# How do you measure the height of a mountain?

Oct. 19 2007 3:01 PM

# How Tall Is Mont Blanc?

## Together, we can measure mountains.

The highest peak in the Alps has grown 2.15 meters in two years, surveyors announced last weekend. According to the data, Mont Blanc now rises 4,810.9 meters above sea level, thanks to extra snow on the mountaintop. How do you measure the height of a mountain?

Climb to the top and plant a GPS receiver. Scientists time how long it takes for radio signals to travel between the receiver and several orbiting satellites. This yields enough data to determine—to within a centimeter—the elevation of the receiver relative to the satellite, which sits at a known distance from the center of the Earth. But that's the easy part, because knowing the absolute elevation of the receiver doesn't tell you how high it is above sea level. And when scientists talk about the height of a mountain, they're referring to the distance from sea level to the peak.

The hard part's figuring out where sea level actually lies, since the height of the ocean surface is believed to differ by more than 100 meters   across the globe. The planet isn't a perfect sphere—the fact that it rotates and has variations in its density means that the strength of gravity isn't uniform in all places. (The rotation forces the globe to flatten at the poles and bulge at the equator, sort of like a tomato.) As a result, some parts of the Earth attract more water than others; for example, the sea level is especially high near New Guinea but very low south of India.

To correct for the changes in sea level, geodesists turn to equations that solve for something called a geoid, basically the surface that would exist if oceans extended into land, say through a series of canals. In other words, they try to figure out where the sea level would be if the water were lapping up against—or indeed flowing through—the base of the mountain. To accomplish this, they plug in variables, including the local gravitational force and the positions of the GPS receivers and satellites. The final calculation of this imagined sea level can be off by a meter or two, which means the measured heights of mountains may not be that precise.

Before GPS technology was invented, geologists and cartographers assessed mountains with high-school trigonometry and high-powered protractors called theodolites and transits. If you stand at some known distance away from a mountain and figure out the angle from where you are on the ground to the peak, then you can calculate its vertical height. In the 19th century, British surveyors in the Great Trigonometrical Survey of India measured a certain very tall mountain at 29,002 feet as they triangulated their way across the subcontinent. Not bad, considering some of their readings were taken from 160 miles away. When an American expedition measured Mount Everest with GPS in 1999, scientists discovered the mountain was 33 feet higher, or 29,035 feet above sea level.

Explainer thanks Dale Benson of U.S. Geological Survey, Michael Hamburger of Indiana University, Peter Molnar of the University of Colorado, and Ben Petersen of Land Surveyors' Association of Washington.

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