Munro or no?

The BBC and other media recently reported that Scotland could lose one of its famous and baggable Munro mountains. By that I don’t mean the rock in question will vanish, but the status of Beinn a’Chlaidheimh as a mountain of at least 3,000 feet (914.4 metres) above sea level could be rescinded as the result of a new GPS survey conducted by the Munro Society. This is not quite in the same league as Pluto losing its planet status, but the emotional fallout could in certain quarters be just as severe.

In short, the Munro Society has recorded the height of Beinn a’Chlaidheimh as being 913.96 metres, or 2998 feet. Official Ordnance Survey records have the mountain’s height at 916 metres (3,005 feet), putting it less than two metres into the Munro class. Given the closeness of these figures to an arbitrarily defined limit tied to the use of an antiquated unit of measurement, one has to question whether the survey result falls within the accuracy of the tools used.

The Global Positioning System (GPS) makes use of a network of 30 satellites orbiting at an altitude of around 20,000 kilometres, to fix the three-dimensional position of receivers on the ground or in the air. Horizontal accuracy is typically between 10 and 20 metres, in the case of consumer-grade receivers, and a few centimetres with specialised land survey equipment.

Altitude precision, on the other hand, tends to be much less, and for this reason the expensive wristwatch devices used by runners and other sporty types are useless for recording elevation profiles during training sessions. Altitude accuracy can be improved with differential GPS (e.g., WAAS/EGNOS), and cross-calibration with a barometric altimeter, but is rarely better than two metres. Sequential measurements of altitude during a running or road cycling session can show a wide spread, and statistical filtering sensitive to a number of assumptions is required to give a readable elevation profile.

Calculating the position of an object through triangulation is sensitive to the particular geometry at the time, and with satellites moving across the sky in a complex orbital pattern, conditions are rarely optimal for achieving high accuracy in GPS measurements. You can appreciate this by visualising different scenarios, and understanding the basic principles of GPS.

Take, for example, a situation in which one or more of the satellites included in a position fix is low in the sky. Trace a path between that satellite and your receiver, and you should see that a small uncertainty in the position of the satellite will grow into a much larger wiggle error at the other end of the long path. But then a wide spread of angles can be conducive to accurate triangulation.

On the other hand, if you have a bunch of satellites close together and high in the sky, the angles are small, and it is more difficult to combine these into an accurate position for the receiver. This is down to basic trigonometry and measurement uncertainties due to clock errors and radio wave path determination. The optimum configuration is a minimum of four satellites at 40 or 55 degrees above the horizon, with one in each cardinal (NESW) direction.

Other complicating factors include atmospheric distortion due to water vapour and geomagnetic disturbances. These change with time, with both cyclical variations such as day to night, and also long-term trends and abrupt transitions. The upshot is that a single GPS measurement of position must be taken with a large pinch of salt. Repeated measurements should be made over what could in practice be an unfeasibly if not impossibly wide range of conditions.

Such caveats aside, one can rely on GPS land surveys, and the high degree of accuracy in mission critical mapping applications is testament to this. But the residual errors, whether they be random (statistical) or systematic (skewed) are significant and quantifiable. Do such errors impact on the Munro Society’s measurement of the height of Beinn a’Chlaidheimh? Undoubtedly.

Even though the Munro Society took great care in its survey, one should question whether the results show convincingly that the mountain peak is below 3,000 feet. Note that the quoted elevation accuracy is statistical rather than instrumental. The overall measurement is valid, taking into account conditions at the time the individual measurements were made, but that is as far as it goes. For the Munro Society to prove beyond all reasonable doubt that the mountain peak is below 3,000 feet would require that the measurements be repeated day and night over the space of a year, and the entire process repeated annually over a few 11-year solar cycles. For obvious reasons, that isn’t going to happen.

Given the closeness of the survey results to the Munro limit, I would advocate setting an uncertainty on the Munro limit itself. That is, one could classify as Munros all those Scottish mountains the peaks of which are at least 3,000 ± 10 feet above sea level. A sea level which, it should be noted, is based on a mathematical model, with an in places significant difference from measured reality.

Real-world complexity and messiness requires real-world flexibility in interpretation and control.