Graeme M (who also comments as Billy Bob) has asked if he could continue the discussion on sea level that began under the article about the new paper from Kurt Lambeck et al (2014). He wrote: "I'd really like to get to the bottom of why I am wrong in this one".
The discussion had shifted to the fact that the oceans are not flat, which is what Graeme M seems to be disputing. I'll start the ball rolling with some of my thoughts together with some of the basic science and observations (measurements).
Height of the sea vs sea level
The height of the sea above the sea floor at any point is of interest to certain groups and individuals. However the discussion was not about the height of the sea at any point in the ocean, it was about sea level - the surface of the sea relative to some reference point.
Sea level vs land level
Sea level is mainly of interest in regard to its relationship to land surfaces. On land, the point at which the land stops and the sea starts will be affected by a number of things, such as an increase or decrease in the volume of water, ocean currents, wind, tides, a vertical shift in the land (subsidence or lifting), and coastal erosion.
There are different ways of expressing sea level.
Global mean sea level and volume of the ocean
Global mean sea level - is a way of monitoring the changes over time in the total volume of water in the ocean. It does not indicate precisely how sea level will change on any particular stretch of coast. The volume is determined by the mass of water and its density. Water expands as it warms (thermal expansion). Water evaporates and condenses, giving fluctuations in the mass of water. Glaciers and rivers flow into the oceans adding to the mass of water. Fresh water is less dense than salty water.
An NOAA chart shows that global sea level has increased by more than 60 mm since 1992:
The sea level has not changed by the same amount everywhere, as this trend map from NOAA illustrates. The map shows the change in sea level globally, since 1993, as measured by satellite altimetry:
Local sea level relative to land
The above map shows the change in sea level from the perspective of the ocean itself. To see it from the perspective of land, there are tide gauges and instruments to measure changes in the height of the land surface. These instruments monitor the change in sea level relative to the land, as well as determining the extent to which changes over time are caused by changes in the height of the local sea or changes in the the height of the local land surface (is the land rising or falling or is the sea rising or falling or both).
Below is a link to chart showing sea level changes from the perspective of land at different places around the world:
The above is an introduction. Comments are welcome on the topic of sea level.