Finding the site of Boudica's last battle: multi-attribute analysis of sites identified by template matching.

Steve Kaye, February 2015

Abstract

This, the third essay on the attempt to find the site of Boudica's last battle, improves on previous techniques. A terrain model of the southern UK was searched, by use of a template matching algorithm, to find all the topographic depressions of width approximately 500 to 2000 m and depth 15 m or greater (other attributes were applied) that matched Tacitus' description of the battle-site. After some initial editing of the original sites (2700) to remove those with selection errors and the most obvious of faults, the candidate battle-site list was reduced to 862. These were then subjected to a weighting and ranking process via the application of ten attributes.

A crucial step was to examine the choice of routes available to the Roman commander, Suetonius Paulinus, as he considered withdrawal from London after Boudica's destruction of Colchester and the rout of the 9th Legion. The pros and cons for each route are described, discussed and the results compared. The findings were: that Suetonius did not march north-east towards Boudica; that the London to Lewes road to the southern coast would not have been chosen as all the prospective battle-sites are less than one day's march from London; that taking Watling Street to the Kent ports would have been a strategic and tactical error; that marching further north than St. Albans along Watling Street could have led to conflict with flanking and rearward attacking rebel forces; that turning west at St. Albans to follow Akeman Street was a superior choice but one limited to prospective battle-sites (3, 5, 7, 8, 10, 11 etc.) in the Bulbourne river valley, south-east of Tring, if the absence of burning and destruction at Alchester Roman fortress is correct; that the other southern route from London via Stane Street was strategically sound, and that tactically the prospective battle-sites at Dorking (1 and 2) were outstanding; and finally, that taking the Portway directly west out of London was strategically the most suitable of routes and one Suetonius would probably have viewed most favourably.

A simple combination of the ranked sites and the most likely choice of route from London would logically indicate that the actual battle took place in the west at Ogbourne St. George (4), Donhead St. Andrew (6), or Shalbourne (9). However, in acknowledging that not all events, dispositions, circumstances etc. were known, it was concluded that the next investigative phase will be best served by examining not only the western Portway locations but also those along Stane Street at Dorking, and the higher ranking sites within the Bulbourne river valley along Akeman Street.

Acknowledgements: many computations and maps in this essay were created in SAGA and QGIS. Special thanks to Dr. H.Y. Kim for enhancing for this study his template matching software, Ciratefi. Nici Lilley, yet again, has kindly applied her editing skills to this essay; as always, any remaining errors are my own.

Note 1: unless specified otherwise, all quotations taken from the Annals (Book 14, 30-37) by Tacitus are the translations of Church and Brodribb, 1888. Other translations were available; all have their own peculiarities and differences, but the author simply prefers Church and Brodribb's work for its Victorian flavour.

Note 2: another personal preference was to not use Cassius Dio's account of the rebellion in his Histories which seems to the author to owe more to the requirement to entertain than to elucidate.

Note 3: the time format used is hour:min, e.g. '10:13' is 10 hours and 13 minutes.

Introduction

In the Summer of either 60 or 61 AD Suetonius Paulinus, the Roman governor of the 18 year old province of Britain, defeated in battle a rebellious tribal force led by the Queen of the Iceni, Boudica. The Roman victory secured the south of Britain for approximately 350 years until direct rule from Rome was extinguished across the islands.

The site of the battle is unknown.

This essay is an account of the author's latest efforts in deploying analytical techniques and modern hydrological and topographical data, in combination with the known archaeology and historical accounts, to find the most plausible of candidate battle-sites.

Figure 1: Location map.

A brief description of Boudica's rebellion

The following overview is based on a description in Kaye, 2013a:

A précis of events in 60 or 61 AD, based on Tacitus (Annals, Book 14, 30-37), would mention that Gaius Suetonius Paulinus was the Roman Governor of Britain who commanded the 2th, 9th, 14th and 20th Legions, together with an unknown number of auxiliary and cavalry units, and that he was interrupted in his conquest of the Druidic stronghold on Anglesey by news of a rebellion by the Iceni, a tribe in modern East Anglia led by Boudica, a queen driven to revenge by Roman oppressors. The Iceni, together with other local allies including the Trinovantes located in modern Essex, stormed and destroyed Colchester, the principle Roman town in Britain. Meanwhile, the 9th Legion, led by its commander Petillius Cerialis, marched from its fort (possibly Longthorpe near Peterborough) but was met en route, at an unknown location, by the already victorious Britons. The infantry were destroyed; Cerialis and his cavalry rapidly fled and may have found sanctuary in a fort.

This news may have reached Suetonius as he marched from Anglesey towards London with cohorts and auxiliaries from the 14th and the veterans of the 20th Legions. The bad news would be compounded when Suetonius heard that the 2nd Legion, probably based in Exeter, was not marching to join him as he may have ordered. Suddenly, Suetonius had lost approximately half of his effective combat strength; he was marching elements of the 14th and 20th Legions through hostile territory towards London and faced the possibility of meeting a horde of Britons, possibly numbering in the hundreds of thousands. On reaching London he decided to abandon the proto-city and marched his men, plus any civilians who could keep up, away from the Britons who went on to destroy the settlement.

Supposedly a less destructive fate befell St. Albans to the north of London. The horde of Britons followed Suetonius as he attempted to march away from the greatest danger to his army but unknown circumstances, or a change in relative fortune, led him to offer battle with his 10,000 armed men. The Roman legionaries, auxiliaries and cavalrymen were victorious, apparently killing eighty thousand Britons for little loss.

A new method to search the topographic domain: template matching

In earlier work (Kaye, 2010a and b; 2013a) the topographic descriptions given by Tacitus were used to define the data range of a number of attributes and, from these, specify a set of criteria for candidate battle-sites. The criteria were employed to visually search for sites across the south of Britain. This work in 2010 resulted in 263 sites; the work in 2013 used the same base set of visually selected sites but reduced them to 110 following work on the hydrological requirements of the Roman force. These were then weighted and ranked to produce a final list of 'most likely' battle-sites. However, it was recognised that the subjectivity involved in visually identifying candidate battle-sites was detrimental and therefore a new, more objective method was employed in this latest study: template matching (Wikipedia article).

The essence of template matching is to graphically interrogate a main scene such that sub-scenes can be identified within the main scene, e.g. a car on a motorway, or a battle-site on a map of topographical parameters, as in this study. The sub-scene is searched for by way of a pre-defined template; in the case of the car a template of a particular car registration number could be created and the sub-scene of that number found, or not, within the main scene. In this study the templates were various depictions of topography that might be locations of candidate battle-sites (Figure 3).

As already mentioned, a significant benefit of using template matching was the increased objectivity of the study. This was matched by the use of computing power to enhance the search process, such that the range of topographic attribute values could be enlarged, resulting in more candidate battle-sites being found.

With regard to the claims of reduced subjectivity, it is not the author's view that the techniques used in this study are wholly objective; that state would be impossible to achieve. Indeed, at each stage of the process subjective judgements have been made, for example the choice of software, limits to modelling or which sites to downgrade. Furthermore, readers will observe that the deeper into this essay they proceed, the greater the subjectivity. This was an inevitable consequence of the overall process when choices of suitability or probability had to be made, and the results linked to the archaeological record and historical accounts.

Template matching to find the initial set of candidate battle-sites

The template matching software used was Ciratefi (Araujo and Kim, 2011) which operates on colour imagery and is rotation-, scale- and translation-invariant (except for affine or perspective transformations). The ability to operate on a coloured main scene was critical for this study.

Figure 2: the main scene used in the Ciratefi template matching exercise. The detailed insert is of a section along the western-facing Chilterns escarpment. Coloured areas are: plains in yellow; ridges in red; ridge slope areas of less than 5 degrees in green; slopes greater than 5 degrees in purple. Areas without colour are those without ridges, slopes, etc. and with topographic depressions less than 15 m in depth, e.g. low relief plains and valleys. The coastline is displayed to aid the reader and was not included on the main scene. The bounding graticule is in metres; OSGB36, British National Grid (the same for all maps in this essay).

The main scene (Figure 2) for the template matching algorithm was a terrain model made from SRTM 90 m data (re-sampled to 50 m) and various derived or measured parameters chosen to model Tacitus' description of the topographical features of the battle-site. The key passage in the Annals is in Book 14.34:

Suetonius had the fourteenth legion with the veterans of the twentieth, and auxiliaries from the neighbourhood, to the number of about ten thousand armed men, when he prepared to break off delay and fight a battle. He chose a position approached by a narrow defile [faucibus], closed in at the rear by a forest, having first ascertained that there was not a soldier of the enemy except in his front, where an open plain [aperta planities] extended without any danger from ambuscades. His legions were in close array; round them, the light-armed troops, and the cavalry in dense array on the wings. On the other side, the army of the Britons, with its masses of infantry and cavalry, was confidently exulting, a vaster host than ever had assembled, and so fierce in spirit that they actually brought with them, to witness the victory, their wives riding in waggons, which they had placed on the extreme border of the plain.

Church and Brodribb later translate that the Roman army, "kept its position, clinging to the narrow defile as a defence” (14.37).

These Latin translations would appear to be unambiguous: the Roman front-line was in a defile. However, as Hughes (2014) has pointed out, there have been a number of different translations resulting in ambiguity regarding Tacitus' true meaning. What seems to be agreed upon is that some form of topographic depression was involved and that the Romans stayed within it during the initial phases of the battle. Whether this depression was a defile or valley can be reduced to a semantic difference if the topographic values are defined to accommodate both forms. To that end, in this study the main scene (Figure 2) was configured to display both shallow valleys and steep defiles by first computing the topographic position index (TPI) of the whole area shown in Figure 2. The area of interest was then reduced to a radius of 1500 m from any high TPI features (ridges, various slope forms etc.); followed by removing any depressions whose depth was less than 15 m (from valley floor to adjacent ridge or elevated area); and then by displaying any areas whose slope in degrees was equal to or greater than five; finally, any plain or valley widths less than 500 m across were removed, it being reasoned that the Roman front-line of legionaries would probably not have occupied less for fear of being surrounded by the much greater number of rebels. (Note: this did not preclude the finding of candidate sites less than 500 m across.) In using Figure 2, the main scene, the template matching exercise would search for candidate battle-sites across most of southern Britain, with only the flattest of land surfaces, whether within elevated areas or low-lying, being excluded. Having produced the main scene the next step was to create the templates to search for the sub-scenes within it.

These were produced with regard to the many permutations of topographic depressions that the various Latin translations of Tacitus (Hughes, 2014) might reasonably allow. A written description of each template would be onerous for the reader; hopefully the nine displayed in Figure 3 demonstrate the large range of depressions considered in this study.

Figure 3: the nine templates used to search for sub-scenes in the main scene, Figure 2. Colours assigned as in Figure 2. In general, the yellow areas are plains bordered by red-brown rising margins; yellow plains also occur at higher elevations. Note that, compared to the originals, these images have a lowered resolution, colour fidelity and clarity.

Each template was applied in turn to the main scene in Ciratefi which, being scale-, rotation- and translation-invariant, found 2700 matches in the area east of the River Severn (Figure 4), each different in terms of size (the sites were shown as circles with the diameter closely matching the width of the topographic depression), the direction in which the depression opens or closes, or general alterations due to the form of the depression margins and plains. This deliberately-chosen large number of matches would suggest little possibility of the true Boudican battle-site not being present. The centroid locations of these 2700 template matched sites were the datum points for more detailed analysis.

Figure 4: the original 2700 matches from the template matching exercise. The black dots are the expanded centroid locations of the template matches (circles with diameter equal to the width of the found topographic depression). The area west of the river Severn was excluded from the study because it was thought unlikely that Suetonius would not have sought shelter in a fort, for example Kingsholm near Gloucester, if he had marched that far west. Note that there are some obviously erroneous sites, e.g. in France and the Isle of Wight; these, and others for different reasons (see text), were removed from the study.

After some initial editing to remove matches that were either too large, too small or simply in inappropriate topographic locations, for example the tops of ridges, the number of template-matched sites fell to 2187. In addition, many were slightly repositioned by tens of metres so that their circular boundaries were contained by the depression margins, often shown by slopes greater than five degrees, as it was assumed that their diameters would equate to the length of a front-line composed of Roman legionaries (Figure 5). Typically this placed the centroid of the matches close to the lowest elevations within the depression.

Having re-located some matches, the next step was to remove all those that had grossly detrimental characteristics for the Romans. The reasoning was that Suetonius had been in control of the direction of travel from London, had marched for at least one day and probably many days (a topic which will be discussed later), and he chose to offer battle in his preferred location – Tacitus writes of Suetonius, “he prepared to break off delay and fight a battle", and later still, “[he] having first ascertained that there was not a soldier of the enemy except in his front, where an open plain extended without any danger from ambuscades" (Annals 14.34). Having the advantage of time, due to his army's superior marching speed (Kaye 2013a and c), it seemed inconceivable to reason that Suetonius would not have selected the most suitable of battle-sites, and probably the best in any area or along a particular line-of-march.

Figure 5: examples of the widths (diameter) of template matched sites in the Thames Valley (between Pangbourne and Reading). The widths of the sites defined by the template matching software, Ciratefi, were used to slightly relocate the sites to positions bounded by the depression margins, often between slopes greater than five degrees. The concept employed was that the widths matched the likely length of the Roman front-line of legionaries. Colours assigned as in Figure 2.

As an aside, it could be argued that the computational approach used in this study, one that examines every square metre of the topography in the south of Britain, far exceeds the knowledge that Suetonius could possibly have deployed in selecting his battle-site, i.e. that the encompassing, all-knowing search of this study would find sites that Suetonius could not have known of in advance of reaching the locale. The counter-argument is that the south of Britain is a relatively small area, a fact that frequently eludes the modern mind, but would have been apparent to a Roman commander used to traversing much larger spaces in Europe and north Africa. A small area is more easily known, especially to a Roman Governor who probably spent a large part of his previous two years of tenure riding, or being carried in coaches, across the breadth of the province. This activity, at a pace slow enough to allow study of the passing landscape, is profoundly different to the modern observer peering forever forwards down the modern road, and would build a base of topographic knowledge that may have been called upon during the Boudica uprising. Suetonius would not have been alone in gathering this knowledge: the same would have been true of his sub-commanders, headquarters staff, local unit commanders, those charged with patrolling their local area and, finally but possibly significantly, those indigenous tribesmen and leaders who supported the Romans. All these people would have either spent their lifetimes in getting to know their own land and those of their neighbours, or may have spent 18 years since the invasion in 43 AD marching and riding across the terrain. In combination this knowledge would have been comprehensive, even possibly mapped and, if the right individuals were in attendance, known to Suetonius in some manner. For surely the simple question to be asked of those around him, supposing that he did not have his own answer, was, “where is there a battle-site approximately one kilometre wide, flat and open to the front, bounded by ridges or elevations to protect the flanks of the front-line, and has sufficient water for the men and beasts?”. If, for example, an answer came from a local tribal chief, then a unit of cavalry led by an experienced officer could be dispatched to reconnoitre. Answers from others would be judged on the informant's merit. In conclusion to this argument, for the modern mind to suppose that the ancients did not have and were not capable of having a deep knowledge of the land they traversed and, in the Roman case in Britain, controlled, is to unjustly underestimate their combined capabilities. Furthermore, as will be described in later sections, the majority of top candidate battle-sites were on, adjacent or within a few kilometres of a major military Roman road (many being within view of a road). Therefore, this modern study could be said to replicate the knowledge Suetonius either held or had available to him.

Returning to the description of finding the battle-sites, logic suggests that Suetonius would not have chosen a site with the most obvious of faults: one where the river supplying sufficient water for his army's needs (0.00891 cubic metres per second [m3/s]) either flowed towards his front-line or was otherwise under the control of the rebels thus leaving him without sufficient water; or the Roman front-line faced significantly uphill; or the front-line faced a direction rotationally opposed to the most likely direction of march from London; or one where the route from London to the battle-site was so convoluted and/or retrograde that the rebels could have approached and flanked the Romans from a number of directions so that there was a low probability that there was “not a soldier of the enemy except in his front”.

Each of the remaining 2187 template matches were examined for these faults; those found wanting were removed from any subsequent calculations resulting in a new active list of 862 sites (Figure 6).

Figure 6: the distribution of 862 active candidate battle-sites (red) overlying the original 2700 template matched sites (pale purple). Background is of elevation (normalized height); Roman major roads in black, not all of which would have existed in 60 or 61 AD.

Ten normalised attributes for 862 battle-sites, weighted and ranked

To summarise this section: the calculated or measured values of ten attributes were assigned to the 862 active sites; the value of each site was then normalised with respect to the others (0 to 1), and then weighted and ranked.

The 10 attributes will be briefly described.

Normalised height - where local elevations were examined and allotted a value of 1, to the highest, and 0, to the lowest position. In this study the mean of normalised heights of all grid cells within a polygonal area was used as a measure of local elevation amplitude, with the highest being most favourable to the Romans.

Terrain ruggedness (vector) - corresponds to the average elevation change between any point on a grid and its surrounding area. In this study three polygon areas around a candidate site were measured for ruggedness and the mean calculated. Each was then normalised, and the average of all three polygons used as the gross measure of ruggedness. The three polygons were: the width of the depression in which the site was situated (valley or defile width which also equalled the original width of the templates found by Ciratefi – remember that the original template circles were slightly moved to occupy the mid-point of the depressions, i.e. they were typically bounded by increasing slope values) and twice and thrice this width. The use of three polygons gave a measure of overall ruggedness within and adjacent to the site; this may be interpreted as a combined measure of a) local suitability for the Roman front-line and b) an indicator of the ruggedness of the topography surrounding the front-line, e.g. the more rugged, the less likely the site might have been flanked by the rebels.

Suitability of Roman front-line length – the point of this attribute was to determine the range of suitable front-line lengths, taken as the diameter of the template matched site found earlier (usually the width of the depression - see Figure 5), and those partially or wholly detrimental to the Romans and therefore, less likely to have been Suetonius' choice. To reiterate, Tacitus wrote that 10,000 Roman armed men were at the battle, comprised of legionaries from the 14th Legion plus veterans from the 20th that together constituted the front-line soldiers, and auxiliaries and cavalrymen on the flanks. Most modern commentators suppose, and likewise in this study, that the legionary numbers possibly equated to a full legion, c. 5,000 men (note: there is no evidence for this supposition). Of the battle formation Tacitus wrote that:

His [Suetonius'] legions were in close array; round them, the light-armed troops, and the cavalry in dense array on the wings. (Annals 14.34);

and later at the point of contact he wrote:

At first, the legion kept its position, clinging to the narrow defile as a defence; when they had exhausted their missiles, which they discharged with unerring aim on the closely approaching foe, they rushed out in a wedge-like column. Similar was the onset of the auxiliaries, while the cavalry with extended lances broke through all who offered a strong resistance. (Annals 14.37).

It was clear that the Romans were aligned across a defile (the topographic depression), and that the two armies came together along one long battle-line to which the rebels had directly advanced. Tacitus gave no suggestion of the rebels flanking or surrounding the Roman battle-line. Hence, to determine the likely length of the front-line it was necessary to define a measurement that would exclude, or varyingly penalise, those Roman front-line widths that would have been seen either as untenable by Suetonius or would have invoked a different tactic by Boudica.

As already mentioned, the heavily-armed and armoured legionary 5,000, i.e. those most capable of resisting and repulsing the initial, most dangerous attack, formed the continuous front-line with the auxiliaries and cavalry stationed at the margins. The two latter groups were assumed to be stationed on elevated and rising ground, often with slopes exceeding five degrees, that compensated for their lighter armour and arms. Most commentators suggest that the probable front-line length of the legionaries was 1,000 m (note: there is no evidence for this supposition); this seemed a reasonable starting assumption which, estimating that a single legionary occupied one metre, resulted in five ranks of legionaries facing the charging rebels.

Some soldiers (legionaries and/or auxiliaries) would have been engaged in guarding the marching camp but Tacitus does not give these sorts of details and neither can the number be confidently assigned. In addition, the statement by Tacitus that Suetonius, “having first ascertained that there was not a soldier of the enemy except in his front”, might equally relate to the camp, rather than just the front-line. The camp-guard might therefore have been small in number, the front-line playing the major part of that role. Irrespective of those points, in this study no justifiable, unambiguous mechanism could be found to lower the 10,000 to take account of guarding the camp: consequently the whole body was assumed to have been at the battle-site.

Figure 7: graph and polynomial trend-line of Roman front-line widths. Weighting factor values (y axis) between 700 and 1300 m front-line width (x axis) were held close to 1 (at 1000 m and rank depth of 5), being thought acceptable to the Romans as rank depth decreased from 7 to 4. For other widths the weight factor rapidly decreases as detrimental effects would have rendered the Roman front-line increasingly untenable (see text). Note that the point at 1000 m is elevated simply to raise the polynomial trend-line (and derived equation) which would otherwise dip at this point.

After due consideration of the many aspects related to this attribute, it was decided to produce a polynomial equation, and subsequent distribution, that resulted in little numerical difference for widths between 700 and 1300 m but had steep flanks, on both sides, to either 0 or 2000 m (Figure 7). The steep flank, 0 to 700 m, was designed to reflect detrimental effects, such as the increasing likelihood that the rebels would have surrounded a compact Roman force occupying a relatively small depression. For example, a 500 m wide front-line might contain ten ranks of legionaries, a depth that Boudica might have thought too strong to breach by simply charging. In which case the better option might be to attack or flank the Roman margins with the aim of surrounding the legionaries. That method would have had two significant benefits for the rebels: firstly, considerably more rebels would have been directly engaged with the Roman soldiers; and secondly, Suetonius would have had to weaken the legionary front-line to withstand flank and rear attacks on his position.

What of Suetonius' thoughts on the matter? He deliberately chose a depression with elevating margins, presumably with the intention of protecting the flanks of the front-line with the auxiliary and cavalry. He probably thought that if he presented a long enough front-line, one not overly deep, then Boudica would not be dissuaded from a frontal, massed attack – the imperative, therefore, was to persuade by presentation an attack option that Boudica thought was likely to succeed but in actuality favoured the Romans. Therefore, Suetonius would not have chosen a defile that made his legionary front-line appear unbreakable because he would have reasoned that that would encourage Boudica to flank his position, an outcome that Suetonius must have thought might lead to destruction. This reasoning was further supported by Tacitus praising Suetonius for not having the enemy behind him, that is, it made little sense for Suetonius to select a battle-site where the enemy were only to his front and then encourage them to surround his position.

Hence the steep penalty for front-line lengths of 0 to 700 m.

For widths 1300 m and above the overriding detrimental effect was the decreasing number of ranks which would have been progressively less able to withstand the charging rebels, for example, by 1666 m the number of ranks would have fallen to three; at 2500 m there would only have been two ranks, numbers that Suetonius would surely have thought too low; his men would probably have agreed! This pointed to another related factor: morale. Tacitus gave the impression that the veteran legionaries were not demoralised by their predicament, a state of mind which must have, to some degree, reflected their agreement with the choice of battle-site and presumably the width and depth of the front-line. The question as to whether the supposed near-to-optimum rank depth (7 to 4) used in this essay was that actually deployed or not, may only be answered by finding the true battle-site.

Wetness – a simple attribute, derived from a standard topographic indicator, the Topographic Wetness Index. In this study of a Summertime episode, the feature 'wetness' was used to differentiate not only the bogginess of a site but also vegetation and local terrain roughness (that which is under foot). To generalise, areas prone to winter wetness tend to have dense, high vegetation covering rough ground, while drier areas are often grass-covered and smoother (note that tree-cover as a parameter was not used in this study because so little is known of its extent). The former would have been detrimental to the Romans, hindering their front-line formation and later planned advance through the rebel horde, whilst the latter would have been beneficial.

Distance to London – another simple attribute, resulting in a value of one at London and linearly decreasing to 0 as distance increased. The purpose of the attribute was to assign a value to increasing Roman fatigue, decreasing food supplies, loss of soldiers due to skirmishing and injury, and loss of horses and pack-animals as the army progressed further from London.

Distance from main Roman roads – the distances from the Roman roads shown in Figure 6 were linearly lowered from one to zero as the value increased. Not all of the roads depicted would have existed in 60 or 61 AD but those between military forts and major towns probably did in most areas in the south of Britain. Such military roads were Watling Street (Wroxeter to London to Dover), the Fosse Way (Exeter to High Cross, possibly further), the Portway and off-shoots further west (London to Silchester and beyond), Akeman Street (St. Albans to Alchester to Cirencester) and Stane Street (London to Chichester). The general assumption was that closeness to a road benefited the Romans as less time was spent marching off-road to reach the battle-site and, the reverse situation, allowed Suetonius to quickly withdraw from the battle-site if, for whatever reason, he deemed that necessary. It also allowed easier communications with other units in Britain, improved the reliability of re-supply (if any) and reinforcement (which did occur), plus a site close to a road was likely to be more familiar to the Roman commanders. Legionary morale would be improved due to an understanding of the preceding points and a hope, probably false, that if the battle was lost then there existed an escape route.

Induced stress on the British rebels – this was an attribute designed to model the strain imposed on the rebel forces as the campaign progressed (Kaye, 2013a). Elements of the calculations were: a factor composed of elevation and hydrogeological parameters designed to convey strain due to food, fodder and firewood shortages if the battle-site was located in upland areas, typically but not exclusively chalk or limestone; the distance marched from London; and the distance from a river(s) that could supply the water need of the rebel horde (0.04 m3/s when the rebels followed the Romans).

Distance from river(s) supplying sufficient water for the Romans – it was standard practice for Roman armies to build or re-occupy marching camps prior to a battle, as indeed it was for every night while marching, and Suetonius may have had additional reasons to follow this practice. His superior marching rate over that of the rebels may have meant he was waiting at the battle-site for a number of days; he had an unknown number of civilians who had to be protected, not least on the day of battle; he probably had a large number of pack-animals and quantities of supplies that had to be safeguarded; and finally the possibility of withdrawal into a marching camp, if the battle went against the Romans, would have raised the morale of the soldiers.

(Note that, in this section and henceforth, all river parameters and measurements, both discussed and displayed, are of the reconstructed rivers in the summer of 60 or 61 AD (after Kaye, 2013b and 2014)).

Figure 8: histogram of distances from temporary marching camps (307) to rivers supplying sufficient water.

Figure 9: graph of the cumulative frequency of 307 temporary marching camps against distances from rivers supplying sufficient water. The exponential equation was used to calculate the attribute 'Distance from river supplying sufficient water for the Romans'.

Like individual humans, armies are more dependent on water than they are on food. It was for this fundamental reason, plus defence and cleanliness, that earlier work on the statistics of temporary marching camps in the UK (Kaye, 2013b) showed that, of the 307 camps examined, all were within 1500 m of the reconstructed river(s) for 60 or 61 AD capable of supplying sufficient water to the resident force (0.00891 m3/s for Suetonius' army), and approximately 65% of camps were within 200 m (Figure 8). The distribution of distance versus supply was exponential, the equation of which was used to calculate this attribute (Figure 9). The distributions of frequency and relative frequency in Figure 8 show more variability than the cumulative, especially in the lower distances from camps (50 to 200 m); nevertheless, the overall picture, of what might be assumed to have been a standard practice, was best exemplified by the cumulative frequency equation. But in the case of Suetonius' camp, there was an obvious difficulty.

Given the probable importance of the marching camp to Suetonius, it may be reasonable to assume that its water need took precedence over that of the battle-site, which may have been even further from the river. However (and stating the obvious for clarity) the location of the marching camp was not known. Hence, the distances between the river and camp, and camp and front-line, were also unknown. What was known was the distance between the river and the candidate front-line, to which the exponential equation was instead applied. This tacit acceptance of a failure of knowledge probably does not negate the usefulness of the calculated attribute when applied en masse to a large number of candidate battle-sites, but it may do so if applied to differentiate a small number of sites located in markedly differing terrain, i.e. this may be a problem in the future if the number of candidate sites are greatly reduced.

Effect of a river flowing through the front-line – having sufficient water nearby was undoubtedly beneficial to the Romans, but having that water flow through the front-line was not, for obvious reasons. This attribute therefore penalises such battle-sites (482 of the 862) by assigning a value of one to rivers that flowed at either end or beyond a front-line, linearly through to zero when the river flowed at the centre. Additionally, a weighting based on the width of the intruding river was also applied – the greater the width, the greater the penalty. Of course, the problem with this attribute was assuming that the reconstructed locations of rivers matched the meander location of the actual river in 60 or 61 AD. In many instances the modern and ancient locations will broadly coincide, especially for those river valleys carved primarily by greater flows during glacial and periglacial periods. In further mitigation, it was decided that ignoring the possible effect of rivers flowing through tight valleys and defiles, and hence more likely to flow through the front-line, was not appropriate because Suetonius would have been less likely to have chosen such a site.

Effect of blocking or trapping by large rivers – for this attribute various river parameters were calculated to find those that had the capacity to either block or trap the Romans. For example, the unwadeable river Thames flowed through the narrow Goring Gap (Figure 10) and clearly demonstrated that there were various locations where a Roman front-line could have been trapped either in battle, due to defeat and retreat, or because the rebels might have chosen to contain the Roman force and starve it. Suetonius, an experienced general, would not have placed his force in a location pregnant with such predicaments.

Figure 10: the unwadeable Thames in the Goring Gap. The red battle-sites were locations where the Romans might have been trapped or blocked, resulting in battle-sites unlikely to have been chosen by Suetonius. Topographic colours as assigned in Figure 2.

Attribute values were defined by use of a method employed in earlier work (Kaye, 2014) where river widths, depths, velocities, instability indices and thalweg depths were calculated. After examination it was decided to use the thalweg depth as an indicator of the unsuitability of the battle-site, it being generally more representative of the overall range of river depths than the average depth. As already mentioned, the aim of this attribute was to apply a penalty to sites adjacent to rivers that could have been dangerous to the Romans or, in some manner, hinder their battle-site manoeuvring. Simply selecting those rivers or stretches that were unwadeable would not suffice. Hence a lower threshold was applied, with only battle-sites that had rivers within 500 m and thalweg depths greater than 0.5 m being penalised. Thus a value of one was applied to depths equal or less than 0.5 m and decreasing to zero for the greatest depths. Only 283 sites were penalised, the majority on the lower reaches of the main rivers, e.g. Thames, Kennet, Avon, Medway and Colne. The 0.5 m threshold was chosen after considering what Suetonius might have thought dangerous. Such a depth under normal circumstances would not be a barrier to soldiers or cavalrymen. However, and for example in the case of the Roman front-line not withstanding the rebel force, then a general retreat to the marching camp might have been required, resulting in panicked, harassed and demoralised Roman soldiers massing at a 0.5 m deep river and becoming trapped. The result would probably be massacre.

Having acquired values for the ten attributes, the next step was to apply weightings reflecting their relative importance (Table 1), i.e. to derive a weighted ranking. To adjudicate on relative importance was necessarily subjective, but after the examination of various statistical techniques to produce machine-derived weightings, it was concluded that more easily-described subjectivity was preferable.

Table 1: preferred weightings applied to the ten attributes (where the attribute value for each candidate battle-site would be multiplied by the weighting).

To begin with, it was realised that the wetness attribute pertained more to the winter, rather than the summer, and should be down-weighted by 0.5; what wetness measures, or reflects (for example locally rough ground) probably did influence the choice of battle-site but much less so than other attributes.

A weighting of 1.0 was applied to four attributes (Table 1), these being sufficiently represented by their normalised values relative to those attributes considered more important. For example, one of the four at 1.0 was 'Distance to London' but the other distance attribute, 'Distance from main Roman roads', was considered relatively more important, for the reasons given earlier under the attribute description of the same name, and set to 1.1.

Another example of relative importance was shown between the 'Distance to London', 1.0, and the 'Terrain ruggedness' of a battle-site which was given a weighting of 1.1. The applied logical distinction is emphasised, probably too simplistically, by considering a commander marching away from a larger enemy force across a landscape that becomes progressively more rugged the further he walked; he would not choose to stop and offer battle if, having marched a few kilometres further, he would find a better battle-site: that is, finding the best battle-site for survival and victory is more important than the effort expended in marching a little further. So it was thought for the Romans and Suetonius.

A similar logical premise was used to separate those attributes weighted either 1.1 or 1.2, 'Normalised height' and 'Terrain ruggedness', versus 'Distance from river supplying sufficient water' and 'River flowing through the front-line', respectively. The 1.1 weighted attributes reflect the topography of the candidate battle-site, while the 1.2 attributes reflect the hydrological conditions, but which was more important? One premise was that a most favourable battle-site, located in topography best suited to Roman tactics and matching Tacitus' description, would not have been chosen if the nearest water supply was many kilometres away because Suetonius probably had to wait a number of days for the British to arrive, plus he also had to avoid the possibility of besiegement in a location without water. A second premise, in the topography versus hydrology debate, concerned a topographically-optimum battle-site but with a river that flowed through the front-line; clearly the presence of the river degraded the battle-site depending on the location of the river – at or beyond the margins or otherwise - and its width or depth, i.e. the presence of the river was a dominant attribute relative to the topographic, hence 1.2 versus 1.1, respectively.

A general requirement when applying weightings is not to choose factors that unreasonably enhance one attribute over another or to disproportionately distort the values assigned to all attributes. The weighting factors should be assigned logically, proportionately and, in part allowing for the failure of those two requirements, at least in a manner that can be readily understood, if not agreed upon. To those ends, Table 2, a comparison of the best weighted and unweighted sites, showed that the weightings applied in this study could be considered benign: of the top ten weighted sites, six were also in the top ten unweighted sites, and of the top 20 weighted sites, 16 were in the unweighted top 20.

Table 2: a comparison of the ranked positions for weighted and unweighted candidate battle-sites. Column one shows the rank for the unique identifiers assigned to candidate sites in columns two and three. Column four shows the position of the 'Ranked weighted site' in the unweighted rank order, e.g. weighted site 596 shown as number one, occurs at position 7 in the unweighted ranking.

The similarities, therefore, between the weighted and unweighted sites indicated that the applied weightings had probably not unreasonably favoured any one attribute, or disproportionately distorted the original attribute values.

The distribution of the summed, normalised, attribute values and their weightings, i.e. rank order, is shown in Figure 11 (left), where the sites approximately between 50 and 700 exhibit a regular fall in weighted value. The distribution tails, 1 to 50 and 700 to 870, have steeper gradients. Figure 11 (right) shows the top 20 weighted sites in rank order; sites from 7 to 20 roughly share a gentle, negative slope but those 1 to 6 can be placed on a steeper trend-line. This indicated that the attribute values and weightings were preferentially separating the higher sites from each other and the common background, i.e. sites 1 to 6 were more likely to be correctly ranked relative to each other and, as a group, significantly prominent – head-and-shoulders, so to speak – above the main body of sites, 7 to 700.

Furthermore, of the weighted sites 1 to 6, 3 occurred in the same unweighted range (Table 2) which demonstrated not only the appropriateness of the applied weightings, but also that these sites were prominent simply by virtue of their attribute values, i.e. it might be thought more likely, of this set of attributes and the manner of their calculation, that the real battle-site lies within this weighted range.

Figure 11: the weighted and ranked candidate battle-sites; 1 to 862 on left, 1 to 20 on right. The numbers are unique identifiers for each candidate battle-site. Sites 548 and 1348 share the same location and rank, 11 (red dot in both graphs); one has not been removed because both were identified by different templates in the template-matching exercise.

The locations of the ranked candidate battle-sites

A different form of distribution, that of location, is shown in Figure 12, where the top 100 candidate battle-sites are shown overlying an elevation map of the study area. The first observation was that most of the sites occurred within, or on the margins of, the chalk and limestone uplands of the study area – the north Cotswolds, the Chilterns, the North and South Downs, the general area of Salisbury Plain, the North Wessex Downs and the Mendips. A second observation was that there were no sites north of Alcester with the exception of sites 49 and 70. Site 49 at Church Stowe, adjacent to Watling Street and a site championed as the actual battle-site (Pegg, 2010), was the only site along that road north of the Chilterns at Dunstable (another championed site ranked 63 and 84 (Horne, 2014)). Not surprisingly, given the low topography of the region, the whole of the study area east and north of London was bereft of top 100 candidate sites.

As an aside, the finding in this study of the championed candidate sites at Church Stowe and Dunstable gives further credence to the template matching approach. It suggests that individual reasoning, applied to the topography and Tacitus' text, has been replicated in the method.

Figure 12 was sub-divided into regions allowing the showing of the ranks for each candidate site – Figures 13 to 16.

Readers who wish to display the locations of the top 100 sites are invited to make use of a Google Earth KMZ file located on the author's website – top-100-sites.kmz (http://www.bandaarcgeophysics.co.uk/arch_intro.html/top-100-sites.kmz). Location details for the top 20 are shown in Table 3 (see after Figure 16).

Figure 12: distribution of top 100 candidate sites across the study area. The sites are colour graded from 1 in red through yellow and green to 100 in blue. There is some visual overlapping of sites. The original template matched sites, sized according to their width, are pale purple. Details of this map, with candidate battle-sites numbered according to rank, follow in Figures 13 to 16. Main Roman roads in black. Background is elevation. Graticule at 50 km.

Figure 13: distribution of those top 100 candidate sites in the north Cotswolds. Site colours as in Figure 12. The original template matched sites, sized according to their width, are pale purple. The reconstructed 1st century rivers are limited to a flow rate of 0.00891 m3/s, that required by the Romans. Main Roman roads in black. Background is elevation. Graticule at 10 km.