Guest Contributor – Ralph Storer

Introduction

If readers would like to contribute an article for the Guest Contributor page heading please contact me, my email address appears on the About Me page heading.  The 0nly two things I ask is that the article should be hill related and importantly I should not end up in court through its publication!  Otherwise the choice of subject matter is down to the Guest Contributor.

About the Author; Ralph Storer

RALPH STORER is an experienced hillwalker who has hiked extensively around the world.  Despite being a Sassenach by birth, he has lived in Scotland since studying psychology at Dundee University and has a great affinity for the Highlands.  He is the author of the acclaimed Ultimate Guide to the Munros series of guidebooks among others.  As well as disappearing into the hills for a regular fix of nature, he also writes novels and sexological non-fiction, and produces darkwave music on his home computer.

The Height of the Matter

by Ralph Storer

Calf Top is a grassy 610m mountain in the Yorkshire Dales. Or is it?  It’s certainly in the Yorkshire Dales.  There it is on OS Landranger map 98. But is it a mountain or a hill?  One of the accepted cut-off points to distinguish a mountain from a hill is 2,000ft.  The metric equivalent of 2,000ft is 609.6m, so Calf Top is a mountain, right?  Then why, until 2010, was it only a hill with a height of 609m.  What’s going on?  How did it suddenly gain a metre and become a mountain?

The answer is that it was re-measured using GPS equipment and given a height of 609.58m, which was rounded up to 610m by the OS. However, the exact figure is 2cm short of the height required to call it a mountain.  To confuse the issue even further, the OS suddenly upped the height by a further 6cm in 2016 without re-measurement. Again, what’s going on?  The answer is more complicated than you might think.

Most of us have no more than a vague notion of how the heights of hills and mountains are calculated.  We may know that trig pillars are no longer used and we trust that GPS mapping will produce more accurate results, but that’s about it.

On early maps no heights were recorded. On Pont’s 16th century map of Scotland mountain groups were shown using a simple mountain-shaped icon.  Roy’s 18th century map used shading, but again no heights were recorded.

First attempts to estimate height were based on the fact that air pressure diminishes with altitude.  This is because, the higher you get, the less depth and hence weight of atmosphere there is above you.  Using a barometer, the differing air pressures at sea-level and the top of a mountain can therefore be used to calculate height.

At the beginning of the 19th century Ben Macdui in the Cairngorms was thought to be higher than Ben Nevis on the west coast.  Using barometric readings, this was disproved in 1810.  The Rev. George Keith climbed Macdui with his barometer while his son did the same on Nevis.  The rev. recorded a height of 4,300ft (it’s now 1,309m/4,296ft), while his son calculated Ben Nevis to be 4,350ft (it’s now 1,344m/4,409ft).

A barometric calculation will never be more than approximate because air pressure changes according to other factors besides altitude, such as weather.  A more accurate method is triangulation, which the OS began to use in the 19th century to produce the first maps that have a level of detail we’d recognise today.

How does triangulation work? Beginning with a base line of known length, a triangle can be formed by drawing intersecting lines at measured angles to the line ends.  The length of the two new sides can then be calculated and each used to form the base lines of more triangles, and so on until the whole country is covered.  Points within the triangles can be pinpointed by similar trigonometry. When the land isn’t flat, a vertical angle can be used to calculate the height of a point.  From this a further calculation can be made to obtain a 2D distance for a flat map.

For the first Principal Triangulation of the United Kingdom a 7ml baseline was measured on Salisbury Plain in 1794.  The first map of Kent appeared in 1801 and the survey finished in Scotland in 1882, by which time it was losing accuracy owing to the complex terrain.  Not all summit heights were measured, while from ground level a subsidiary summit would sometimes be mistaken for the true summit.  All of this made Hugh Munro’s task of producing his tables of Scottish 3,000ft mountains an immense achievement in 1891.  He measured many mountain heights himself using his own barometer.

In 1935 an updated Retriangulation of Great Britain began.  To   increase accuracy, thousands of trig pillars were installed as objects on which to take more precise bearings.  The survey was completed in 1962, by which time distances were being calculated by Electronic Distance Measurement (EDM), based on the time it takes to reflect a microwave or light wave back from a target object.

You’d think the problems of measuring height and distance had now been more or less solved, but things were about to become more complicated than ever.

When we refer to the height of a summit we usually mean above sea-level, but which sea-level?  Sea-level varies around the world because of the earth’s gravitational field. It’s also affected by a number of other factors including tides, winds, atmospheric pressure, temperature, salinity and geological movement.  In Britain the OS currently uses the mean sea-level (MSL) at the geologically stable location of Newlyn in Cornwall, as calculated by tide-gauge between the years 1915 and 1921.  Other countries have their own MSLs. Holland’s dates back to the 1680s.

This means that the height of Ben Nevis, say, is calculated according to the sea-level at Newlyn, nearly 500 miles away as the eagle flies.  A more accurate measurement would be the mountain’s height directly above the notional sea-level at its base, which would be different from that at Newlyn because of variations in the earth’s gravitational field.  Many hillwalkers would be surprised to learn that this notional sea-level has in fact been calculated using the Global Navigation Satellite System (GNSS).  It’s known as the geoid.

The GNSS is a ring of 24 satellites created by the US between 1978 and 1994.  They encircle the earth at a height of 20,000km above the centre of its mass.  Using signals from 3 satellites, a Global Positioning System (GPS) receiver on earth can pinpoint its 2D location.  With data from 4 satellites it can also determine its height, using a form of triangulation called trilateration.

The geoid is a calculated representation of what the surface of the sea would look like if it continued under the land. It differs from the mean sea-level at Newlyn in that, using the GNSS, it’s centred on the earth’s mass and takes account of the earth’s gravitational field.  This should make it more accurate.  In land-locked mountainous countries such as Nepal, geoid and MSL figures (measured at the Bay of Bengal) can differ by several metres owing to gravitational differences, which is why we now have several competing versions of the height of Mount Everest.

As a result of GPS re-measurement using the geoid, Mynydd Graig Goch (609.75cm) in Snowdonia and Thack Moor (609.62cm) in the Northern Pennines were raised to mountain status in 2008 and 2012 respectively.  Wales gained another 1,000m peak when Glyder Fawr was upgraded from 999m to 1,000.8m in 2010.  Poor Beinn a’ Chlaidheimh in Wester Ross, meanwhile, lost its Munro status in 2012 when it was downgraded from 916m to 913.96m (2,999ft).

But there’s a problem with the geoid.  It’s a mathematical construct that’s under constant revision as computing power grows.  The latest (2015) geoid revision used by the OS is known as OSGM15.  It was as a result of switching to the OSGM15 model that Calf Top suddenly gained another 6cm in 2016.

    

The areas most affected by OSGM15 are in Scotland, including the Isle of Lewis (up by 20-20cm), Trotternish on the Isle of Skye (down by 10-20cm) and part of Argyll (down by 5-15cm).  Nevertheless, Cnoc Coinnich in Argyll was upgraded from 761m to 762.5m in 2016, making it a new Corbett (a Scottish mountain between 2,500ft and 3,000ft high). 762.5m is exactly 2,500ft.

There’s another problem too.  Obtaining a GPS figure is a time-consuming business that involves transporting heavy and delicate equipment up to the summit to be measured, which makes it impractical for wide usage.  The 2010 Calf Top measurement, for example, took four hours to obtain.

For general mapping purposes the OS instead currently uses a variety of other methods that combine photogrammetry with ground surveys.  Photogrammetry is a technique that converts overlapping aerial photographs into a 3D model.  Such mapping is not as accurate as using GPS and it uses the Newlyn sea-level figures rather than the geoid, but it’s simpler and quicker.  Note also that in the last century sea-level rose by a couple of centimetres, which if taken into account would reduce Calf Hill to hill status once again!

And that’s not all.  Did you know that Britain is currently experiencing an isostatic rebound?  This means that it is still recovering from the pressure exerted on the land by the last ice age. In general terms, the north and west of the country are rising while the south is sinking.

All of which means that no mountain height is ever going to be more than temporary and approximate.  Is Calf Top a hill or a mountain?  One thing’s for sure – we haven’t heard the last of the matter.

Reprint from Ralph Storer’s book See You on the Hill