China and Nepal announce new height of Mt. Everest; Here’s how mountain height is determined

China and Nepal recently announced that the highest mountain peak on the Earth Mount Everest is actually 86 cm taller than the globally accepted height of 8,848 m. The agreement marks the end of a long-running debate about the precise dimension of the peak that sits on the border of Nepal and Tibet. The Mt. Everest is called Sagarmatha in Nepal and Qomolangma in China. Several countries around the world have offered varying figures about the mountain’s height until China and Nepal’s recent announcement.

Here’s how mountain heights are measured and how accurate are the measurements

To measure mountain height basic principles of trigonometry, that is part of school syllabus is applied. Just like triangles, a mountain has three side and trigonometry shows if you know any three of the three sides and angles each side makes with the other, all the others can be calculated. For a right-angled triangle, since one the angles is 90 degrees, if you know one of the other angles and one of the sides, you can find rest of the quantities. This principle is for all triangular objects who are too huge to make a measuring tape to use or any sophisticated instrument from the top of the structure.

If we have to measure the height of a building or a pole, mark a point from the ground that acts will act as a point of observation, some distance from the building. Now to measure the height we need the angle of elevation that the building makes with the point of observation and distance of the building from the point of observation. The angle of elevation again is the angle between two imaginary lines from the point of sight to the building top and on the ground. Consider the angle of elevation is E and distance from building to point of observation is then, the height of the building is d X tan (E).

Is measuring mountain height as easy as measuring the height of a building?

Although the principle is the same for all elevated structures that can make an angle with the base but with mountains the base is unknown. The measurement also depends on which surface to your user to determine the height. For practical purposes height from the mean sea level was considered. Also finding the distance of the mountain from point of observation that now appears easy because of GPS and satellite images was not so in the 1950s. Also, now one has climbed the top of Mt. Everest till that time.

So, to deal with the problem of geographic inaccessibility, geologists would measure the angle of elevation from two different observation points in the same line, whose distance can be measured. Now with two different angles of elevation, there are two different triangles with a common arm. Now following trigonometry, the height of the mountain can be calculated without reaching there, fairly precisely. That is how mountain heights were earlier calculated before the advent of GPS or other modern navigation means.

How precisely can trigonometry help find mountain height?

High-school math is efficient enough to accurately calculate the height of small hillocks, a mountain whose top can be observed from a close distance from its base. For the world’s highest peak, there are several additional factors that need to be accounted for. Finding the actual base of the mountain or where it exactly meets the flat ground is difficult. Also, you have to see if the point of observation and base of the mountain are at the same horizontal level.

Since Earth’s the surface is not uniformly even, high-precision levelling is required where special instruments are used to determine the mean sea level by calculating step by step the difference in height starting from the coastline. This is how the height of any city is measured from sea level.

Varying gravity in different parts of the earth is another additional factor. Huge mass like that of the Mt. Everest can make gravity pull seal level upwards. Local gravity is also needed to be considered to calculate the local sea level, the reference base for finding mountain height. Sophistical portable gravimeters that can be called to mountain tops have made the process easier in present times.

Again triangulation process gets complicated with high altitude peaks as the air gets lighter as we go higher. Change in air density causes refraction, bending of light rays and hence the line of sight from the observation point to the mountain peak is also altered. Hence refraction results in an error in finding the angle of elevation. Correcting the refraction index is complicated and hence alters the height derives to certain extent.

How technology can help in finding current mountain height?

GPS satellites help in accurately giving coordinates to determine heights of mountains. GPS gives more precise coordinates compared to the earlier used ellipsoid model. Drones with Laser beams (LiDAR) can also be used to determine the actual coordinates. But GPS or laser beams do not take local gravity into consideration hence the data is fed into another model that values the gravity to determine the final outcome.

When such modern models like GPS, LiDAR and devices gravimeters were not available during 1952-54, the task of finding Mt. Everest height had to go through several challenges.

What does the new height of Mt. Everest announced by Nepal and China mean?

The Survey of India measured the height of the mountain in 1954 and inferred that it is 8,948 metres and the figure was globally accepted too. The measurement did not have access to GPS or other sophisticated devices in those times. In recent years, several scientists tried to measure the height again using GPS and laser beam and derived different figures, that vary by few feet from the globally accepted height. The varying height was explained as a change in the geological process that is altering the height.

But scientists believe, the height of Mt. Everest is increasing very slowly due to the movement of the tectonic plates. As the Indian tectonic plate moves northward, it pushes the surface up, increasing the height of Mt. Everest. The movement of the tectonic plates only created the great Himalayan range of mountains of which Mt. Everest is a peak. Movement of tectonic plates also makes Nepal prone to earthquakes. After the 2015 earthquake that shook the country, it became evitable that the height of Mt. Everest should be measured again to learn its impact on altering that area’s geology.

Considering all the above factors, 86 cm rise of Mt. Everest is not surprising but 86 cm is too less a rise in an 8,848 m high mountain peak. The detailed reports with the calculation by Nepal and the Chinese government is still to be published in any journal. Significance of the new figure can be analysed only after that.