How to measure a mountain….
There was a stir last year when they discovered that Mount Everest was 86cm taller than the official record dictated. What I hear you say? How can a mountain grow?
In 1856 India carried out the Great trigonometric survey, triangulating the peak of Everest to the plains around the mountain determining its height to be 29,000 ft. At the time Andrew Scott Waugh (the surveyor general) who headed up the team believed a round number would not be perceived as credible so he added 2 ft to the elevation recording it at 29,002 ft! In 1954, a new official elevation was set down at 8848m (29,028ft) above sea level and that figure has stood fast despite foreign teams from across the globe in subsequent years calculating measurements that were plus or minus a dozen metres of this. However In 2020 a new recorded height 86cm above that 1954 number was calculated by a joint Nepalese Chinese team putting the height of Mount Everest at 8848.86m. It is incredible that the much more manual 1856 technique produced a similar result to the survey of 2020.
The mathematical methods used to measure the height of mountains has not changed significantly from when Everest was first measured in the 1800’s. It’s trigonometry dear Watson! At this point I can hear Cost centre 2 groaning as this is not a topic he enjoys. The basis of the calculation is that by quantifying the length of one side of a triangle (a base) and knowing the angles from the ends of this length (towards the peak of the mountain for our purposes) a mathematical formula can be utilised to determine the hypothenuse. This is useful because the hypothenuse is the sloped side opposite the right angle of a triangle. So now we know the length of the hypothenuse together with one of the angles up to the peak allowing us to calculate the height of the right angled triangle which in this case is the mountain elevation.
In practical terms in 1856 the distance between two points on a flat plain (and it needs to be flat, usually within line of sight) were determined and then using something called a Theodolite, a measure of the angles between the top of the mountain and each point was produced. So as per trigonometry, with two of the angles, a measurement of the base, the hypothenuse (distance from one point to the top of the mountain) was calculated from which further maths allowed the computing of the mountain elevation as explained above. To ensure accuracy multiple calculations using this approach were carried out.
As an aside a Theodolite weighed c500 pounds taking 12 men to carry and was used to survey land across India in the 1800’s — so this approach was an incredibly laborious task but successful.
In recent times, satellites have brought more accuracy to the computation process. Bounced signals off receiver towers derive highly specific location data by measuring the time it takes for a signal from the satellite to arrive at a receiver. GPS receivers can be temporarily placed on the mountain peak to utilise this technology. Another alternative to on the ground measurement is Photogrammetry. This builds 3D models from high resolution photographs (Lidar) taken from the air. So far it has been useful for surveying large swathes of land but does not offer the accuracy of the manual process. Additionally both GPS and Lidar measurements need to be adjusted for various natural factors (signal blockages or reflections due to surroundings on the ground). Therefore GPS tends to be used in conjunction (as another input) into the highly manual and physical process of mountain measurement I described above (as was the case with the latest official Everest figure). I met a company recently that very excitingly utilise Synthetic Aperture Radar (SAR) to develop highly precise images of the Earth. I haven’t read that it has been used for mountain measurement yet but it is used for landscape mapping.
But you didn’t think it was that simple did you? Before you even begin taking measurements, you need to answer several prosaic questions. Do you measure elevation from sea level (your plain) or from the centre of the Earth? This is important because as we have discussed previously, the Earth suffers a bulge in the Equator so measuring from different physical points on the surface can impact comparative calculations made through time or with other mountains. Where is the peak of a mountain — the tip of the hard rock or should it include the snow on top of the peak which can add several metres onto the calculated elevation?
And then it comes to adjustments as nature is very unforgiving. Weather erosion can reduce the height of a mountain over time; conversely tectonic plate pressure can push the peak of the mountain upwards and earthquakes…..well that’s another exasperating issue. Gravity adds to the party by varying at different points on the Earth. This means sea level can differ dependant on the location which requires the calculation of local gravity to determine local sea level for when you are carrying out measurements. But even local sea level is not a constant as the Earth’s surface is not uniform so mean sea level is acquired by a process called high precision levelling using specific instruments. Finally air density which lessens as we rise causes light rays to bend (refraction) which impacts the manual procurement of vertical angles and needs to be adjusted for. Sorry — I sort of tricked you into thinking all you needed was trigonometry….
A feat here in the UK called Munro bagging entails climbing all 277 mountains in Scotland that are over 3000 feet tall. But because the land is shifting, heights change and so the peaks included in the list of 277 alter over time problematically resulting in disagreements as to completion of the challenge!
So there you have it. Mountains can grow. So next you rest a relaxing gaze on a beautiful mountain scene, I hope I’ve inspired you to take a protractor with you and get calculating…..
