This creates a final layer that shows the least cost path between the locations by selecting a path of cells between those locations with the lowest possible values (ESRI 2011).
With this method, if a user inputs the slope layer, without modification, into these tools, the result is a linear calculation of degree of difficulty. In perpendicular
movement, a 30 degree slope will be twice as difficult as a 15 degree slope and half as difficult as a 60 degree slope. In diagonal movement 30 degrees would be nearly three times as difficult to cross as a 15 degree slope and about a third as difficult as a 60 degree slope.