By Graham Jackson and John Barnard
We have followed with great interest the stimulating articles in your newspaper about the recent survey of Beinn a’Chlaidheimh (hill of the sword) in Fisherfield. These have presented a detailed account of the proceedings and we trust have provided insight into the world of Munros for readers who have followed them.
We are the surveyors who carried out the measurements on Beinn a’Chlaidheimh for the Munro Society (TMS) and we have noted one or two inaccuracies which we wish to clarify, and a couple of questions we can answer.
First, the overall measurement uncertainty in our determination was +/-0.10 metres (or one Kit Kat, to use your journalist's units). The value of +/-0.05m is the measurement uncertainty of the GPS determination itself. In addition, there is the measurement uncertainty associated with finding the exact summit location. This may sound a trivial thing to do, but to achieve this to just a few centimetres is often quite tricky.
There are one or two other minor factors to throw in, too, so that the overall uncertainty becomes about +/-0.10m. This value is actually given in the summary section of the report.
Secondly, your journalist says, “stand beneath a similar-sized hill, look up and ask yourself is it really possible to be sure of the height to within half the length of a Kit Kat?” Well, the answer is “yes”, using the technique of differential GPS.
We never fail to be impressed with the reproducibility of the technique, but it really can measure position and height to +/-0.10m or so, the actual accuracy depending on how long data are collected. This level of accuracy is achieved by measuring height and position relative to one or more GPS instruments (so-called “base stations”) situated at accurately known positions.
In this case it was to six of the Ordnance Survey’s OS Net™ stations. OS Net is a national network of over 100 highly accurate, permanent GPS base stations positioned to within a few millimetres. We will not discuss differential GPS further here, but refer the interested reader to a detailed article we wrote for the “heighting” project and this may be found on TMS's website. The article discusses at length all the measurement uncertainties associated with determining the heights of hills and briefly mentions the principle of differential GPS. The OS website is also a mine of information on GPS technology and surveying techniques.
We also regularly check our GPS kit for both precision and accuracy by repeatedly occupying an OS GPS control point – a fundamental bench mark whose position and height are known accurately. These are often used by surveyors to make sure their GPS equipment is giving correct results. These checks are carried out before and after a survey.
Your journalist recommends a second measurement, presumably as a check in case of a gross error in our measurement. We follow careful, well-established survey procedures to ensure the elimination of gross error, for example in the measurement of the height of the GPS antenna above the point being surveyed.
We consider that a second survey visit to a point would only be valid if the first result was close to the Munro threshold (914.40m) within the accuracy limit of the technique. So, with an accuracy limit of +/-0.10m, the Beinn a’Chlaidheimh result would need to be between 914.50m and 914.30m to make it worthwhile considering a second survey.
The taking of multiple observations is a very common technique in surveying and is used to average-out naturally occurring random errors. We should point out, however, that our survey collected 360 sets of GPS observations over a period of three hours. This was not a single measurement.
Furthermore, the GPS data collected during a survey are cross-checked through a computation of the coordinates of the surrounding OS Net stations. The computed coordinates are compared with the “true” coordinates supplied by the OS. The quality of this “coordinate recovery” comparison is an external check on the quality of the GPS data – and, in the case of Beinn a’Chlaidheimh, confirmed the +/-0.05m accuracy of the final GPS measurement.
The article also refers to OS, saying, “the missing link in all this is the OS’s internal assessment of the surveyors’ findings.” Firstly we would like to acknowledge the OS’s continuing help and advice for our activities. Since starting our GPS surveys, we have received much guidance from GPS surveying experts at the OS and they approve of our survey techniques.
Our Beinn a’Chlaidheimh data-set was independently processed, using different and leading-edge software and techniques to those used by us, and the results evaluated by the OS’s chief geodetic GPS surveying expert. The OS value is quoted in our report and is clearly shown as thus. Incidentally, our calculated value and that determined by the OS differ by just 0.02m.
So, there you have it. We have said the accuracy of the overall measurement is +/-0.10m and therefore the measured height of Beinn a'Chlaidheimh is between 913.90m and 914.10m – which is below 914.40m (3,000 feet), the benchmark that defines a Munro. The result has been submitted to the Scottish Mountaineering Club and we now just await its evaluation of the evidence. In the meantime, sit back and relax. Have a break! Have a Kit Kat!
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