The ocean floor is mapped using satellite measurements of gravity anomalies.
The ocean floor is static, so the measurements can be averaged over a long period to give quite a high level of precision, though unfortunately not to the nearest inch.
In any case, knowing the average depth of the ocean is not really important for measuring sea-level rise.
Sea level is measured at the coast by tide gauges, and globally by satellite altimeters.
The gauge can be an old-fashioned float type, or an acoustic sensor or radar. The rapid changes in height caused by waves can be smoothed out by mounting the tide gauge in a “stilling well,” essentially a vertical tube with an opening at the bottom that is about one-tenth the diameter of the tube itself.
The stilling well damps out the waves but allows tides and surges to be measured.
With satellite altimeters the picture is more complicated, as many adjustments have to be made to account for air pressure, water vapor content, and the like in the atmosphere, as well as scattering by waves and the effects of tides.
The processing is very complex and even then the altimeters need to be calibrated with tide gauges.
For both tide gauges and satellite altimeters, the key to reaching millimeter accuracy is averaging. Satellites average over an area about 4 miles in diameter, and data from both satellites and tide gauges is averaged over time.
In this way tides, waves, storms, and even the seasonal cycle are removed from the data, allowing mean sea level to be determined very accurately.
The global database of monthly mean tide gauge records is kept in the UK by the Permanent Service for Mean Sea Level.
This data shows that over the past century sea level rose at about 2 millimeters per year. Over the past decade, the rate of sea level rise has been nearer 3 millimeters per year, but it is too soon to tell if this is a temporary fluctuation or a long-term change.
Sea level is measured using tide gauges, which are kept sheltered from the waves by a stilling well.
These instruments can only measure the relative height of land and sea, and it is worth remembering that not only the sea changes height: the land moves too as a result of plate tectonics and other natural processes.
Also, tide gauges at major ports are affected by urbanization, as the weight of large cities can cause local subsidence, which may result in a spurious sea-level rise. Intensive settlement has accelerated the removal of groundwater beneath cities such as Adelaide in South Australia, causing them to sink relative to the sea.
All these factors make satellite altimetry a more accurate technique for measuring sea-level rise.
Against this background it seems almost miraculous that sea level has been measured as rising at between 1.7 to 2.4 millimeters a year, as a result of global warming. This is mainly due to the thermal expansion of water, with a small contribution from the melting of ice on land.
Radar altimeters on satellites are used to measure sea level. If the altitude of the satellite is known, the height of the ocean can be determined to within a few inches.
The average of many orbits over a particular location can be used to map short-term changes in sea level induced by variations such as seasonal heating, river discharges, and evaporation.
Over a longer period, averaging begins to show changes in sea level in the oceans caused by such phenomena as the Southern Oscillation and the North Atlantic Oscillation. Averaging of all orbits over all oceans over time yields a measurement of global sea level that shows that it is rising by about 2.3 millimeters a year.
One of the most valuable aspects of the resulting map of sea level is that it mirrors features on the seabed.
Extra mass in the form of seamounts increases gravity and slightly raises the ocean surface above the feature. A depression in the seabed lowers sea level locally.
Satellite altimeters have taken only a few years to map previously uncharted ocean bottom that would have taken 100 years to map using conventional techniques. The information this yields is priceless.
For example, the altimeter maps have been used to identify an impact crater south of New Zealand 12 miles in diameter.
Detection of this crater using ship-borne techniques would have been virtually impossible and too expensive.
