The Angry Corrie 39: Nov-Dec 98

TAC 39 Index

A Bumpiness Index

Statistics, like London governments or life-partners, are often convenient whipping boys. At worst accused of being damned liars, at best dismissed for telling us what we already know. I offer here a sample of statistics that may plead guilty on both counts ... and yet a Bumpiness Index sharpens up our view of the hill areas.

I must firstly sharpen up "Bumpiness", a rather adolescent term. Alan Dawson's The Relative Hills of Britain, page 12, uses the more grown-up "peakedness", but defers to the ancients and their word "kurtosis". My on-line dictionary says this word refers to the peakedness of a statistical curve rather than the hills, but let's accept it in order to give a patina of scientific respectability to our Index. (It reminds me of "clapotis", which sea canoeists use for a jumbled sea where waves from different angles collide to create a similar topographic confusion.)

The method for working out the Index is quite simple, but quite time-consuming too, suitable for wet Sabbath afternoons. Take an OS Landranger map (1:50000) for your chosen area, select 100km2, as marked out by a 10x10 box of grid lines. Then work your way through each of the 100 squares enclosed, counting up all the closed contours that have no other contours inside them, thus indicating a top of some kind.** Once you've totalled up the 100 squares, divide by 100 and you will get the Index for the average square in that area, which can then be compared both to the highest and lowest individual grid square in your chosen area, and with the average Index of other hill areas in the UK.

Here are three contrasting examples from Scotland and England. My first area is on Landranger 55 (Lochgilphead), which covers the very peaked (sorry, kurtosified) country between Knapdale and Lorn around the head of Loch Craignish. I chose area NM8000 (ie the 100km2 bounded by grid references 8000 and 9020), and got counting - on a wet Sabbath, of course, of which there were plenty in summer 1998. The total number of tops shown in my area was 406, and the Kurtosis Average Index is therefore 4.1 per kilometre square. One square alone within the area around Creag a'Chromain (at 817013) had eleven tops: croman in Gaelic means either a hawk, or a hump-backed man, among other things.

A contrasting area has to be the big gentle giant contours of the Cairngorms. I chose Landranger 35 (Kingussie), and selected a 100km2 area around Glen Feshie delineated by grid references NN8090 to 9000. The total number of tops shown is 41, giving a Kurtosis Average Index of 0.4 per km2, a mere one-tenth of the Knapdale Index.

England is not all flat and flabby as Albacentrically depicted. I chose Landranger 98 (Wensleydale) for my analysis (mainly because it's one of only two Landrangers of England I have). The 100 kilometre square selected, SD8070 to 9080, includes Pen-y-Ghent and Fountains Fell, and yields seventy tops, with an average Index of 0.7, certainly kurtosier than Feshieside but smooth as a baby's nappy-liner alongside Knapdale.

How do these examples fit with the twin damnations of statistics mentioned in the opening paragraph? Guilty on both counts, m'lud. Firstly, they do tell lies, in the sense of not telling the whole truth, because the scale of the 1:50000 map, and the ten-metre contour interval, naturally omits some of the actual little peaks on the ground, both those of less than ten metres relative drop to the nearest contour, and those too small to be included for space reasons. Some of these latter can of course be fitted on to the 1:25000 Pathfinder maps: the Pathfinder of the Knapdale area (map 366) has over 700 closed contours in the same 100km2 area, giving an Index of 7.0, nearly twice that revealed by the 1:50000 scale. The square around Creag a'Chromain has 21 tops at this scale compared to eleven on the Landranger. And, as for the second damnation, they do state the obvious - anyone sailing up Loch Craignish, or moving across the land, is struck by the bumpiness of this country - or, as they say in the Kilmartin Inn bar, its kurtosis. (The area has, as my brother observed, a similarity in style to old Chinese silk paintings, with hills arrayed as impossibly steep ups and downs - like a dragon's back - behind the inevitable pig-tailed sage. Confucius he say kurtosis considerably complicates climbing contours.)

I hope this article encourages TACophiles to get to work on wet Sabbaths, on the map of their home or favourite hill area, and to (e)mail the Editor with data allowing a Comparative Kurtosis Index for Britain's hill areas to be drawn up by someone with nothing better to do. And can anyone find a single grid square with more tops in it than NM817013?

Peter Drummond

** A conical hill might have several closed contours, all but one enclosing. In this case only the one that does not enclose others, and is therefore the top, can be counted. In Diagram A therefore, only one top would be counted; in Diagram B three tops.

TAC 39 Index