Maps and Locations on the Earth

Topographic and Bathymetric Maps

Topographic maps show the elevation of Earth’s surface above mean sea level. Bathymetry maps show water depth or depth of the seafloor below mean sea level. An example of a three dimensional bathymetry map is shown in the first figure. Colors represent water depths. Reds and yellows are shallow, blues are deep. The submarine ridge depicted here plunges from sea level (0 meters) to 5000 meters below sea level.

Three-dimensional map of a submarine volcanic ridge.

Some maps have contours on them. On a topographic map, contours are lines of equal elevation. On a bathymetry map, contours are lines of equal water depth. A contour map of the submarine ridge shown in three dimensions above is presented in the second figure. The contour interval is 100 meters meaning that each line represents an increment in water depth of 100 m (for example, contours of 100, 200, 300, 400 m, etc. water depth).

Contour map of the submarine volcanic ridge shown in the first figure.

The underwater ridge is located next to the Big Island of Hawaii. The location of the ridge on the surface of the Earth is specified by latitude and longitude marked on the edges of the contour map. What are latitude and longitude?

Latitude and Longitude

If the Earth were flat, rectangular coordinates (x,y) would be sufficient to describe the locations of points on its surface. However, Earth is a sphere with no sides, and a special frame of reference is needed. The poles of Earth provide this reference frame.

The equator is an imaginary circle around the Earth located halfway between the north and south poles. Other lines drawn parallel to the equator but shifted to the north or south are called lines of latitude. At the equator the latitude is 0°, halfway to the pole it is 45°, and at the poles it is 90°

Lines running north/south through the poles are called lines of longitude (or meridians). Longitude is the number of degrees east or west of the prime meridian (0°) which passes through Greenwich, England.

Lines of latitude

Lines of longitude

Locating Hawaii on the Earth

Cutaway globe showing the location of Hawaii on Earth

Hawaii is in the northern hemisphere and is located 20° north of the equator and 155° west of the Prime Meridian (Greenwich, England) as shown on the cutaway globe to the right.

Calculating the distance between two points on the Earth's surface

Map of the East Pacific between Hawaii and San Diego.

Above is a map of the East Pacific ocean between Hawaii and the southwestern U.S. with latitude and longitude marked on its edges. The coordinates of Hawaii (20°N, 155°W) and Los Angeles (34°N, 118°W) are labeled. A red line connects these two points.

The distance between Hawaii and Los Angeles (the red line on the map above) can be calculated from their latitudes and longitudes.

A: Hawaii (20°N, 155°W)

B: Los Angeles (34°N, 118°W)

Latitude (phi) and longitude (theta) are related to rectangular coordinates (x,y,z) by the relationship

(x,y,z) = (Rsin(theta)cos(90° - phi), Rsin(theta)sin(90° - phi), Rcos(theta) )

where R is the radius of the sphere.

Using these concepts, the distance, D, between Hawaii and Los Angeles can be calculated from the formula

D = R (0.7861)