The authors don't say the rate rise has been consistent or that the rate of sea level rise has not varied since 1972. That's just the denier website eyeballing the chart. And berretta seems to have misrepresented the denier/delayers misrepresentation in that regard.
According to the authors, and as they show in their chart - the increase in observed sea levels is consistent with greenhouse gas warming and can be attributed to the following:
the contribution from ice is increasing. More ice has been melting in the past few years (particularly since the 1990s).
there is less water on land and more in the ocean - the amount of water in dams is increasing slightly while the aquifers are being depleted more rapidly, giving a net decrease in water on land
Water is expanding because the oceans are getting warmer.
The cryospheric contributions increase through the period (particularly in the 1990s) but the thermosteric contribution increases less rapidly. We include an improved estimate of aquifer depletion (0.3 mm yr -1 ), partially offsetting the retention of water in dams and giving a total terrestrial storage contribution of -0.1 mm yr-1. Ocean warming (90% of the total of the Earth’s energy increase) continues through to the end of the record, in agreement with continued greenhouse gas forcing.
