In the text of last week's paper by Hay et al on sea-level rise I noticed a claim that the results "may contribute to the ultimate resolution of Munk’s sea-level enigma". I'd never heard of this enigma before, and with a name like it was hard to resist a bit of further study. I found a copy of the relevant paper here.
Changes in sea level (relative to the moving crust) are associated with changes in ocean volume (mostly thermal expansion) and in ocean mass (melting and continental storage): ζ(t) = ζsteric(t) + ζeustatic(t). Recent compilations of global ocean temperatures by Levitus and coworkers are in accord with coupled ocean/atmosphere modeling of greenhouse warming; they yield an increase in 20th century ocean heat content by 2 × 1023 J (compared to 0.1 × 1023 J of atmospheric storage), which corresponds to ζgreenhouse(2000) = 3 cm. The greenhouse-related rate is accelerating, with a present value ζ̇greenhouse(2000) ≈ 6 cm/century. Tide records going back to the 19th century show no measurable acceleration throughout the late 19th and first half of the 20th century; we take ζ̇historic = 18 cm/century. The Intergovernmental Panel on Climate Change attributes about 6 cm/century to melting and other eustatic processes, leaving a residual of 12 cm of 20th century rise to be accounted for. The Levitus compilation has virtually foreclosed the attribution of the residual rise to ocean warming (notwithstanding our ignorance of the abyssal and Southern Oceans): the historic rise started too early, has too linear a trend, and is too large. Melting of polar ice sheets at the upper limit of the Intergovernmental Panel on Climate Change estimates could close the gap, but severe limits are imposed by the observed perturbations in Earth rotation. Among possible resolutions of the enigma are: a substantial reduction from traditional estimates (including ours) of 1.5–2 mm/y global sea level rise; a substantial increase in the estimates of 20th century ocean heat storage; and a substantial change in the interpretation of the astronomic record.
In other words, there is a major reconciliation issue. Sea-level has been rising at 18cm/century, apparently accelerating to 21cm/century after 1950 due to thermal expansion of the oceans due to the greenhouse effect. Another 6 cm/century can apparently be explained by an increase in mass of the oceans mainly due to ice melt. So the total rate of rise (21) less the two global warming effects (6 and 3) still leaves 12 cm/century to be explained. As Munk notes, it's hard to do this by reference to ocean heat content if we are to believe the data and it's hard to do it by reference to ocean mass because an increased melt would have been picked up in our monitoring of the Earth's rotation.
To my mind this is pretty important and it seems rather surprising that I've never heard of the enigma before. Indeed Munk notes the relative obscurity of the issue in his paper:
How could this enigma have been overlooked in such an intensely studied subject? It has not! Prior to the Levitus compilation (5), it was taken for granted by many of us that the residual historic rise would eventually be reconciled with thermal expansion as more information about ocean interior temperature became available. The authoritative IPCC 1990 chapter on sea level by Warrick and Oerlemans† refers to an “unexplained part” of past sea level rise starting in AD 1850. The IPCC 1995 report concludes that, “the rise in sea level has been due largely to the concurrent increase in global temperature over the last 100 years, … including thermal expansion of the ocean and melting of glaciers, ice caps and ice sheets.” Recent progress in the documentation and understanding of interior ocean heat storage have served to sharpen the enigma. The favored interpretation in terms of thermal expansion is now difficult to reconcile with the observed dataset except possibly in the deepest ocean layers, where there are almost no systematic observations.
In fact, the astronomical data - there are three separate lines of evidence which all agree with each other - do not leave much room for any ice-melt increase in sea level at all:
The simplest interpretation of the overall rotational evidence is that [ocean-mass] sea level rise is less than 5 cm/cy ...
However, when you refer to the Fifth Assessment Report chapter on sea-level rise you find that there is a strong suggestion that the enigma has been solved, at least for very recent decades:
For 1993–2010, allowing for uncertainties, the observed GMSL rise is consistent with the sum of the observationally estimated contributions (high confidence) (Table 13.1, Figure 13.7e). The two largest terms are ocean thermal expansion (accounting for about 35% of the observed GMSL rise) and glacier mass loss (accounting for a further 25%, not including that from Greenland and Antarctica). Observations indicate an increased ice-sheet contribution over the last two decades (Sections 4.4.2.2, 4.4.2.3 and 13.3.3.1) (Shepherd et al., 2012). The closure of the observational budget since 1993, within uncertainties, represents a significant advance since the AR4 in physical understanding of the causes of past GMSL change, and provides an improved basis for critical evaluation of models of these contributions in order to assess their reliability for making projections.
The figures suggest that for the eight years from 2005 to 2013, the rate of sea level rise has been 30cm/century, explained by 10cm/century of thermal expansion (based on Argo data) and 20cm/century of ice melt (based on GRACE satellite observations). Note these figures are rough, and converted from Fig 13.6 of AR5 WG1.
I'm therefore slightly bemused that Hay et al think that there is still an enigma that needs to be solved, unless they are referring to the 20th century only. But more interestingly, if the astronomical data is saying that the change in sea level due to mass changes is less than 5cm/century, how can this be consistent with the GRACE satellite data saying it is 20cm/century or so? What does the astronomical data say now and is it consistent with GRACE? Does anyone know?