It is fairly difficult to model topographic cost components owing to landscape changes over time and lack of high-quality geographic data. But it is even more difficult to model social and cultural cost contributions. Most LCP studies including such costs focus on visibility issues (e.g. Bell and Lock 2000; Rahn 2005; Zakšek et al. 2008). Visibility issues play different roles in LCP reconstruction: If landmarks can be seen from a distance, the chances of getting lost are small. Furthermore, in a position with high visibility the chance of surprise attacks are reduced to zero, so a large viewshed increases the safety of the traveller. If travellers do not want to be detected, concealing the path in areas that cannot be seen from a distance is important. Discussing the problems and pitfalls of viewshed generation in detail is beyond the scope of this article and the reader is referred to introductory textbooks on GIS in archaeology (Wheatley and Gillings 2002, 201–16; Conolly and Lake 2006, 225–33). Lock and Pouncett (2010) point out that a cone of vision is to be considered in LCP analysis rather than the 360° viewshed, which assumes that the walker is spinning around at regular intervals.
It is plausible that the average viewshed on a ridgeway location is greater than that of random points in any study area. For this reason it is difficult to identify the main factor governing the choice of ridgeway routes. Did people walk on crests because of the large viewshed or because these locations were dry and the gradient not too steep? Moreover, even in a dense forest with low visibility, it is easier to follow a ridge than any other topographic feature, except for streams – however, streams are often surrounded by boggy terrain and such a path may entail crossing many subsidiary creeks, especially in areas with substantial amounts of rain, such as the Bergisches Land in Germany.
To model attraction or taboo, the amount of the attracting or repelling influence must be estimated as well as the distance where the influence is no longer felt. In Llobera's approach (2000), the boundary of the influence zone is determined by the viewshed of the attractor or taboo site. In addition, Llobera suggests different decay functions, two of which are:
(1) decay(d) = magnitude – (magnitude*d)/dmax
(2) decay(d) = magnitude * e-k*d
where magnitude is the amount of influence at the site location which (1) decreases linearly with increasing distance d, until at distance dmax the influence is no longer felt or (2) decreases faster than linear, with k selected in such a way that the function is close to 0 at distance dmax. The third option is stepwise linear and depends on the number of locations out of sight. The two decay functions above are introduced here because they can be generalised to other influence zones, not just viewsheds: the extension of the model to noisescapes is straightforward.
The decay functions may not only be employed for point objects but for lines and polygons as well. Existing routes are an important example: Once a route was created, by animals or by people previously living in the region, the route will be used, because it is easier to follow an existing route than to construct a new one. An example is the Roman road system in England, which provided a basic network in medieval times (Hindle 2002, 6, 31). On the Gough map (about 1360 AD) covering most of England, almost 40% of the routes shown follow the line of Roman roads.
Therefore existing routes are considered as attractors and are still attractive to people living at some distance because they know that the route is there, even if they cannot see it from their settlement. Only if the route is disrupted, for example by the breakdown of a bridge or if new requirements are to be faced such as the introduction of wheeled traffic, the old routes may become – partly – obsolete and will be replaced by new ones. In practice, this is difficult to model, and it is for this reason that the GIS books propose taking the existing routes into account but none of the archaeological LCP studies considered in this article includes this aspect (Table 1), although the decay functions proposed by Llobera (2000) can be implemented fairly easily.
If high toll fees are introduced on existing routes, people will try to avoid them. Hindle (2002, 13) mentions that in the 18th century traders tried to circumvent the tolls of the newly turnpiked roads. This can be modelled by increased costs for roads with tollgates which might be considered as a taboo zone.
Similarly, a river may be considered a taboo zone with an exponential decay function, as people will avoid wet feet, and the probability of getting wet feet will reduce with increasing distance to the river, and the decrease is quite rapid once the riverbed is left behind.