Probabilistic Modelling for Incorporating Uncertainty in Least Cost Path Results: a Postdictive Roman Road Case Study

Joseph Lewis

doi:10.1007/s10816-021-09522-w

Abstract

The movement of past peoples in the landscape has been studied extensively through the use of least cost path (LCP) analysis. Although methodological issues of applying LCP analysis in archaeology have frequently been discussed, the effect of DEM error on LCP results has not been fully assessed. Due to this, the reliability of the LCP result is undermined, jeopardising how well the method can confidently be used to model past movement. To strengthen the reliability of LCP results, this research proposes the use of Monte Carlo simulation as a method for incorporating and propagating the effects of error on LCP results. Focusing on vertical error, random error fields are calculated and incorporated into the documented and reproducible LCP modelling process using the R package leastcostpath. By graphically communicating the impact of vertical error using probabilistic LCPs, uncertainty in the results can be taken into account when interpreting LCPs. The method is applied to a Roman road case study, finding that the incorporation of vertical error results in the identification of multiple ‘least cost’ routes within the landscape. Furthermore, the deviation between the roman road and the probabilistic LCP suggests that the location of the roman road was influenced by additional factors other than minimising energy expenditure. This research finds that the probabilistic LCP derived using Monte Carlo simulation is a viable method for the graphical communication of the uncertainty caused by error within the input data used within the LCP modelling process. Therefore, it is recommended that probabilistic LCPs become the default approach when modelling movement using input data that contains errors.

Highlights

The movement of past peoples in the landscape has been studied extensively through the use of least cost path (LCP) analysis (Verhagen et al, 2019; White & SurfaceEvans, 2012)
When visually comparing the LCPs (Fig. 4), it is apparent that the single LCP produced without incorporating vertical error (Fig. 4(A)) does not fully capture nor communicate how the vertical error in the digital elevation model (DEM), and subsequently the cost surface, propagates to the LCP result
The probabilistic LCP has identified that the large deviation from the Roman road in the northern section remains after vertical error is accounted for

Summary

Introduction

The movement of past peoples in the landscape has been studied extensively through the use of least cost path (LCP) analysis (Verhagen et al, 2019; White & SurfaceEvans, 2012). The reliability of the LCP is strengthened by yielding outcomes that better approximate reality, or in other words, the LCP and Probabilistic Modelling for Incorporating Uncertainty in Least Cost Their interpretation is less susceptible to change if the LCP modelling process is run with the same input data incorporating a different, but likely, realisation of error. The use of uncertainty propagation can be applied to all input data containing errors within the LCP modelling process, this research focuses on the impact of vertical error on the calculated LCP. This is demonstrated through a case study that aims to postdictively model a Roman road in Cumbria, England. By calculating the slope in all directions and preserving the anisotropic property of slope, the LCP can differ depending on whether it is calculated from A to B or B to A (Herzog, 2014a)

Background

Results

Discussion and Conclusions