The curvature of the earth affects visibility studies when using a DEM (Digital Elevation Model) and needs to be taken into consideration as pointed out by Conolly and Lake in 2006 although little work has been done in archaeology to explore the implications of this warning. Although some GIS packages such as ArcGIS offer push button solutions to include or not the effects of curvature, without understanding the underlying technical aspects the practitioner can be led to misleading interpretations.

In this paper we propose a new method to calculate and assess the combined effects of curvature and atmospheric refraction on visibility studies. The long barrows of the Danebury region in England are used as case study. The mathematical models of curvature and refraction are presented and an optimized method for fast correction of DEM values is described based on pre-calculating correction values and applying these to the DEM by matrix subtraction.

Regarding refraction, the earth’s atmosphere works as a lens with a bending effect – the result is that this enables to view further from any viewpoint. Here we adapt a ray bending model in which 1/6 is added to the value of the earth’s radius and a refraction matrix is pre-calculated and applied to the DEM in the same manner as curvature.

Visibility is calculated within the range of 10km for the 18 long barrows and a further 18 random locations in the landscape were selected. Each visibility map was divided into 10 bands of radius 1km for each location. The reduction in the number of visible cells when compared to standard visibility analysis is from 2% (short distances) to over 20% (longer distances).

In order to find common properties of visibility concerning barrows and random locations, this paper reports on the Kolmogorov-Smirnov (K-S) tests performed for each visibility band across the 18 barrows and 18 random locations to determine whether visibility bands at the long barrows follow the same distribution of visibility in the landscape. Finally, to find out how each visibility band changes across all barrows and random locations, visibility bands were analysed independently, with the combined effects of curvature and refraction. The studies on curvature and refraction have shown that these can have a dramatic effect on visibility thus contributing to understanding spatial relationships based on GIS visibility.