# Geo-Joint: Taking the Measure of the Mountain

As Maps.com’s editor, I have to check a lot of map data for accuracy. Though names for streets and buildings often change, the currently accepted form is usually a settled affair. What you might think of as less variable are figures given for mountain heights. Of course, an earthquake here, or an eruption there might add a few inches or shear off a number of feet, but outside of that, there ought to be pretty close agreement on a solid figure—after all, it’s set in stone, right? Well, it depends upon your definition of “close” and what it is you’re actually measuring. Those are just a couple of the variables of determining mountain heights, and the further you dig into the process, the more factors emerge to tweak the results.

Extreme distortion of scale illustrates the variable strength of gravity on the earth’s surface, and therefore the the lumpy shape of the geoid in 3-D.

The strength of gravity varies greatly worldwide, causing highs and lows in sea surface heights.

The first thing to take into account is the shape of our planet. Terra firma is not as firma as might be supposed. Remember, it’s spinning around at about a thousand miles an hour, so the part farthest from its spinning axis, the equator, has enormous forces stretching it outward. Instead of being a perfectly round ball, Earth is about 32 miles greater in diameter at the equator than when measured from pole to pole. So the Earth is a little shorter and wider than that perfect sphere—a shape sometimes referred to as an oblate spheroid, or an ellipsoid. Even so stretched, it would seem straightforward enough to measure the height of a mountain upon this shape, but no.

Take some sightings like this, apply some trig, and presto: a mountain height!

What are we measuring these mountaintops against? What does it mean to say a mountain is X number of feet high? Well, higher than sea level, of course, but the tide rises and falls by different amounts, all over the world. So the first trick is to average all of that to a base figure. However, even after finding mean sea level at a particular place, there is the problem that seawater is not evenly distributed over the planet. To some degree, this is due to the variable thickness of the Earth’s crust. Areas of greater mass cause water to be attracted to them by means of gravity. The height of the sea varies by hundreds of feet between different places on the globe in part because of this and even more so by the effect of winds and currents piling water up in certain regions. The locations of the continents and the shapes of their coastlines affect this uneven distribution. If that weren’t enough, seawater density, salinity, temperature, and the effects of atmospheric pressure all influence the height of the sea.

Scientists have found a workaround for all of this by devising a concept called a geoid. The geoid is what the ocean surface would be shaped like if it were only affected by gravity and the rotation of the Earth. It assumes an even distribution of seawater through the continents by means of imagined parallel canals crossing continental masses. As only gravity and rotation are in play, the other factors mentioned above no longer complicate the picture. Being under fewer influences, this model results in an Earth that is more idealized—not so smooth as a perfect sphere, but broadly lumpy. It provides a generalized basis from which height can be measured. It is, of course, arrived at by mathematics far, far, far beyond the scope of this explanation, but the elevation of the geoid is known both on the watery surface, and under the land surface, of the planet. It’s the worldwide expression of zero elevation.

How they used to do it—the Great Trigonometrical Survey of India was an enormous undertaking.

Back before the geoid was a fully developed tool, surveyors measured mountains in an extremely laborious way. Starting at sea level, they would perform an exercise known as triangulation, which involves some fairly straightforward trigonometry as teams worked their way into the interior to ever higher topography, towards a mountain peak. Reading angles horizontally from point to point established the relative location of, for instance, towns, from an established starting point or datum. Additionally, by taking sightings of a distant highpoint from two locations along a line going straight towards that highpoint, the knowledge of the angles and distances travelled produced elevation figures. British surveyors did this in a very big way when they sought to fully map India and determine the height of Mt. Everest during The Great Trigonometrical Survey of India, conducted over several decades in the 1800s. They began at the Indian coastline and worked their way for hundreds of miles toward Nepal. Though political complications stopped their approach more than 100 miles short of Everest itself, their many measurements sited from multiple angles produced a height of 29,000 feet, exactly. Feeling that people would think the figure was just a rounded guess rather than a careful measurement, they reported the height to be 29,002 feet. In any case, more modern and precise calculations done decades later came to conclude that Everest’s height was 29,029 feet, remarkably close to the original figure.

When geodesists, the folks who study the shape of the earth and positions on it, finally got satellites into their bag of tricks, accuracy took a big leap. Knowing the precise height of orbiting instruments allowed these scientists to know just how far given points on Earth’s surface were from its center. That information in concert with gravitation readings helped refine the geoid, and allowed for more accurate elevation figures. The mathematics and formulas used are quite detailed, and the complexities of natural forces mean that “sea level” under mountain peaks can only be determined to a certain degree of accuracy. There may always be a foot or two of leeway in any measurement, and different teams of geodesists may use different technologies based on different data sets to arrive at a height. It is not unusual to find mountain height figures on the web that differ by tens of feet, or more. Sometimes this results from the simple fact that some measurements include the height of snow and ice, and others prefer to reference the solid rock beneath that frozen water. Some mountains were measured long ago, and their heights are kind of legendary. Newer measurements may take some time to be widely accepted, and some researchers have been shown to have fudged or short-cut the process of measurement. Though there are any number of professional and academic organizations vitally interested in mountain peaks and climbing, and government bureaus teeming with statistics, no one seems to have the ultimate say-so on mountain heights.

It wasn’t easy to get the first elevation figure for Mt. Everest, and refinements are ongoing.

Ecuador’s Chimborazo—shorter than Everest, but it sticks out farther from the center of the planet.

Mauna Kea has a broad, mellow profile, belying its impressive true size.

Mt. Everest itself, the tallest on earth, has gone from 29,029 to 29,035, to 29,022, to 29,017 feet depending upon the nationality of the surveyors, and their instrumentation. 29,029 seems to be the longtime favorite, but whatever its height, Everest still isn’t the point farthest away from the center of the Earth. That distinction goes to Mt. Chimborazo, in Ecuador. The mountain itself measures about 20,500 feet tall (some quick research results in three widely varying figures), well short of Everest’s height above sea level. But because of that planetary bulge at the equator, Chimborazo is around 6,800 feet farther from the center of the planet than is Everest. And Mauna Kea, on the Big Island of Hawai’i, has a much greater rise from its seafloor base to its peak than Everest has from sea level to its top. Like most records, it’s all in how you define the rules of the game, and when it comes to mountain heights, the goalposts are always moving.

That equatorial bulge gives Chimborazo the edge. And Mauna Kea’s feet plant themselves way deep under its surrounding seas.

Still not convinced the experts have the right height for Everest? Make a trek and measure it yourself! But don’t forget your Nelles map of Nepal, available from Maps.com.

PHOTO CREDITS:

caption: How they used to do it—the Great Trigonometrical Survey of India was an enormous undertaking.

source: Wikimedia Commons: Survey of India (Public domain)

caption: Take some sightings like this, apply some trig, and presto: a mountain height!

source: Wikimedia Commons: Régis Lachaume, 2005 (Public domain)

caption: The strength of gravity varies greatly worldwide, causing highs and lows in sea surface heights.

caption: Extreme distortion of scale illustrates the variable strength of gravity on the earth’s surface, and therefore the lumpy shape of the geoid in 3-D.

source: NASA: NASA/University of Texas Center for Space Research (Public domain)

caption: It wasn’t easy to get the first elevation figure for Mt. Everest, and refinements are ongoing.

source: Wikimedia Commons: Rdevany (CC by SA 3.0)

caption: Ecuador’s Chimborazo—shorter than Everest, but it sticks out farther from the center of the planet.

source: Wikimedia Commons: Bernard Gagnon (CC by SA 3.0)

caption: That equatorial bulge gives Chimborazo the edge. And Mauna Kea’s feet plant themselves way deep under its surrounding seas.

source: oceanservice.noaa.gov: National Ocean Service/NOAA (Public domain)

caption: Mauna Kea has a broad, mellow profile, belying its impressive true size.

source: Wikimedia Commons: Aiden Relkoff (CC by SA 4.0 International)