Sea-level rise is the most feared impact of global warming.
There has been unnecessary alarm caused by poor data, bad analyses, and wild guess computer model projections.
There are changes in global sea level (eustatic sea level), and changes in local relative sea level.
Sea-level changes are measured relative to a defined reference level ... but remember that Earth’s surface is dynamic, not static.
Seas rise at about 1mm to 2mm a year = harmless.
Seashore land subsides (sinks) too.
A tide gage can't tell the difference.
Past sea-levels are measured or inferred from geological evidence.
Modern observations use tide gauges.
Since the early 1990s, satellite data have been available too.
Either melting ice and/or a warming ocean might cause sea levels to rise.
The last ice age reached its peak about 20,000 years ago, with sea level at about -400 feet (-120 meters) lower than today.
Geological sampling shows rapid melting, up to 26mm per year over short periods between about 15,000 and 10,000 years ago, after which the rate of rise declined to 1–2mm per year.
The 26mm per year rises are linked to breakout floods into the oceans, from large Northern Hemisphere pro-glacial lakes.
No large meltwater lakes exist today, so such high rise rates of rise are unlikely to be repeated.
In addition, the Antarctic ice cap has expanded, not decreased, in the past 20 years -- a melting ice cap would have caused an increase in the rate of sea rise.
In his papers Nils-Axel Mörner (1983, 2004, 2011) established a maximum possible glacial eustatic rate of change of 10mm per year, or 1.0 meter per century.
Local relative sea level is traditionally measured at ports using tide gauges, some of which have records extending back to the eighteenth century.
After correcting for subsidence (land sinking), or land uplift, the longer-term tide-gauge records show a twentieth century sea-level rise of +1 to +2 mm per year.
The UN's IPCC (2001) estimated an average rate of eustatic rise between 1900 and 2000 of +1.6 mm per year.
Gobal average sea level has been rising gently for the past 100+ years by simple observation.
The precise rates of change are an open question.
There was no significant increase in the rate of sea-level rise during the twentieth century, in contrast to climate model projections for an increase of the rate.
If the late twentieth century global warming was as extreme as the IPCC claims it has been, why can that warming be detected in global sea-level data?
The rate of increase in atmospheric carbon dioxide levels grew dramatically after 1950 (from a 1900–1950 mean rate of rise of 0.33 ppm/year, to a 1950–2000 mean rate of rise of 1.17 ppm/year)
But the mean global sea-level rate of rise did not trend upwards after 1950.
Since the early 1990s, sea-level measurements have been made by microwave radar and laser ranging from various orbiting satellites, including the U.S. TOPEX-Poseidon, the European Remote-Sensing Satellite (ERS), Geosat Follow-On (GFO), EnviSat, and Jason series.
Satellites and tide gauges do not measure the same thing.
Tide gauges measure relative to a fixed land benchmark.
Satellites measure relative to a mathematical model of the shape of Earth’s gravity field (geoid) that's not well characterized, and varies over time.
With satellite “sea-level change,” up to 50% of the change results from geoid changes -- as a result, satellite measurements are more than +3mm per year.
Another problem with satellite measurements is that significant differences occur with different sensors used by different research groups.
Satellite altimetric measurements that show +2 mm per year, and especially those showing greater than +3 mm per year, are likely to be wrong (versus +1–2 mm per year from tide gauge data.
The important question is not, “Is sea level rising?”
Geological, tide gauge, and satellite records all agree it is ... but the rise rate has not accelerated as a result of additions of CO2 to the air since 1950.
PS:
Note that when sea level rises, corals grow up to the higher sea level, easily keeping pace with the sea-level rise.
We have many coral islands in the world, despite a sea level rise of more than +400 feet (+120 meters) in the past 20,000 years.
When sea-level rise stops, the coral grows sideways.
Atolls are not a "dipstick" to measure sea-level rise.