Spatial analysis based on cost functions

Abstract

Each model of past movement based on historical and archaeological evidence nowadays relies implicitly or explicitly on a cost function estimating costs of movement in terms of time, calories or some other currency for the study area and period of time considered. Cost functions are the basis of two popular GIS-based areas of spatial analysis in archaeology: site catchments and least-cost paths. A site catchment is the region accessible from a site, and often archaeological studies analyse the resources within this region. A least-cost path (LCP) is the route minimizing the costs of movement between two given locations. In archaeological studies, the aim of LCP calculations is often to reconstruct ancient routes or a route network or to identify the principal factors governing the construction of known roads or road segments. For generating a site catchment, GIS programs compute an accumulated cost surface (ACS). This is also the first step for LCP generation; therefore, the Dijkstra algorithm implemented in most GIS programs for this purpose is outlined. The cost function applied for calculating the ACS typically depends on slope, soil type, vegetation cover or the presence of streams. Several slope-dependent cost functions and a list of terrain factors are presented. Moreover, issues with least-cost applications are discussed, including barrier implementation, restricted number of possible movement directions, and the calculation of slope-based costs for a path taken in one or two directions. The aim of the case study is to compare the site catchments of a Roman farm and a temple at different scales based on a cost model derived from Roman roads. The concluding section discusses validation and stability of the outcomes of the methods presented and some additional issues such as modelling movement beyond walking. Finally, some other cost function based approaches are outlined. Two popular geographical information systems (GIS)-based areas of spatial analysis in archaeology are based on cost functions: site catchments and least-cost paths. In fact, the most basic application of a cost function is the generation of a least-cost site catchment (LCSC). The LCSC includes all areas that can be reached by expending less than a user-selected cost limit. The term isochrone is often used for the boundary when costs are measured in terms of time. The initial step in LCSC and least-cost path (LCP) calculation is the decision concerning the principal factors governing movement costs, and establishing an appropriate cost function combining the costs of these factors. The results of the LCP algorithm are independent of the units of measurement chosen, i.e. they do not change if all costs are multiplied by a constant factor. LCP technology can also be applied to reconstruct Roman long-distance water supply systems.