Cost paths across the Wolds, part 1

Cost paths across the Wolds, part 1

More than just a buffer

In my last post I explained how a few simple buffers helped us test a theory. The results were quick to come by, but rather crude in their analytical value. Drawing circles around points on a map is all very well, but it doesn’t take into account the landscape. In this case, the study area is the Yorkshire Wolds, characterised by low, rolling chalk hills. It’s a place where you wouldn’t just walk in a straight line from A to B; things get in the way!

25-30km buffer intersections from the five closest Roman forts

So I thought I’d dedicate this post to a couple of techniques that go one step further, using cost path analysis. We’re going to focus on our early Roman archaeological site and the surrounding forts.

This post’s a two-parter. First, I’m going to explain the principle behind the process, illustrated with some maps. Then, for those of you who want a bit more detail, I’ll outline the steps I took to achieve these results.

Travel, but at what cost?

We’re going to work out the best, most efficient, way of travelling to and from our site using maps. So how exactly do we decide the best route to get from A to B?

Digital Elevation Model (DEM) of the Yorkshire Wolds and surrounding landscape

Well, the shortest straight-line distance between two places may involve walking up and down many hills, or across other obstacles. So in some cases it may make more sense to travel a little bit further to walk around hills on flatter ground. This is known as a Least Cost Path (LCP).

Rather than considering simple straight line map distance, we need to be thinking in terms of cost distance. Effectively we need to establish what the total cost of travelling one path is compared to travelling another. Not just this though, we need to consider the total cost of every possible path to work out which is best. This is where GIS really comes into its own.


There are a huge amount of variables that can slow us down when charting a path across a landscape.

The most obvious one – and one we’ll focus on here – is slope. Very steep slopes will slow you down when going up them, whereas gentle slopes will probably speed up your journey when travelling down.

Ground cover is another big one. Roads are quicker to walk on than grass, which are considerably quicker than crossing a boggy marsh. We also need to think about who is actually making the path. Is it a 21 year old athlete or an ox-drawn cart? Weather conditions will also play a significant role in calculating a cost distance. I could go on… but won’t.

I don’t know the land cover during the early Roman period for large parts of the Yorkshire Wolds, and I’m not about to start speculating. All you need to know is that I have decided to focus solely on slope here.

Cost distance

Now we understand the basic lie of the land, we can start pushing this information through the GIS.

First we produce an isochrone map using slope as a cost factor.

The times illustrated on the map assume walking at 5km/h on typical terrain, under normal conditions. It does not take into account delays, breaks or obstacles. Therefore, all times labelled on these maps are for illustrative purpose only. In reality these times probably represent the quickest time a walker could travel.

Isochrone map showing time taken to walk from the site when slope is considered

This shows areas on the map that take the same amount of time to get to from the site. Hayton is 5 hours away, Malton and Staxton are 6 hours away, and Stamford Bridge and Brough 7 hours away.

The isochrone lines to the southeast of the site are smooth and equally spaced because the land is generally flat. On the Wolds to the north and west the lines become more uneven because of the cost incurred travelling across slopes.

This is what the isochrones looks like if the slopes are not factored in as a cost.

Isochrone map showing time taken to walk from the site when slope is not considered a cost

You’ll notice that the lines are still slightly uneven in places. That’s because the calculation is still working out the time to go up and down. But what it’s not doing is recognising that some slopes have a negative effect on routes of travel.

Here you can see the comparative distance you could cover if walking for 5 hours from the site.

Comparison between 5 hour isochrones, with and without slope costs

Least cost path (LCP)

We know that moving across the Wolds would have added to the journey time. We now need to see the LCPs (most efficient routes).

When calculating the cost distance the GIS was also working out optimal movement directions. By plugging both the cost distance and movement direction back into it, we end up plotting the route back from each of the forts to the site.

Et voila, we now have the LCPs to and from our site…

LCPs between Roman forts and site, with and without slope

The red lines represent the LCPs when slopes are a costing factor, and the blue lines are LCPs when they are not considered.


There a couple of interesting things that show up on the map.

Firstly, the LCPs that consider slope as a cost are not straight lines of travel. Rather than including lots of ups and downs, the routes favour less steep gradients. Often this means a slight deviation from a direct route. This is illustrated when we compare the LCPs from Malton and Staxton. The route from Staxton is 2km shorter than it is from Malton, but takes a bit longer.

Here I’ve worked out the height and slope profiles of both routes.

LCPs from Staxton, showing terrain and slope profiles
LCPs from Malton, showing terrain and slope profiles

We see in both that the LCPs where slope is considered deviate from a straight line in favour of gentler sloping ground. Although the distance is greater, the cost of moving across the landscape is reduced because steep slopes are avoided.

Also of interest is the correlation between the routes from Malton and Stamford Bridge and the locations of known Roman roads. They almost converge at a crossroad (near Wetwang), at which point they follow a similar path through one of the dry valleys to the site. Presumably Roman surveyors had a good understanding of the terrain and factored slopes in when building the roads.

LCPs between Roman forts and site when slope is considered

The distances and projected times of the LCPs vary. The shortest is from Hayton (22km, 5 hours) and the longest Brough (32km, 7.2 hours). To me it looks like Malton, Stamford Bridge and Staxton are all a comfortable days travel from the site. Hayton a little short, and Brough a bit of a hike.

The spatial distribution of sites in the survey area is pretty even. However, I personally think the journey from Brough looks a bit long. You could really do with a break on the way, somewhere that’s also a days travel from Hayton. I know it’s a bit naughty (because there’s no evidence) but I reckon you could easily fit another site in somewhere to the east of Beverley.

Final thoughts

Is this a true reflection of what it would have been like to cross the landscape in the Roman period? No, but it does give us a bit more of an insight into the role slopes and other factors play in determining routes.

Calculating cost and working out LCPs is certainly useful for giving us an idea about how people can move around a map. Unfortunately in my opinion there are just too many unknowns in play. We don’t know exactly how the landscape would have looked and we can’t account for social or political factors. For instance, there may have been a particularly uncooperative landowner whose land you’d want to walk around.

That said, I do think it’s been a useful excercise. It’s certainly interesting to see how the paths follow the routes of known Roman roads.

Where to next? Well, I might think about overlaying this results with cropmark data for the area. That’s an awful lot of cropmarks after the summer we’ve just had! Or I might look at the LCPs between the forts in the area to see what kind of routes and times they generate. Something for another day perhaps.

For those of you who are interested in knowing a bit more about the techniques I used, please check out Part 2.

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