How does the U.S. Geological Survey measure the elevation of a city or mountain?

In addition to the networks of highways, railroads, and telephone wires that connect the farthest sections of the country, another, less visible system exists by which elevations of towns, cities, mountains, and lakes have been determined.

Points of reference are marked by thousands of bench marks from coast to coast, the work of state surveys, the U.S. Geological Survey, the U.S. Coast and Geodetic Survey, and others. “Monumented” bench marks (which appear on maps as oblique cross symbols with the letters BM) are identified by standard tablets set in concrete or stone posts, firm rock, or buildings.

Nonmonumented bench marks may consist of chiseled squares or crosses in masonry structures, metal pins or nails in concrete, or copper nails and washers in tree roots. This ever spreading network is the means of arriving at our most precise determinations of elevation. Such determinations are not only a matter of general interest to the public; they are highly important for control of topographic mapping and necessary for many surveying and civil engineering operations.

In the United States, geodetic elevations refer to mean sea level, which is the average height of the sea measured hourly over a period of nineteen years. In this length of time the earth completes a cycle incorporating the full sweep of tidal variations.

The first transcontinental line of precise levels started in 1878 at a tidal station in Sandy Hook, New Jersey, which was intended to provide a vertical control along the 39th parallel. Measurements along this line, taken across the entire continent, were described as being on the “Sandy Hook Datum.” The first ties to the Pacific coast were made at Seattle, Washington, in 1907 and at San Diego, California, in 1912.

In 1929 increased knowledge about sea level resulted in a so called special adjustment. Mean sea level apparently slopes upward to the north along the Atlantic and Pacific coasts, and to the west along the Gulf coast. It is also somewhat higher on the Pacific coast than on the Atlantic. New data were obtained from twenty six tidal gauges at twenty one United States sites and five locations in Canada. It is on the basis of those measurements that the elevations we know today were determined.

With a known elevation in hand, surveyors may advance the line of controls by several methods. By far the most common is leveling, which is classified in four orders of decreasing accuracy. (First order leveling, for example, extends over a distance of .05 to 1 mile, measures to an accuracy of .017 foot per mile, and establishes bench marks at least every mile. Third order, on the other hand, is slightly less precise; monumented bench marks are placed within 3 mile limits.) The U.S. Coast and Geodetic Survey is responsible for most first and second order controls. Whenever possible, points are identified and measured along highways and railroads, the most accessible sites available.

A leveling crew consists of a levelman, a recorder, and two rodmen. The standard level is equipped with a telescope for sighting and a leveling device for making and maintaining a horizontal line of sight. This device is either a sort of pendulum, which operates quickly and accurately by the force of gravity, or a cylindrical vial containing a bubble, which must be adjusted manually.

The levelman first sights a rod (graduated in hundredths of a yard) held on a point whose elevation is known. He adds the rod reading to this elevation in order to determine the height of his instrument. He then turns the level in the direction he wishes to progress and sights another rod, usually about 50 feet away. In the most precise leveling, the two rods must be exactly equidistant from the level to prevent any distortion due to refraction or the curvature of the earth. The elevation at the point of the second rod is found by subtracting the new rod reading from the height of the instrument. The level is then advanced to a new setup and the procedure repeated, using the newly determined elevation as a reference. Various checks are made to prevent errors, which can be magnified greatly over substantial distances.

A leveling crew may progress quite happily down a highway or across a field, but dense forests, steep inclines, and mountains present new sets of problems. Siting points step by stepup a massive, icy peak such as Mount McKinley would, of course,be tricky. In such a case a method of determining a low order elevation without ascending the mountain may be employed.

In the most widely used technique, a surveyor starts at Point A of known elevation at the base of the mountain. If he knows the latitudinal and longitudinal coordinates of that point and the coordinates of the peak to be measured, he can calculate the distance between the two points. Another method of determining the distance to the peak is to observe the horizontal angle at Point A from Point B to the peak, observe the horizontal angle at Point B from the peak to Point A, and determine the distance between Point A and Point B.

The distances from Point A and Point B to the peak can then be computed. Using a theodolite, an instrument that measures both horizontal and vertical angles, the surveyor then sights the mountain peak and measures the vertical angle. With these two figures (distance between the points and vertical angle measurement) he can determine the mountain’s elevation trigonometrically. This technique, which measures the vertical angle in one direction only, makes use of what is called a nonreciprocal vertical angle.

Reciprocal vertical angles can be used if one can get to the top of the mountain and perform the same procedure in reverse, sighting Point A and/or Point B at the base of the mountain and measuring the vertical angle to it.

Also, if one gets to the top of the mountain, the distance to Point A and/or Point B could be determined by measuring them with an Electronic Distance Measuring Instrument (EDMI). This sophisticated instrument has a mirror that reflects light to another instrument, in this case at Point A or B, and the distance is calculated automatically on the basis of the speed of light.

Elevation differences computed from both top and bottom are then compared, and if they are within the allowed tolerance, they are combined to arrive at a more accurate trigonometric elevation of the mountain.