Height of Mount Everest

Around the year 1840, Colonel George Everest, Surveyor General of India, got completed the Great Trigonometric Surveys (GTS) project against all odds and his own recurring sickness. During this survey, a peak was spotted in the Himalayan range area shining well above in height over all other peaks. Later, it was confirmed that it was indeed the Earth’s highest peak. In recognition of his special contribution to the GTS, this peak was named “Mount Everest” to honor him.

It became a challenge for mountaineers to climb the Earth’s highest peak and for surveyors to determine its height. While the surveyors got their fi rst success in 1852, the mountaineers succeeded in reaching the top of Mount Everest a century later in 1953.

Pioneering past surveys

In considering the details of the surveying methods and height determination, we must remember that each determined height belongs to its own time domain. Each time, it is as creditable an effort as any other preceding or following it.

The first authentic height of Mount Everest was determined in 1852 by the Survey of India (SOI) from the Nepal side. The height established was 29,002 Indian feet (See Box“On the ‘Right’ Foot”at the end of the paper).

SOI also made the second determination in 1954. This time the height derived was 29,028 Indian feet with uncertainty of ± 10 feet.

The Chinese State Bureau of Surveying and Mapping (SBSM) provided the third height in 1975, which was surveyed from the Tibet side. The reported height was 8848.13 meters with uncertainty of ± 0.35 meter.

Geodetic comments on old surveys

The various aspects of the old surveying methods and terms of reference now differ from the new 3-D modern surveys using the Global Positioning System (GPS). The most pertinent geodetic differences are explained as under:

a. Surveyed point – The vertical angles were observed from distant stations, two to three hundred miles away and 10 to 12 thousand feet lower than the Everest peak. Thus, one could never pinpoint the exact spot being observed.

b. Snowcap depth – As the amount of snow varies all the time, the point observed must have been different at the time of each of the above surveys.

c. Zero references – The Mean Sea Level (MSL) surfaces used by SOI in 1852 and 1954 could not be the same and as such they represented different vertical datums. Furthermore, two Indian MSLs would also differ from the Chinese vertical datum, which was defined by MSL along the Yellow Sea.

d. Basic unit of length – The unit used by SOI was the Indian Foot and it is different from the Chinese Foot (See box “On the Right Foot“at the end of the paper).

GPS surveys of 1998 and 1999

In 1998, the survey teams sponsored by the U.S. National Geographic Society (NGS) succeeded in collecting GPS data at a number of stations on the Nepal side including one at Mount Kala Pathar (or Black Stone) and the famous South Col campsite. NGS team could not collect data at the Everest peak, but was successful in collecting data at a rock outcrop (now known as Bishop Ledge), a few meters below the peak. During the same time, SBSM collected GPS data at fi ve stations in Tibet. This joint survey ensured good network geometry.

On May 5, 1999, two GPS receivers were sent up from the South Col campsite with intentions to place one at the peak and the second at Bishop Ledge. As only one receiver could reach the peak area, top priority was given to occupy the peak only. The GPS data at the peak was collected for about 50 minutes between 10 and 11 am Nepalese Time. The peak was snow-covered (Note: Peter Athans, Everest conqueror, who was on the peak during GPS observations, confi rmed this important aspect). An attempt to measure the cap thickness failed. At the same time, two additional GPS receivers were used to collect the data at the South Col and Mount Kala Pathar stations, which were also occupied in 1998. Chinese team(s) did not collect any GPS data in 1999 on the Tibet side.

It is important to note that the 1999 data set provides just the basic minimum survey connection between the Everest and two other stations. GPS data from the Tibet side, if collected, would have provided a check and improved the confi dence level.

Computations

The computations were jointly performed with Dr. J.Y. Chen, Senior Geodetic Advisor of SBSM, China. I tried but SOI did not respond to participate.

First, a network of all the stations of the 1998 survey was set up and adjusted to ensure accurate determination of the ellipsoidal heights h84 of all the participating stations, including Mt. Kala Pathar and South Col.

As the stations at Mount Kala Pathar and South Col were occupied in both the 1998 and 1999 GPS surveys, it was decided to use them as “anchor” stations. Thus, their absolute positions from the 1998 solution were to be used for computing the 1999 data sets. After finalizing the network solution, the 1999 data sets were used to compute the ellipsoidal height ‘h84; of the Mount Everest.

Next, using the most accurate WGS 84 (EGM96) geoid model, the geoidal height ‘N84’ was computed for the peak. Then, the “True” orthometric height ‘H84’ was computed using the following equation: H84 ~ h84 – N84

Vertical datum

The new height is defined with the WGS 84 geoid as the zero reference or in the World Height System (WHS).

Accuracy estimation

Using the GPS survey technique, the absolute accuracy of the ellipsoid height ‘h84’ is now in 5-10 cm range and thus no more a limitation. As the coverage and quality of gravity for the Mount Everest area is still poor, the absolute accuracy of the geoidal height ‘N84’ was the critical factor. Thus, this restricted the final accuracy of the orthometric height ‘H84’.

WGS 84 orthometric height

The WGS 84 orthometric height ‘H84’ of the snow-covered peak of Mount Everest at 10:30 hours Nepalese Time on May 5, 1999 is 8850 International meter ± 2 meter (1 sigma).

Salient features of the 1999 height

a. The GPS data was collected at the peak itself.

b. Height is defi ned in a 3-dimensional global datum where the geoidal zero is fundamentally different from the local MSL defined zeros.

c. The survey was carried out with the most accurate satellite survey technique.

Is mount everest really higher in 1999?

In 1999, it was the first time that the height of the actual peak was determined in a new vertical datum. Thus, there is no such previous height to compare with. Also, any two surveyed heights of the snowcovered peak would always differ from each other. Furthermore, the ‘uncertainty’ due to the errors in the surveyed heights should be taken into consideration as a significant factor in any new comparison.

Thus, with presently available information, it is interpreted that Mount Everest is neither rising nor losing its height.

Tectonic uplift or subsidence belongs to geophysical interpretation(s) and thus that interpretation is not considered here.

What is next ?

The “waiting” now starts for

a. A new geoid model of improved absolute accuracy, which would help in improving the accuracy of the orthometric height

b. The measurement of the depth or thickness of the snowcap concurrently with the GPS data collection at Mount Everest, which will allow determining the height of the actual rocky peak.

Innovative recommendation

Let us start reckoning for comparison world’s high mountain peaks in high accuracy ellipsoidal heights, which we directly get from GPS surveys. We will then have more confi dence in our “results”.

Conclusions

Heights, as determined in the past, were a great survey achievement, but now they are only historical. GPS is a revolutionary surveying technique and with the availability of an accurate geoid model, the accuracy of height determination has reached an unprecedented level. Thus, it would be simpler to say:

“Now, we know how high is the highest mountain at 1030 Hours Nepal Time, 5 May 1999” in a global geodetic system and with a good absolute accuracy.

It is important to note that each new height determination may not necessarily mean that the Everest is going up or down. But, of course, there will always be a scope for accuracy improvement.

On the “RIGHT” foot

Many units of “Foot” are in use, e.g., Indian, Chinese, British, alaysian,
U.S., and International. Effects on determination of the height of Mount
Everest due to variations among these different units of “Foot” is geodetically too complex and thus not discussed in this article.

Note: There are at least two metric units currently in use. Hence, the new height is specified in the “International Meter”.