Elevation

ELEVATION CAN BE defined as a measure of the height above mean sea level. When specifying a location on (or above) the surface of the Earth, elevation is commonly considered to be the third coordinate, complementing measures of LATITUDE AND LONGITUDE. Similarly, bathymetric measurements provide a depth below mean sea level to the floor of a body of water. Mean sea level is defined as the still water level averaged over time so that periodic changes in sea level—such as those caused by the gravitational effects of the moon and sun—are averaged out.

The choice of mean sea level as the baseline (or datum) for elevation is an arbitrary, though reasonable, option. Based on the behavior of water, early practitioners of geodesy (the study of the shape of the Earth) believed that the oceans of the world were balanced by the Earth’s gravitational pull, forming a perfect sphere with the exception of the transitory distortions caused by waves and the periodic changes due to the tides. This decision is arbitrary since elevation could have been defined as a measure of distance from the center of the Earth or a measure of distance below the highest known point on the Earth, among other possible choices. Since there is no natural zero level for elevation,collections of elevation data should be considered to be of an interval type.

Unfortunately, mean sea level is not constant at all places. There are irregularities in mean sea level because of varying concentrations of mass in different parts of the Earth, and the resultant variations in gravitational pull. Additionally, the effects of currents and differences in water temperature and atmospheric temperature and pressure create variances in mean sea level. Moreover, mean sea level is historically measured with a tide gauge, which is an instrument that uses land-based benchmarks to record the sea level. A change in mean sea level can therefore result from a change in the actual sea level or a change in the height of the land that supports the tide gauge. Given all these distorting factors, mean sea level must be considered as the zero elevation (also termed the vertical datum) for only a local area. When mean sea level has been determined for a local area, this datum is used to compute elevations in surrounding areas with surveying tools and the techniques of leveling and triangulation. 

Elevation can be represented graphically in several different ways. The U.S. Geological Survey (USGS) has historically produced several map series that contain elevation data both in the form of points where known elevations have been surveyed and in the form of contour lines that produce an approximate elevation surface. Contour lines connect locations on the Earth’s surface that have the same elevation value. Generally speaking, elevation contour maps use a constant contour interval (for example, 10 ft) so that the separation between contour lines represents a consistent change in elevation. This results in contour lines that are close together in areas with steep terrain, and further apart in areas with less dramatic elevation changes. The contour interval may not be constant for all maps in a map series, since the best contour interval for a given map is a function of the variation in elevation across the map and should be chosen in such a way that sufficient elevation detail can be visualized.

Although printed contour maps continue to prove useful for many applications, elevation data are increasingly processed digitally. There are several common digital formats, also known as digital elevation models (DEMs). One such DEM is termed a triangulated irregular network (TIN). A TIN begins with a set of points where the elevation has been calculated. These points can occur at any location but ought to occur at points where there is a major change in the shape of the elevation surface, such as at mountain peaks, valley floors, or the edge of cliffs. The denser the number of elevation points, the greater the detail captured by the TIN. In order to generate the elevation surface, a set of nonoverlapping triangles are created by connecting neighboring points.

Each triangle represents a planar elevation surface, and the slope and aspect (the orientation angle of the slope with respect to north) are constant for each triangle. TINs are a very efficient method for storing elevation data, in part because they allow for variation in the density of elevation points based on variability in the elevations being mapped. A more widely used method for digitally representing elevation data is the raster (or grid) method. A raster DEM divides a portion of the Earth’s surface into regularly spaced (and usually rectangular) grid cells, arranged into rows and columns. Each cell contains a single elevation value. Based on the cell values and the values in neighboring cells, the slope and aspect can be calculated for the elevation surface. The raster method allows for easier manipulation of elevation data than the TIN method, although it requires greater amounts of computer disk space to store the large number of regularly spaced elevation values. Rasters are always regularly spaced, so there is no way to vary the density of elevation observations within a single raster to account for greater or lesser variability in relief. High-quality DEMs in raster format are available at several different cell resolutions.