Modelling ‘natural routes’ with GIS

The solution to these representational problems will come, I believe, from the development of new digital mapping technologies – based on current (and as-yet-undeveloped) GIS and database techniques. The processing power of modern computers and the ever-increasing availability of digital data about the Earth’s surface (especially those derived from remote sensing satellites and NASA shuttle missions) allow us to create an ever more detailed model of global topography and climate, facilitating the zooming between macro- and micro-scales. They therefore offer the potential, when combined with analytical models, to create new forms of landscape visualization that can take account of multiple dimensions of routes and networks of interaction. Such modelling remains in its infancy, but as part of the research for this book I have experimented with the use of currently available techniques to create what I call ‘archaeotopograms’ – representations that combine aspects of both landscape and archaeological distributions, discussed further below.

28 This redefinition is akin to Merleau Ponty’s phenomenological redefinition of landscape not as abstract space, but as something always in the process of becoming, a view which also inpsired Ingold’s approach.

Geographical Information Systems (GIS) may be usefully thought of having two aspects: first the visualization of geographic data, and second the mathematical or statistical functions which may be applied to raw data and subsequently re-visualized. While the first aspect has already revolutionized the speed with which basic archaeological mapping has been undertaken, the second aspect introduces new approaches to archaeological problems, often relying on complex statistics, which require careful interpretation. Amongst the most common of these ‘statistical’

GIS techniques applied in archaeology are spatial hierarchy analyses, view-shed analyses and cost-surface/least-cost path analyses. Spatial hierarchy analyses have a long history within archaeology as a result of the discipline’s encounter with the New Geography in the 1960s and 70s (e.g. Chorley and Haggett 1968; Hodder and Orton 1976; Clarke 1977): the drawing of Thiessen polygons (based on the Voronoi tessellation/Delaunay triangulation) is a basic example of this kind of work in which the distance between points (normally archaeological sites) is calculated and this is used to depict a boundary supposedly representing the edge of the

‘site-catchment’ territory. This has been used to suggest the potential boundaries of control between peer sites – for example megaliths or hillforts (Renfrew 1968;

Cunliffe 1971). Of course such analyses are problematic since Thiessen analysis assumes a flat surface – fine if the region in question has no topography – but in most real-world instances the diagrams give a false or misleading impression of potential territories if taken literally (see, for example, critique of the ‘central-place’ model of hillforts in Sherratt 1996). For this reason a variety of more complex techniques of analysis have been developed which are designed to model space and movement across it in more sophisticated ways.

3.3.1 Impedance along vertices: ‘network analysis’ and routes

So-called ‘Routing’ or ‘Network analysis’ is an analytical technique to calculate efficient routing or paths between locations, which relies on a pre-given model of relationships between nodes. In a network, each relationship (a vertex) between each connected node must be explicitly stated and given one or a number of impedance factors. These impedance factors can be based on geometric distance, time or ‘costs’ calculated from other spatial analyses (see below). This form of analysis has had a huge application in modern transport navigation tools (such as used by ‘SatNav’ devices and train timetable calculators), which attempt to solve the ‘travelling salesman problem’ – i.e. how to pass through a set of nodes in the least time or at the least cost. Such techniques might appear to offer a very fertile ground for the analysis of ancient routes (and interaction more generally), but so far their applications have been rather few. The reason for this is that current models cannot handle situations in which all or most of the possible nodes (i.e.

assumed settlements) and the links between them are not known – and this is, in fact, the most common state of archaeological knowledge.

One recent application of these techniques has been to the Aegean in the 2nd millennium, to model the effects of the Thera eruption on interaction networks by removing nodes and therefore linkages (Knappett, Evans and Rivers 2011).

The analysis simulates the consequences of the destruction of settlements by comparing two versions of a network of sites (and the links between them) which are established archaeologically, where the second version does not include those sites destroyed by the eruption or related events. This application is successful

partly because the Aegean can be treated as a relatively neutral surface and the impedance costs can be modelled straightforwardly. The knowledge of settlement patterns in the region is also relatively good – so that while the list of nodes may not be entirely complete, it may be close to it. It also addresses a relatively straightforward comparative question of before and after. Similar highly-focussed analysis might be taken to a land-based situation, such as in the northern Syrian plains where a detailed route network can be constructed through the study of hollow-ways and tells (see Section 2.2.4). However, once the analysis is taken to a larger scale, we cannot be sure that we know all of the ‘nodes’ required for a complete network (i.e. there may be many relevant sites that we have not identified), and we are rarely certain about the temporal co-existence of sites in different locations in any case because the resolution of our data is too low.

3.3.2 Friction over a grid: cost-surface analyses

A related but structurally different tecnique, ‘Cost-surface analysis’ (Conolly and Lake 2006, 214-225, 252-256) aims to create a mathematical or visual model of the relative cost to reach all locations on a surface if travelling from a particular point on that surface using a grid of cells and a model of ‘cost’ of ‘friction’²⁹. Cost-surface functions normally require two main inputs: (1) a ‘cost-of-passage’

or ‘friction map’ grid (which can be represented as a raster image in many GIS programs), whose contents are based on a model of cost or friction that may include factors such as slope, and (2) the origin cell within the grid from which all accumulative costs are to be measured. The resulting output of this function (an ‘accumulated cost surface’) is another grid in which each cell contains a value that represents the relative accumulated cost to travel to this cell from the origin.

Normally this grid is then represented as a raster image to become a human-readable map of relative or effective distance to a point, once travel cost is taken into account. In the case of an archaeological site, for example, this may give an indication of the relative amount of time/effort it takes to travel from the site to various potential resources.

This is a relatively simple idea in theory, but the usefulness of its application to archaeology depends a great deal on how one is to calculate ‘cost’ and how well the algorithm used to calculate the accumulated cost can model the real world. There is more than one type of algorithm available to transform a ‘cost-of-passage’ grid into a ‘cost-surface’ (Table 3.1). The two main types are ‘isotropic’

or ‘anisotropic’. ‘Cost’ or ‘friction’ is most easily understood in terms of time or energy (as opposed to geometric/Euclidean distance). For example, topography can be taken as one friction factor: steep slopes are taken as high ‘cost’ because they take more energy or more time to cross than flat terrain, and slope can be easily calculated in GIS programs from ‘Digital Elevation Models’/‘Digital Terrain Models’ (DEM/DTM) such as the global coverage ‘Shuttle Radar Topography Mission’ (SRTM). However, the geometric value of slope is not a good model of the energy or time required for a pedestrian to cross an area, as is obvious to anyone

29 Cost-surface and least-cost-path analysis could in fact be seen as two specialist kinds of network analysis in which ‘cells’ in a grid rather than ‘nodes’ in a lattice of relationships are the unit of analysis. In cost-surface analysis, cells can only be directly related to adjacent cells in the grid.

Algorithms are used to calculate the ‘cost’ or ‘friction’ of movement from one cell to another. This alternative way of modelling ‘impedance’ is often based on a variety of variables, including but not limited to topography.

GIS suite/programFunctionAlgorithm type and Source?Comments and Further information ArcGIS (Spatial Analyst)CostDistanceAccumulative cost (isotropic) ProprietaryManual (ArcGIS 9.2 Spatial Analyst): http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=Cost_Distance_algorithm GRASS Also accessible in:QGISr.costAccumulative cost (isotropic) ?Manual (GRASS 6.4): http://grass.osgeo.org/grass64/manuals/html64_user/r.cost.html SEXTANTE Also accessible in:SAGA / gvSIG / uDig / openJUMP Accumulated cost (isotropic)Accumulative cost (isotropic)

? Documentation unavailable

General information: http://forge.osor.eu/projects/sextante/ IDRISICOSTAccumulative cost (isotropic) ProprietaryIDRISI 15 Table 3.1. Accumulative cost surface programs (basic/isotropic). GIS suite/programFunctionAlgorithm type and Source?Comments and Further information ArcGIS (Spatial Analyst)PathDistanceAccumulative cost (anisotropic) Proprietary and unpublishedThe base algorithm is proprietary and unpublished. Manual (ArcGIS 9.2 Spatial Analyst): http://webhelp.esri.com/arcgisdesktop/9.2/index. cfm?TopicName=Path_Distance:_adding_more_cost_complexity GRASS Also accessible in:QGISr.walkAccumulative cost (anisotropic) {Aitken1977wa; Langmuir1984ml}Manual (GRASS 6.4): http://grass.osgeo.org/grass64/manuals/html64_user/r.walk.html SEXTANTE Also accessible in:SAGA / gvSIG / uDig / openJUMP

Accumulated cost (anisotropic) Accumulated cost (combined) Accumulative cost (anisotropic) Accumulative cost (combined) ?Documentation unavailable

Other modules:- Cost in predefined routes. Cost in predefined routes (anisotropic). Generate alternative routes. General information: http://forge.osor.eu/projects/sextante/ IDRISIVARCOSTAccumulative cost (anisotropic) Proprietary and unpublishedIDRISI 15 Table 3.2. Accumulative cost surface programs (complex/anisotropic).

GIS suite/programFunctionAlgorithm type and Source?Comments and Further information ArcGIS (Spatial Analyst)CostPath CostPathAs-PolylineLeast Cost Path Proprietary and unpublishedManual (ArcGIS 9.2 Spatial Analyst): http://webhelp.esri.com/arcgisdesktop/9.2/index.cfm?TopicName=Cost_Path http://webhelp.esri.com/arcgisdesktop/9.2/index. cfm?TopicName=Least_cost_path_and_least_cost_corridor GRASS Also accessible in:QGISr.drainDrainage PathThis module can be used to create general Least Cost Paths but is technically a hydrological flow diagram and can be dysfunctional for the purposes of creating a standard least-cost- path because it iteratively chooses the lowest value each cell and terminates when the lowest value is reached like water. Manual (GRASS 6.4) http://grass.osgeo.org/grass64/manuals/r.drain.html SEXTANTE Also accessible in: SAGA / gvSIG / uDig / openJUMP

Least cost pathLeast Cost Path ?Documentation unavailable IDRISIpathwayLeast Cost Path Proprietary and unpublished Table 3.3. Least-cost-path programs. Table 3.4. Least-cost corridors programs.^{GIS suit}

e/programFunctionAlgorithm type and Source?Comments and Further information ArcGIS (Spatial Analyst)CorridorCorridorManual (ArcGIS 9.2): http://webhelp.esri.com/arcgisdesktop/9.2/index. cfm?TopicName=Corridor

who has had to climb and descend a mountain. The ‘braking’ energy required to avoid falling when descending can sometimes be more than that required for climbing at lower gradients. Thus alternative algorithms have been written which are supposed to take account of this ‘anisotropic’ cost (Table 3.2), some of which have been based on publications of laboratory measurements of the energy cost of walking at different slope (for a summary, see Conolly and Lake 2006, 217-221).

The problem is that many of the cost-surface algorithms commonly available for the average archaeologist to use are not well documented, so that it is sometimes difficult to compare or critique them. Exceptionally, the anisotropic algorithm used by GRASS (r.walk) is well referenced (Table 3.2), from which we learn that the formula used is based on data taken from walking in Scotland. Despite the fact that isotropic algorithms are not really applicable to real-world geographical applications (of which archaeological reconstruction is one), the additional complexity has made uptake of anisotropic algorithms relatively slow.

3.3.3 Finding paths: least-cost-path analyses and corridors

Least-cost-path takes cost-surface and cost-of-passage direction models a step further to calculate a specific path between two points according to cost which should, in theory, represent the path with the lowest possible accumulative cost.

Least-cost-path analysis has enjoyed some success in the process of modern road planning, as it helps to suggest the optimum economic route to build a road through a landscape: ‘costs’ such as land-prices and fuel prices translate easily into quantifiable models. Similarly, related algorithms can be used in hydrological modelling (required for flood protection planning, for example) in order to predict the likely path that water will flow downhill. These tools have been borrowed in archaeology to allow researchers to suggest likely paths between a site and its resources, or to compare known routes with predicted models in order to identify the possible factors behind path location (for example Kantner 2004; Bell, Wilson and Wickham 2002; Pelfer 2007; Newhard, Levine and Rutherford 2008). Indeed the generation of least-cost-paths is normally the main aim of cost-surface analysis within archaeological research. Because of the dependence on cost-surface, the usefulness of the least-cost-path is dependent to a high degree on how the model of cost is designed and on the algorithms’ fitness for the task. The most accurate way to calculate least-cost is to calculate the cost of all possible paths and then rank them. However this is a highly computationally intensive procedure (and potentially unrealistic from the point of view of the modelled human actor), whose worst-case computation time increases exponentially with the amount of data. It is therefore far more common for programs to approximate least-cost.

For example, in a very basic iterative ‘drain’-based approximation, the program will search around the current start point to find the adjacent cell with the lower (or lowest) cost, and then look for the lower (or lowest) cost cell adjacent to this new cell iteratively etc. until a ‘destination’ cell is reached. More often a ‘direction raster’ is used to better calculate the next cell. Different approximation procedures can give rather different results, as was highlighted by Gietl et al.’s comparison between GRASS, ArcGIS and IDRISI on the same data (Gietl, Doneus and Fera 2008). Again the base algorithms are not well documented so that it is difficult to compare or critique (Table 3.3). At the small-scale, most of the currently available

procedures produce straight lines over steep hills and cannot reproduce the more realistic spiral/zigzag climb which many roads and tracks adopt – an algorithm for which was put forward by Colischonn and Pilar (Collischonn and Pilar 2000).

An alternative type of least-cost is a ‘least-cost-corridor’. At its simplest this involves the sum (or average) of two cost-surfaces from two different points; a

‘corridor’ between the two points can then be established by filtering out costs above a certain (but arbitrary) value. This procedure can be achieved easily in most GIS programs, and ArcGIS even includes a dedicated tool to create it (Table 3.4). This technique has had wide application in ecology, for example in the establishment of natural reserves for deer. So far I am not aware of any previous archaeological applications – but the potential relationship between these mathematical corridors and the restricted ‘route corridors’ within which roads and trackways shifted suggested possible applications for this study.