Department of Archaeology


Cumulative Viewshed Analysis: a GIS-based method for investigating intervisibility, and its archaeological application

DAVID WHEATLEY

To be published in G.Lock and Z.Stancic (eds.) 1995 Archaeology and GIS: A European Perspective. London: Routlege. Not for citation without the permission of the author.

Introduction

This paper introduces a general method, which may be called Cumulative Viewshed Analysis, which can be used to make inferences about the relationships of intervisibility between related sites within a landscape. The method is not statistically complex, and therefore can be considered to be quite robust. All stages of the method may be implemented using currently available GIS and statistical software, requiring only that a suitable elevation model be available, together with the locations of the sites. Although cumulative viewshed analysis may well find wider application, the method has been developed in response to a particular research problem, namely an attempt to understand the spatial relationship between archaeological monuments.

Cumulative viewshed analysis

Visibility from single sites

The calculation of a line of sight map or 'viewshed' for a point location, given a digital elevation model is a relatively trivial computing problem and is available within the current functionality of many GIS. In a raster system the calculation requires that, for each cell in the raster, a straight line be interpolated between the source point and each other cell within the elevation model. The heights of all the cells which occur on the straight line between the source and target cells can then be obtained in order to ascertain whether or not the cell exceeds the height of the three dimensional line at that point. Figure 1 shows diagramatically how this operates: the example top right shows the case for the existence of a line of sight, while the example bottom right shows the case for no line of sight. It is usual, in most cases, to add an additional value to the source cell to account for the height of the human eye above the surface.

The result of each of these discrete calculations is either a positive (Figure 1, top) or negative (Figure 1, bottom) result, conventionally coded as a 1 for a visible cell or a 0 for a cell which is not visible. When performed for the entire raster, the result is a binary image, those areas of the landscape which have a direct line of sight from the target cell coded as a 1 and those with no line of sight with 0. Such images are commonly referred to as visibility maps or viewshed maps and have already found some application within archaeology: Gaffney and Stancic, for example, investigating the Greek period of the Island of Hvar, generated a viewshed map for the watchtower at Maslonovik, Hvar. This then demonstrated that a similar watchtower at Tor would have been visible from Maslinovik, which would in turn have been able to pass warnings to the town of Pharos and their result supported the assumption that such towers formed 'an integral system connected to the town and Pharos whereby watch was kept for any approaching danger' (Gaffney and Stancic, 1991 p.78).

Viewshed maps were also suggested by Ruggles et al (1993) as part of a method for investigating the locations of the short standing stone rows of the island of Mull. This method suggested that viewshed maps for each of the standing stone row sites should be combined to create a binary multiple viewshed map consisting of the logical union of the individual maps. From this, prominent landscape features on which the stones may have been aligned could be identified, and viewshed maps generated from these locations. Finally a count could be made of the number of stone row sites falling within these landscape features, and 'the landscape features which best explain the observed placing of the stone rows are those for which this number is greatest' (p127). An example of this method applied is not provided by the authors.

More interesting, perhaps, is the claim by Lock and Harris (forthcoming) that viewshed maps from long barrows of the Danebury region consistently fail to overlap: 'in almost every case the Barrows appear to have been located so as to exclude other Barrows from its viewshed'. This is interpreted as evidence that the Barrows are territorial markers. If the visual interpretation of Lock and Harris is correct (and the images leave little room for doubt) then there should be a means of testing the existence of such a relationship.

Intervisibility within samples of sites

In situations where the intervisibility within a group of sites is of interest, it is possible to obtain a viewshed map for each site location. These individual maps can then be summed, using simple map algebra techniques, to create one surface. This surface then represents, for each cell within the landscape, the number of sites with a line of sight from that cell. For a sample of n sites, the value of this surface will obviously consist of integers which are constrained to vary between 0 and n. Such a map may be referred to as a cumulative viewshed map for the sample of sites within the particular region of interest. The phrase cumulative viewshed map is used here to distinguish this summed result from the multiple viewshed map referred to by Ruggles et al 1993 which is the logical union of a series of individual viewshed maps.

Having generated a cumulative viewshed surface from a sample of sites, it is then possible to perform a point-select operation on this surface based on the site locations, and thus to obtain, for each site, the number of other sites which are visible from it. An adjustment is necessary to account for the line of sight from the site to itself before an hypothesis can then be constructed to test for intervisibility among the sample of sites: this can be made either by subtracting one from the cumulative viewshed surface before the point select operation, or by subtracting one from the result of each point select.

Testing for intervisibility

Once these operations have been completed, the cumulative viewshed surface can be regarded as a statistical population - the population of the number of visible sites of all the cells within the study region - while the new attribute values of the sites can be regarded as a sample from that population. Given these, it is straightforward to construct a pair of testable hypotheses as follows:

H0 - That the sites are distributed irrespective of the number of other sites which are visible
H1 - That the sites are not distributed irrespective of the number of other sites which are visible

Using the GIS capability to summarise the characteristics of the cumulative viewshed map (population) and the site attributes (sample), it is then possible to construct a one-sample hypothesis test, at an appropriate confidence interval, to accept or reject this hypothesis. The ability to perform a one-sample test as opposed to a two-sample test, which would involve generating a second sample of random points from the region and obtaining the values of this random sample on the cumulative viewshed surface is of some importance. Unlike the traditional two-sample approach to regional analysis, the one-sample approach makes use of all the available information, and as Kvamme (1990) has pointed out: 'one sample statistical tests which compare a site sample against a background standard are conceptually and statistically superior'

There are a variety of tests which may be appropriate to this situation, but one particularly well suited test is the Kolmogorov-Smirnov goodness-of-fit test, described by Kvamme (1990 p373). This allows the comparison of an empirical sample distribution against an expected referent distribution. The test is performed by plotting the cumulative distributions of the sample and population respectively and obtaining the difference D between these two curves. The maximum value of D, Dmax is then compared with a critical value d obtained from the sample size and the required confidence interval. For alpha = 0.05, for example, and in a two-tailed test the value of d can be calculated from equation 1.1.

1.1

If Dmax exceeds this critical value d, then the sample distribution can be said to be significantly different from the population distribution and H0 may be rejected.

The selected confidence interval will depend to some extent on the circumstances. Although it may seem good practice to select as high a confidence interval as possible in order to avoid the error of claiming a relationship where there is none - a type I error, this must be contrasted with the (admittedly less serious) error of failing to identify a significant relationship - a type II error (Shennan, 1988, p.52). In the specific practice of archaeological analyses, this balance usually results in the adoption of alpha = 0.05, with the implication that a type I error may occur five times in every hundred experiments. However, it should be noted that some situations may dictate a greater level of confidence, and the reader contemplating the application of this technique should consider the context of the study, and the use to which the results will be put.

The method applied - intervisibility of Long Barrows

Long Barrows in the Neolithic

As an example of how the application of this technique to archaeological sites may provide new insights into the role of monuments within society, we may consider two groups of archaeological monuments in southern England. Before describing the application in detail, some background is needed, although this is necessarily a brief overview.

The sites are earlier Neolithic funerary monuments known as Long Barrows and are by far the most visible and numerous remains from this period in southern England. As such, they are central to the interpretation of Neolithic regional sequences. One group of these sites occurs on the Marlborough Downs close to the later monuments of Avebury and Silbury Hill while another occurs immediately south of this on Salisbury Plain, around the later site of Stonehenge (Grinsell, 1958; Ashbee, 1984).

The geographical groupings of barrows (and other monuments) such as the two used in this study have frequently been interpreted as the remains of discrete political groupings in the past. Renfrew, for example, interpreted the barrows themselves as family tombs, and used the barrow groups to argue for the existence of five Wessex 'chiefdoms' which he characterised (after Sahlins, 1958) as 'a ranked society, hierarchically arranged, sometimes in the form of a conical clan where the eldest descendent in the male line from the clan founder ranks highest, and the cadet branches are ranked in seniority after the main line.' (Renfrew, 1973; p.542)

More recent accounts have, probably rightly, been a less specific about the precise nature of the social groupings which are represented by the barrows. Thomas and Whittle (1986), 'envisage a group rather smaller than the local community as a whole (whatever the absolute size and geographical distribution), closely bound kinship and other ties'. The assumption that these groupings of monuments represent social entities of some sort within Neolithic societies certainly seems justified by the density of monuments; and by the distinctness of the geographical groups. Each group occurs on a defined area of chalk uplands and cannot be adequately explained solely in terms of differential survival. These groupings are also of a physical scale which would have permitted fairly regular travel within each area, involving distances of the order of 10km: perhaps a day's walk over the moderate terrain of the chalklands. Even the previously cautious Thomas (1991) concludes that the ' extreme density of settlement throughout the Neolithic in the Avebury area possibly entitles us to consider it as a single political unit ...' (1991 p163). For the purposes of this example it is assumed that the groups represent some sort of social or political entity, the precise nature of which is unclear.

Typology of the monuments

As well as these geographical groups, the barrows can be broadly divided (e.g. by Ashbee 1984) into earthen mounds, which generally consist of a rectangular or trapezoidal mound of chalk and turf with flanking ditches, and stone chambered mounds (frequently referred to as 'Cotswold-Severn' tombs). These are similar in that they consist of an elongated mound, but differ from the simpler earthen mounds in that they also contain stone chambers and frequently have impressive stone facades at the larger end. The distributions of these two types of tomb are broadly complementary - the stone tombs occur to the north and west of the Avebury area while only earthen barrows occur to the south - but overlap in the Avebury region, where both types occur. The Salisbury Plain group contains only earthen mounds.

Activities at the Long Barrows

The first phase of activity at these sites may be defined as the selection of the location and the construction of the mound. This was followed immediately by a phase of use at the monument, frequently involving deposition of human remains before some mounds were then deliberately blocked prior to disuse. A final phase of continued existence after the primary use of the site might also be defined, during which the sites remained as important ritual foci. Much attention has been given to the use and blocking of the tombs, while discussion of the construction has usually centred on the architectural form of the tomb or on the mobilisation of labour (e.g. Renfrew 1973). However, little comment has been passed on the monument's role within Neolithic society after disuse, although clearly the monuments must have remained important places within the landscape, marked as they were by structures which were sometimes very imposing.

In this context, a number of recent discussions of the earlier Neolithic of these two areas (e.g. Devereux 1991, Thomas 1993) have emphasised the role of monument visibility and intervisibility in the interpretation of the social developments and it was with this in mind that the visibility of the Avebury and Salisbury Plain tombs appeared to be an area worthy of attention. If the tombs can be shown to have been constructed in locations which take account of the visibility of other monuments, then this may provide an insight into not only the functioning of the tombs after disuse but also the context of the construction of the later tombs.

The analysis

Worked example

To apply cumulative viewshed analysis to the two groups of monuments, the locations of reliably identified long barrows were obtained from existing sites and monuments records, and from archaeological accounts (e.g. Barker 1985, Richards 1984, 1990). This provided a group of twenty-seven sites in the Avebury region and thirty-one in the similar area around Stonehenge. These locations were imported to the format for analysis in the IDRISI GIS package (see Figure 2).

Elevation models were already available for each of the study areas, having been interpolated from Ordnance Survey 1:50 000 digital height data in the form of contours at 10m vertical interval, with a claimed root mean square error of between 2m and 3m. As an acceptable compromise between processing time and resolution, each 20km by 20km study area was represented as a 250x250 raster, giving a cell size of 80m square.

A viewshed (line-of-sight) map was then generated for each barrow. These maps represent, depending on which way you consider it, either every cell in the landscape which could (theoretically) be seen from the barrow, or every cell in the landscape from which the barrow can be seen. An example viewshed map is given in Figure 3). All of these viewshed maps for the barrows in each region were then summed using simple map algebra also available within the IDRISI package. The two resulting maps (shown in Figure 4) are a transformation of the elevation model into a surface in which every cell contains the number of barrows visible from it. The areas of each value in each cumulative viewshed map could then be obtained.

Next the number of barrows visible from each long barrow in the region was obtained using attribute extraction. These values, of course, include the line of sight from each barrow to itself. The cumulative viewshed map for each area was then incremented by one to account for the visibility of each barrow with itself, and could then be treated as a background population in order to test the null hypothesis that the long barrows in each region are sited with no regard for the number of other barrows with a line of sight from their location. These results, for each area, are shown in Tables 1 and 2 , these are then presented as cumulative percentage graphs in Figure 5.

Results

It should be clear from the two graphs that the barrows generally occur in locations with more lines of sight than the background cumulative viewshed population, although this feature is considerably more marked for the Stonehenge group than for the Avebury group. However, it is unclear whether this deviation from the expected distribution of barrows can be explained in terms of pure chance or whether the deviation is statistically significant.

To test this, a one-sample Kolmogorov-Smirnov test was undertaken for each area, adopting a 0.05 confidence level as discussed above. Large sample theory (Kvamme, 1991 citing Thomas, 1986 p.506) dictates that the critical value, d is approximately 1.36/sqareroot(n) for the 0.05 significance level, which gives a d of 0.26 for the Avebury region and 0.24 for the Stonehenge group. Dmax for each group was then obtained from the results in Tables 1 and 2 .

For the Avebury series it can be seen that Dmax (0.18) does not exceed d (0.26) and the test therefore does not allow the rejection of Ho at the 0.05 level. For the Stonehenge group, however, Dmax (0.38) does exceed the critical value d (0.24) allowing the rejection of the hypothesis that the deviation may be caused by chance.

Statistical interpretation

The method has revealed, in simple terms, that the long barrows of the Stonehenge group tend to occur in locations from which high numbers of other barrows may be visible, and that this association is significant at a 0.05 confidence level. The method failed to provide any evidence, however, that the barrows of the Avebury group are anything but randomly distributed with respect to the same variable.

As with all statistical tests of association, however, a note of caution should be inserted. Apart from the obvious scepticism which should apply to any unrepeated statistical test (the LOS maps take some considerable time to calculate, and so time constraints have so far prevented repetition of the experiment), association must be carefully distinguished from causation. Clearly this test might be interpreted as revealing an intention on the constructors' behalf to site long barrows in areas of high visibility. It is equally plausible statistically, however, that another variable (such as proximity to water or elevation) which is itself associated with the area of the viewshed may be the causing factor. On the other hand, if another variable such as elevation, can also be shown to be associated with the barrow locations, then this also cannot be shown to be causative.

It must therefore be left to the archaeologist to interpret the results of such tests, and in this case it seems rather more likely (to the author at least) that the situation of the Stonehenge long barrows on areas of high ground is a side effect of their visibility rather than the alternative, that the visibility of other barrows is a side effect of the selection of high ground.

Error and uncertainty in viewshed maps

Errors are inherent in all data, and geographic databases are no exception to this. The primary sources of quantitative error within the analysis are (1) elevation values (2) quantization effects of rasterizing the elevation model (3) interpolation errors introduced by the isoline to DEM algorithm and (4) locational displacement of sites. These errors may then be propagated into secondary errors in (1) individual viewshed maps, (2) cumulative viewshed maps and (3) the attribute values of sites.

Such errors have been investigated by Fisher (1991) who urges caution over the uncritical use of operations which show locations as either in or out of a viewshed. In a subsequent paper (Fisher 1992) he develops the notion of a 'fuzzy viewsheds' which incorporate uncertainty into the calculation of a viewshed map, by registering a measure of certainty for each cell instead of a simple boolean 1 or 0. Such an approach is beyond the scope of this application but clearly offers a method of incorporating uncertainty within the methodology, requiring simply that the boolean viewshed maps from each site location be replaced by fuzzy set maps generated with appropriate parameters derived from the RMS of the elevation model and estimated errors within other parameters.

Another source of information concerning the accuracy of Cumulative viewshed analysis may come from sensitivity studies. In these the height of the viewer can be increased or decreased and the experiment repeated in order to assess the impact of the choices of parameter on the experimental result. It has not been possible to undertake sensitivity analyses in this case but it is encouraging to note Lock and Harris' comment that 'A sensitivity analysis with a Barrow offset height of four meters showed almost no variation in the patterns so discerned' which compelled them to conclude that the pattern observed was 'unlikely to have occurred through chance but was the result of very careful siting procedures undertaken by native peoples'.

Other than this, however, the only genuinely reliable source of error estimation lies with field observation and, although far from conclusive, the author can report that an afternoon spent identifying features on the horizon from Windmill Hill in the Avebury region provided a very good correlation with the theoretical viewshed map of the same site.

Archaeological interpretation

One particular problem which can be identified in the application of the method to this data is that the landscape was considerably more wooded in this period of prehistory than it is today. For this reason, a line of sight need not infer intervisibility. In mitigation, there is considerable evidence to suggest that barrows tended to be built in cleared areas of the landscape: South Street, for example, was built within a cultivated field (Ashbee et al 1979), and others such as Horslip, Beckhampton Road and West Kennet have all been shown from molluscan analysis of to have been built in open areas.

If we accept the hypothesis that many of the Stonehenge barrows were deliberately located in areas from which other barrows are visible, then some archaeological explanation must be presented for this practice. Furthermore some explanation must also be provided for the fact that the neighbouring, contemporary group of tombs in the Avebury region shows no evidence of the same process.

One clue as to the social function of these locations has already been mentioned: the incorporation of earlier monuments within later ones, as at the Dorset Cursus. Here Barrett et al (1991) have shown that the builders of the cursus included references to earlier monuments in the design of cursus. This involved not only the incorporation of a long barrow into the cursus bank but also, most interestingly, revealed that the builders deliberately altered the course of the cursus to enclose a long barrow so that it 'framed' the midwinter sunset viewed from the cursus terminal. Such physical and visual references to earlier monuments are perhaps an attempt to appropriate the status and associations of an older monument into the new structures, and the same mechanism could be at work in the positioning of the Stonehenge long barrows. In a society in which appeals to past traditions and practices are very apparent in other aspects of the funerary ritual it seems distinctly possible that visual references to other barrows may have constituted part of the mechanism by which social structures were reproduced and re-negotiated.

More specifically this could imply that those who directed the building of the monuments felt that the ability to see existing monuments added authority to the new structure through appeals to the historic authority of the existing monuments. Those in control of the new monuments, would then gain added legitimacy, and be in a better position to retain their own status and authority. This is not to imply that there was no counter to such strategies: other claims to social authority may be evidenced by the use of different locations and types of monument for ritual activities. What may have been revealed by this analysis is just one of many tactics employed by these people to negotiate and transform systems of authority and control.

But if this is the true, then a slightly different mechanism must be at work in the Avebury region. Here there seems to be no evidence that the barrows are located with reference to the visibility of other barrows. A number of possible reasons might be put forward for this. Firstly the appearance of megalithic tombs in the Avebury sequence is different from Salisbury plain. In the Avebury sequence, the monuments may have been focused less on the surrounding landscape than on the architecture of the tombs. The creation of the impressive stone facade at West Kennet might be seen to add authority and importance to the tomb as well as focus attention on the activities of those performing at the entrance. In the Avebury region, those who held power, were appealing more to monumentality in the structures, and less to their relationship with the past in their attempt to maintain their position.

The difference between the two regions is in itself interesting, and might be explained in terms of the resources of the different locations themselves: those who build the monuments on Salisbury Plain may have had no access to large sarsen stones because they are found naturally in the Avebury region. On the other hand the difference may have been a deliberate assertion of cultural difference: two groups of people constituting themselves in opposition to one another and expressed through different practices.

In this context, one final archaeological remark may be made concerning the result obtained by Lock and Harris (forthcoming). Although not tested within precisely the same framework which was used here, there seems to be convincing evidence that the group of barrows investigated by these authors were situated for deliberate non-intervisibility from one another, a characteristic which, it is argued, supports the notion that these barrows were used as territorial markers. The simple fact that this result is different from that obtained here need not imply that it is wrong: it has consistently been emphasised here that different mechanisms are at work in the different area. There must be a suspicion therefore that the people responsible for the construction of the barrows of the Danebury region had different motives again to those of the Avebury and Salisbury Plain region in their choice of location.

Conclusions

This paper has outlined a new method for investigating the spatial organisation of monuments within an archaeological landscape. Through the example of Neolithic Long Barrows, it has been shown that the method is straightforward to apply using relatively inexpensive GIS technology, and can produce interesting and unexpected results.

The interpretation of the result of the case study must remain extremely tentative: it must be accepted that claims for intervisibility among the barrow groups rest on a particular view of the environmental conditions during the Neolithic, and further evidence regarding the size of the cleared areas around the monuments is needed in order to evaluate the result further. In archaeological terms, such results are not straightforward to interpret because of the need to consider the difference between the statistical association which may be shown by Cumulative Viewshed Analysis, and causation which can only be inferred from the archaeological context of the particular study.

Whatever the merits of the particular archaeological interpretation of the results of the example application, it is hoped that the paper has suggested that Cumulative Viewshed Analysis may form a useful tool for the investigation of a variety of different monument types.

Acknowledgements

The author gratefully acknowledges the Royal Commission for Historic Monuments (England) and the Science and Engineering Research Council who have made this research possible and also Dr Stephen Shennan and Dr Arthur ApSimon for their comments and contributions.

References


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