Gautam carried some unusual baggage - a ground-penetrating radar and a top-of-the-line satellite navigation device. Unlike most climbers, he and his team remained at the summit for nearly two hours so they could take the measurements they needed. Gautam suffered a serious case of frostbite, and his colleague nearly died
Is Mt Everest shrinking? Nepal on a mission to measure the world's tallest mountain
Sometime early next year, the new height will emerge from a modest cluster of offices on the ground floor of a government building in Kathmandu, home to the country's Survey Department. Susheel Dangol, the chief survey officer, recently installed a keypad-entry system for his department just to safeguard the Everest data.
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"Everyone is curious about the project," he said with a grin. During an interview, his cellphone rang with a call from a senior official in the country's Land Ministry inquiring about the progress of the work. Dangol has developed a stock response to those who ask about the final figure: At the moment, I'm unable to say.
Dangol, 38, oversees a team of 80 people who have hiked, driven and helicoptered across Nepal to gather the data required for an updated measurement. Among their challenges: transporting a US$200,000 Canadian-made gravimeter - which measures the force of gravity at a given location - along juddering Himalayan roads to nearly 300 different spots.
The question of Everest's height is intimately linked to its modern history. It is known in Nepal as Sagarmatha and in Tibet as Chomolungma. The search for the mountain's English name began after it was declared the world's tallest peak by surveyors in India in 1856. (Its namesake is George Everest, the prior chief surveyor of India, but even he wasn't crazy about having the mountain named after him.)
Dangol's team is tackling its task with two methods. The first is to measure Everest the old-fashioned way using trigonometry. Such calculations produced the first-ever tally of Everest's height, as well as the measurement taken in the 1950s by an Indian team that serves as the current standard.
But that technique will serve as "a check, a redundancy," said Christopher Pearson, a research fellow at the University of Otago in New Zealand who consulted with Nepal on the project. The pathbreaking part of the effort will come through the second method, which relies on a combination of readings from a satellite navigation system and a complex model of sea level.
Enter Gautam, a 15-year veteran of the survey department. The 35-year-old had already summited Everest once before in 2011. This time, however, his four-person team was carrying 90 pounds of equipment in addition to their regular climbing gear. They planned their ascent to arrive at the summit in the middle of the night so their work would not be disturbed by other climbers.
While most climbers limit their time at the roof of the world to descend quickly from the "death zone," Gautam and his team "did not have that privilege," he recalled. They stayed at the summit for an hour and 45 minutes, taking readings with a Global Navigation Satellite System device and a ground-penetrating radar that can gauge the difference between the actual rock summit and the snow that covers it.
Wearing bulky mittens against the extreme cold, Gautam and his team couldn't operate the small knobs on their equipment. So they took off the mittens and worked in fleece gloves instead. For weeks afterward, Gautam had no sensation in his fingers. The frigid temperatures also damaged his feet: He lost the tip of his left big toe to frostbite and now wears only sandals, rather than shoes.
On the descent, all their food and water was gone, and Gautam's colleague ran out of oxygen, a life-threatening situation. Their climbing guide managed to borrow a bottle from another Sherpa who was heading up the mountain, Gautam said, saving his colleague's life.
Although the data they carried with them on the way down weighed nothing, "its preciousness made it so heavy," said Gautam.
Yet the satellite readings from the Everest expedition are not sufficient. They give the mountain's "ellipsoidal" height - the height of the summit above a smoothed geometric model of the Earth. The readings do not reveal an object's precise height above sea level.
Judging exactly where sea level would begin beneath Everest's massive tons of rock turns out to be a key question. Generating the model of sea level required lugging a gravimeter, which is carried in a large suitcase-like box, to 297 spots in Nepal. "We have to be cautious and drive slowly," Dangol said. At each measuring point, the machine must be calibrated before taking readings for two sessions of three minutes each.
The data collection will be completed next month, Dangol said. Then the processing will begin: six people, sitting in a room equipped with high-speed computers and specialized software, for three to four months, checking and rechecking the figures. It will be a "closed camp," Dangol said. Not even he will know the results at first.
Nepal's effort has been "incredible," said Pearson, the surveying expert in New Zealand. "Staggeringly, it has all worked, and they have all the information they need to get an accurate height."
Dangol is already looking forward to next year, when Nepal plans to unveil Everest's new height - both the rock height and the snow height, down to the centimeter. That will be "kind of like a thesis defense," he said.
Even the loss of part of his toe did not dull Gautam's pride in his work. "We are so happy because we finished our difficult task," he said. "I was ready to take [a] risk for the nation."