Is Calf Top a new 2000ft mountain?
BackgroundCalf Top (Section 35B, OS Map 98, Grid Ref SD664856) is a candidate for precision surveying because of the possibility that its height might exceed 2000ft. On the summit area there is a Trig Point and the OS database records its Flush Bracket height as 609.60m (2000.0ft). Assuming the Flush Bracket height is correct, if any natural ground exceeds this height, Calf Top would be a new English 2000 foot mountain.
In December 2006 we surveyed the summit area of Calf Top with a Leica Automatic Level and Staff. We were able to locate the exact position of the summit, but had to assume that no higher ground existed under the foundations of the crumbling stone wall that passes over the summit between the Trig Point and our identified summit position. Our measurements showed the summit position to be 0.15m LOWER than the Flush Bracket, thereby estimating the height of Calf Top to be 609.45m and below 2000 feet.
The 2006 survey relies on the accuracy of the Flush Bracket height. Since our acquisition of survey grade GPS technology, we have been able to measure heights accurately and absolutely. When checking the heights of Flush Brackets, we have found differences of up to 0.30m between our measurements and those in the OS database, although most agree to within a few centimetres. This motivated us to return to Calf Top and re-measure its height accurately by GPS.
On 15 April 2010, we carried out another survey of the summit of Calf Top. The position we identified as the summit was exactly as we found in 2006 and we measured its height to be 0.16m lower than the Flush Bracket using automatic level and staff. We collected 2 hours of GPS data and the post-processed height came out as 609.61m. This result is marginally above 2000 feet. The OS Flush Bracket height would be 609.76m, 16 cm higher than the OS figure.
The GPS height was forwarded to the OS and on their suggestion, which was our view too, a repeat survey was carried out. This took place on 20 May 2010. The main difference was that we collected 4 hours instead of 2 hours of GPS data and the post-processed result this time for the height of Calf Top was 609.62m. Again the measured height just exceeded 2000 feet. The agreement between the two data sets of 0.01m suggested that the data quality was excellent.
Both GPS data files were submitted to the OS who processed them through their leading-edge "Bernese" software. The OS confirmed the good quality of both datasets, merged the files, and obtained a height of 609.58m. In this case Calf Top fails to make 2000 feet by 0.02m (13/16th of an inch).
ConclusionsThe Ordnance Survey has quite correctly decided to put a new height of 610m on its maps as 609.58m rounds to 610m. However, this implies to map users that Calf Top is a new 2000 foot mountain.
So how accurate are the measurements to justify any claim? From data on replicate GPS datasets collected over the time periods used in the Calf Top surveys, we expect the statistical error in the height measurement to have a standard deviation of 0.02m. In addition we estimate a further uncertainty of up to +/-0.02m in height when the GPS is placed on the soft mossy ground at the summit. On previous surveys, where our data have been processed through Leica GeoOffice and through Ordnance Survey's Bernese software, the latter has given heights 0.02 to 0.03m lower. (This is due to the different models in the software that calculate and correct for distortions as the satellite signals pass through the Troposphere). If we take three times the standard deviation as the precision of the GPS measurement and combine that with the uncertainties in the height position and differences between the software, we believe the height measurement has an accuracy of better than +/-0.10m.
When available we have always taken OS results calculated from our data to be definitive and have quoted them in preference to our results. In this case, the probability that a measurement of 609.58m +/-0.1m exceeds 2000 feet is slightly less than 50% and therefore objectively Calf Top cannot be re-classified as a 2000 foot mountain.
An alternative approach that gives equal weight to the two software models is to take an average of the OS figure and our own result after weighting the measurements by the collection times. In this case the estimated height is 609.596m, falling short of 2000 feet by 4mm. Hence the probability that Calf Top exceeds 2000 feet is again just below 50%.
So is Calf Top a new 2000 foot mountain? In previous surveys we have followed the principle that in order for a hill/mountain to acquire a particular status, the probability that it qualifies must equal or exceed 50%. This criterion is implicit in all the major hill lists. Objectively, our view is that whichever of the two credible methods is used to estimate the height of Calf Top, the balance of probability is that it does NOT quite attain 2000 feet.
John Barnard, Chris Crocker, Graham Jackson and Myrddyn Phillips
PostscriptOn 26 August 2016 Ordnance Survey adopted a new, more accurate geoid model. The previous transformation from latitude/longitude to OSGB36, called OSTN02, was replaced with OSTN15. This resulted in small changes to the height of hills. OS reprocessed the survey data for Calf Top and obtained an increased height of 609.606m. Consequently Calf Top went from being somewhat more likely to be below 2,000ft high to being slightly more likely to be over 2,000ft.