Does anybody know if there is an official way of measuring mountains that most countries use?
Teddy asked me for a comment on this, so here it is.
When the matter involves cutting edge science and engineering, there is no official way for anything. According to the famous MIT physicist Walter Lewin, any measurement given without its error is a pure rubbish. If we look at the Chinese measurement of the height of Mt Everest from 2005, we can see the number as 8844.43 m +/- 0.21 m (no snowpack on the summit). That at least puts the measurement in a certain range, which could be taken as scientifically rigorous.
While trying to figure out what Chinese surveyors did with the Mt. Everest altitude measurement this year, I was not able to find any publication, showing pictures of their surveying equipment, except one picture taken on the summit with something like a reflecting geodetic prism (see here
https://abenteuer-berg.de/en/chinese-surveyors-on-the-summit-of-mount-everest/ ). The Chinese links provided in the tread here do not show any equipment either. Someone can only see Chinese surveyors trying to use oxygen masks at lower altitude.
In a video posted on May 27, 2020, it is said the surveyors are going to use satellite technology.
In another video, 53 surveyors are mentioned to take part in the expedition.
https://www.scmp.com/video/china/3083376/china-sends-surveyors-top-mount-everest-bid-measure-worlds-tallest-mountainTraditional and modern equipment are credited to be used for the feat.
In a publication from May 28, 2020, there is some more information and pictures. One can see a beacon, but it is not clear if it was brought to the summit. The beacon might be incorporated within the reflector geodetic prism I mentioned above, but that is not clear. Eight surveyors are credited to have reached the summit for measurements.
https://news.cgtn.com/news/2020-05-27/Chinese-measurement-team-reaches-Mt-Qomolangma-summit--QPczn2tmAo/index.htmlIn principle such measurements are routine and performed for more than two centuries, while the accuracy increases from many tens of meters down to millimeters nowadays. In order to complete a measurement, someone needs a theodolite, which is an optical precision instrument for measuring angles along a horizontal and a vertical planes. The theodolite is placed over a point on the Earth’s surface, which has its cördinates calculated. Level staff is placed on the point of interest that has to be measured. After taking readings, the calculation is trivial, as it relies on simple trigonometric functions as sine and cosine. The real struggle comes with errors determination which are of different types (temperature, humidity, Earth’s gravity, etc. for both points – the referent and the measured ones, and if possible for several points in between.
Modern instruments can work without a level staff, as they emit light or radar signals and measure the time necessary for the reflected signal to return back. They can measure distances directly to visible points on a rock surface, but to strengthen the return signal someone has to place a reflecting prism on the point of interest.
In order the errors in the measurement to be decreased, the point of interest has to be measured from different points, viewing the point of interest at different angles. The reference points has to be with their known cördinates. Such endeavor in high mountainous rugged conditions is a hard task, as heavy equipment has to be carried along long distances, and different teams to work simultaneously from several points beneath the peak, in order to fit the measurement into the short window of opportunity (2.5 hour as said for the surveyors that have reached the summit with their equipment). In addition there should be clear direct visibility between lower points of observation and the point on the summit. According to a friend of mine, who is a professional surveyor, the hurdles in such measurement, by means of a ground method, would be unsurmountable for obtaining a result in the centimeter accuracy. He would expect a tens of centimeters accuracy, with using the most modern equipment and measurements across distances larger than say about 2 km. The shortest horizontal distance between Mt. Everest and any rock ground, north of the summit, that I was able to measure on Google satellite maps, was 3.8 km. The real distance, along an oblique line, would be in the range of 5 km.
All mentioned so far leave space for only one method to be used here – the satellite GPS one. It uses the same basic principles – measures distances between a referent point and a point of interest. Here the accuracy that can be achieved is in the range of millimeters. The points of reference are where the GPS satellites are at the moment of measurement. Their position is constantly measured while satellites fly above Earth at height of 20,000 km. Satellites emit a radar signal and measure the time for the reflection to come back. With light speed known, measurement is easy on the first step. Again, here the most important are the errors, which are numerous – the Earth geoid’s shape, which affects the gravitational force, the direction of satellite movement (ascending and descending), positions of the Moon and Sun, the presence of large snow packs (glaciers = added more gravitational force), etc. All these are aggregated and clients get their real position on the ground. Precision depends on ground instruments and the stationary time at the point of interest. Longer time = more satellites connected = higher precision. If the measurement could be helped by a ground-based geodetic mark with high precision cördinates, the accuracy becomes even higher. That is why the Chinese team used the help of their telecom operator and Huawei – to secure reliable connection for high speed data transfer. To increase the reflectivity from the point of interest reflecting prisms are placed on the ground. They shine bright when radiated by the satellite emitter.
Finally, a few words about tectonics and earthquakes.
The height of Everest is globally accepted as 8848 m. It is measured by an Indian team in the middle of 20th c. In 1975 and 2005 the same height is confirmed by Chinese teams. The second time the reading is 8844.43 m +/- 0.21 m, but if counted the snowpack on the summit as 3.5 m we get the same height of 8848 m. In 2019 the height was measured by a Nepalese team, but results were not announced yet. Nepal and China agreed to announce both results from 2019 and 2020 together.
The tectonic plate of the Indian subcontinent is moving northwards with an annual velocity of ca 5 cm. The collision of the Indian Plate with Eurasian Plate results in the formation of the Tibetan Plateau and its mountainous rim on its south. Part of Tibet is escaping as a triangular wedge moving to the east. In fact Indian plate is driving within the Eurasian Plate, intercalating it. This process causes the Himalayas to rise at high speed. The region of Everest is considered as rising at an annual speed of 6 cm. Since the Indian survey in 1955, 65 years have passed. This would amount to a cumulative rise of Everest of 3.9 m, for this period. If we count only the last 15 years since the Chinese measurement in 2005, we would calculate 0.90 m rise.
Simultaneously the whole mountain range together with the Tibetan Plateau compensate elastically over the Earth’s mantle due to the increase of the crust’s mass (remember India is driven in between layers of the Eurasian Plate (Tibet)). That means the region sinks to some extent, exactly as a loaded ship sinks a little bit in water, but that cannot negate the whole cumulative tectonic uplift. The deflection of the crust/mantle boundary (MOHO) is estimated as −18.3 ± 8.6 mm/year for the main part of Tibet (
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018JB016334)
That is about 30% of the rising speed of Everest with a negative sign. So if we remove the MOHO deflection we will get even bigger rise.
On April 25, 2015, an earthquake happened, M 7.9 (Gorkha earthquake) in the region of Everest. The earthquake is of the thrust type, what is characteristic for collisional regions around the globe. The active fault surface, which was the source of the quake, is dipping gently to the north, at 11 degrees angle with the horizontal plane (
https://www.sciencedirect.com/science/article/pii/S1674984716300027).
The displacement along the fault surface was southward, effectively rising the whole region of Everest, located above the fault surface. The maximum displacement during the quake was of 5.2 m. The average displacement has not been calculated in the article cited above. If take, for instance, the average displacement to be at say 2.6 m, then we can get the maximum and average rise of Everest, only due to the earthquake:
5.2 х sin(11 degrees) = 0.99 m
2.6 х sin(11 degrees) = 0.50 m
Adding this to the average annual rise of Everest since 2005 we can get:
0.90 + 0.99 = 1.89 m
0.90 + 0.50 = 1.40 m
So, to answer at Teddy’s question for the Everest height after 2019 (Nepal) and 2020 (China), I would bet something between 1.5 and 2.0 m rise since the 2005 measurement.
So my expectation is the result to be between 8849.5 and 8850 m (including the snowpack on the summit).
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