3.4: Measuring the Depth of the Ocean

The depth of the ocean is usually measured two ways: 1) using acoustic echo-sounders on ships, or 2) using data from satellite altimeters.

Echo Sounders

Most maps of the ocean are based on measurements made by echo sounders. The instrument transmits a burst of 10–30 kHz sound and listens for the echo from the sea floor. The time interval between transmission of the pulse and reception of the echo, when multiplied by the velocity of sound, gives twice the depth of the ocean (figure \(\PageIndex{1}\)).

Figure \(\PageIndex{1}\): Left: Echo sounders measure depth of the ocean by transmitting pulses of sound and observing the time required to receive the echo from the bottom. Right: The time is recorded by a spark burning a mark on a slowly moving roll of paper. After Dietrich et al. (1980: 124).

The first transatlantic echo soundings were made by the U.S. Navy Destroyer Stewart in 1922. This was quickly followed by the first systematic survey of an ocean basin, made by the German research and survey ship Meteor during its expedition to the south Atlantic from 1925 to 1927. Since then, oceanographic and naval ships have operated echo sounders almost continuously while at sea. Millions of miles of ship-track data recorded on paper have been digitized to produce data bases used to make maps. The tracks are not well distributed.

Tracks tend to be far apart in the southern hemisphere, even near Australia (figure \(\PageIndex{2}\)), and closer together in well-mapped areas such as the North Atlantic. Echo sounders make the most accurate measurements of ocean depth. Their accuracy is ±1%.

Figure \(\PageIndex{2}\): Locations of echo-sounder data used for mapping the ocean floor near Australia. Note the large areas where depths have not been measured from ships. From David Sandwell, Scripps Institution of Oceanography.

Satellite Altimetry

Gaps in our knowledge of ocean depths between ship tracks have now been filled by satellite-altimeter data. Altimeters profile the shape of the sea surface, and this shape is very similar to that of the sea floor (Tapley and Kim, 2001; Cazenave and Royer, 2001; Sandwell and Smith, 2001). To see this, we must first consider how gravity influences sea level.

The Relationship Between Sea Level and the Ocean’s Depth

Excess mass at the sea floor, for example the mass of a seamount, increases local gravity because the mass of the seamount is larger than the mass of water it displaces. Rocks are more than three times denser than water. The excess mass increases local gravity, which attracts water toward the seamount. This changes the shape of the sea surface (figure \(\PageIndex{3}\)).

Let’s make the concept more exact. To a very good approximation, the sea surface is a particular level surface called the geoid (see box). By definition a level surface is a surface of constant gravitational potential, and it is everywhere perpendicular to gravity. In particular, it must be perpendicular to the local vertical determined by a plumb line, which is “a line or cord having at one end a metal weight for determining vertical direction” (Oxford English Dictionary).

The Geoid

The level surface that corresponds to the surface of an ocean at rest is a special surface, the geoid. To a first approximation, the geoid is an ellipsoid that corresponds to the surface of a rotating, homogeneous fluid in solid-body rotation, which means that the fluid has no internal flow. To a second approximation, the geoid differs from the ellipsoid because of local variations in gravity. The deviations are called geoid undulations. The maximum amplitude of the undulations is roughly ±60 m. To a third approximation, the geoid deviates from the sea surface because the ocean is not at rest. The deviation of sea level from the geoid is defined to be the topography. The definition is identical to the definition for land topography, for example the heights given on a topographic map.

The ocean’s topography is caused by tides, heat content of the water, and ocean surface currents. I will return to their influence in chapters 10 and 17. The maximum amplitude of the topography is roughly ±1 m, so it is small compared to the geoid undulations.

Geoid undulations are caused by local variations in gravity due to the uneven distribution of mass at the sea floor. Seamounts have an excess of mass because they are more dense than water. They produce an upward bulge in the geoid (see below). Trenches have a deficiency of mass. They produce a downward deflection of the geoid. Thus the geoid is closely related to sea-floor topography. Maps of the oceanic geoid have a remarkable resemblance to the sea-floor topography.

Figure \(\PageIndex{3}\): Seamounts are more dense than sea water. They increase local gravity, causing a plumb line at the sea surface (arrows) to be deflected toward the seamount. Because the surface of an ocean at rest must be perpendicular to gravity, the sea surface and the local geoid must have a slight bulge as shown. Such bulges are easily measured by satellite altimeters. As a result, satellite altimeter data can be used to map the sea floor. Note: the bulge at the sea surface is greatly exaggerated; a two-kilometer high seamount would produce a bulge of approximately 10 m.

The excess mass of the seamount attracts the plumb line’s weight, causing the plumb line to point a little toward the seamount instead of toward Earth’s center of mass. Because the sea surface must be perpendicular to gravity, it must have a slight bulge above a seamount as shown in figure \(\PageIndex{3}\). If there were no bulge, the sea surface would not be perpendicular to gravity. Typical seamounts produce a bulge that is 1–20 m high over distances of 100–200 kilometers. This bulge is far too small to be seen from a ship, but it is easily measured by satellite altimeters. Oceanic trenches have a deficit of mass, and they produce a depression of the sea surface.

The correspondence between the shape of the sea surface and the depth of the water is not exact. It depends on the strength of the sea floor, the age of the sea-floor feature, and the thickness of sediments. If a seamount floats on the sea floor like ice on water, the gravitational signal is much weaker than it would be if the seamount rested on the sea floor like ice resting on a tabletop. As a result, the relationship between gravity and sea-floor topography varies from region to region.

Depths measured by acoustic echo sounders are used to determine the regional relationships. Hence, altimetry is used to interpolate between acoustic echo sounder measurements (Smith and Sandwell, 1994).

Satellite-altimeter systems

Now let’s see how altimeters measure the shape of the sea surface. Satellite altimeter systems include a radar to measure the height of the satellite above the sea surface and a tracking system to determine the height of the satellite in geocentric coordinates. The system measures the height of the sea surface relative to the center of mass of earth (figure \(\PageIndex{4}\)). This gives the shape of the sea surface.

Figure \(\PageIndex{4}\): A satellite altimeter measures the height of the satellite above the sea surface. When this is subtracted from the height \(r\) of the satellite’s orbit, the difference is sea level relative to the center of Earth. The shape of the surface is due to variations in gravity, which produce the geoid undulations, and to ocean currents which produce the oceanic topography, the departure of the sea surface from the geoid. The reference ellipsoid is the best smooth approximation to the geoid. The variations in the geoid, geoid undulations, and topography are greatly exaggerated in the figure. From Stewart (1985).

Many altimetric satellites have flown in space. All observed the marine geoid and the influence of sea-floor features on the geoid. The altimeters that produced the most useful data include Seasat (1978), GEOSAT (1985–1988), ERS–1 (1991– 1996), ERS–2 (1995– ), Topex/Poseidon (1992–2006), Jason (2002–), and Envisat (2002). Topex/Poseidon and Jason were specially designed to make extremely accurate measurements of sea-surface height. They measure sea-surface height with an accuracy of ±0.05 m.

Satellite Altimeter Maps of the Sea-floor Topography

Seasat, GEOSAT, ERS–1, and ERS–2 were operated in orbits with ground tracks spaced 3–10 km apart, which was sufficient to map the geoid. By combining data from echo-sounders with data from GEOSAT and ERS–1 altimeter systems, Smith and Sandwell (1997) produced maps of the sea floor with horizontal resolution of 5–10 km and a global average depth accuracy of ±100 m.

Figure \(\PageIndex{5}\): The sea-floor topography of the ocean with 3 km resolution produced from satellite altimeter observations of the shape of the sea surface. From Smith and Sandwell.