1. Cost Surfaces in Archaeology: Recent Trends

1a. History and theory of use of Cost Surfaces

In recent years, the modelling and analysis of landscapes in archaeological GIS has begun to move towards increasingly sophisticated techniques for representing the land surface. There now exists an archaeological literature critically reviewing, for example, the results of various algorithms for generating DEMs, or comparing the accuracy of raster and vector terrain models for representing landscape features (Carrara et al. 1997; Kvamme 1990; Nackaerts et al. 1999). This critical literature has implications for, among other things, the analysis of site territories or catchments, or the calculation of pathways and travel costs between points on the landscape.

The first use of methods similar to cost surfaces in archaeology was that of Vita-Finzi and Higgs, who proposed analysing local economies through a field method involving walking four or more radii outwards from the site for a set time (Higgs and Vita-Finzi 1972, 33). These four directions could then be linked together to create a non-geometric zone containing all easily accessible lands, a rough 'cost-suface' approach. Given the logistics involved in collecting this data, this method does not seem to have been employed to any great extent, if at all, whereas geometric catchments found much wider application (Hodder and Orton 1976; Renfrew 1973; Roper 1979, 123-124). With the popularisation of GIS as an accessible tool for archaeologists, the cost-surface approach has seen a revival, which can probably be ascribed to the increasing availability of digital elevation data and the increase in desktop computer processing power.

For site territories, then, there has been a progression from an initial use of more simplistic methods, for example making use of concentric circular territories and Thiessen polygons, to a wider use of non-geometric catchments, including cost-surface approaches, where territories are defined in terms of the energy or time required to travel from the central site to a certain 'border'. This border can be defined in various ways, either by setting an arbitrary maximum effort, such as the equivalent effort of travelling 5km over flat ground, or in terms of travel time, for example two hours' walk from the central site, and it is argued here that there is general agreement that catchments or territories generated in this manner are more informative than simply drawing a set of concentric rings around a site.

While the implementation of cost surfaces in archaeology can be problematic (see Methodological problems), the basic premise is relatively simple. A raster data file is created covering the area of interest, so that each raster is given a value which represents the relative difficulty of traversing the parcel of the Earth's surface it represents. This difficulty can be the result of a variety of factors depending on what specific process is being modelled: road planning will have different requirements from those used to calculate surface water runoff. In terms of human movement across a landscape, a variety of equations exist for expressing the relationship between the slope of a land parcel (raster) and the difficulty of a human traversing it. These include both isotropic (independent of direction of movement) and anisotropic (direction of movement affects movement cost) algorithms, a selection of which are summarised in van Leusen (1999) and Wheatley and Gillings (2002).

In terms of pathways and travel costs, again, there has been an increase in the sophistication of the techniques involved, both in terms of improving algorithms for representing the surface, whether that be in terms of increased sophistication in interpolating the transitions between raster cells (Abdelguerfi et al. 1998; Carrara et al. 1997; Florinsky 1998; Gao 1998), or in increasingly sophisticated equations for generating cost surfaces (Abdelguerfi et al. 1998; Kvamme 1990). The typical GIS user can now pick and choose between these various anisotropic equations and implement them directly using a variety of GIS packages (Arc/INFO-GIS, GRASS-GIS, Idrisi, etc.), without this task requiring much in the way of specialist knowledge or training. It is no longer necessary to write a specialised program or script to accomplish this, as the functionality has already been built into the package as purchased.

So the application of cost surfaces to archaeological questions of territoriality and movement now represents a well-established methodology within archaeological GIS. Beyond this, several recent papers have proposed tentative methodologies for extending the concept of the cost surface, in order to model not only the physical but also the social preferences affecting travel. Llobera has suggested ways in which social repulsion or attraction to particular monuments or locations could be modelled, creating cost surfaces simulating people's desire to approach or stay away from certain landscape features (Llobera 2000). Lee and Stucky, writing from a more theoretical GIS perspective, propose a series of friction models based on the visibility or invisibility of raster cells, enabling them to produce pathways that they classify as 'scenic', 'hidden', 'strategic' and 'withdrawn', as well as the more usual Euclidean and lowest-energy-cost paths based merely on slope and geometry (Lee and Stucky 1998). In an archaeological context, the viewed area of travel routes and their potential association with the location of adjoining sites has been examined by both Bell and Lock (2000) and Chapman (2003). At the more functional level of energy expenditure, the potential to model the differential energy cost of moving across different types of terrain: roads, trackways, grassy fields, forests, swamps and so on is also frequently discussed, even in introductory GIS texts such as Wheatley and Gillings (2002, 155).


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