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Munk's sea-level enigma

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, and (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?

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Reader Comments (27)

According to Bob Tisdale ocean surface temperatures have risen slightly but through natural processes, PDO/AMO, ENSO etc. but global lower water temperatures have fallen so ocean heat content may actually have fallen over the period.

Jan 18, 2015 at 11:20 AM | Unregistered CommenterJohn Marshall

I may have missed something, but surely mountains erode and fill the sea up. Plus of course tectonic activity raising bits of land must open up mid ocean trenches and drop the sea level too..

The point is of course, to what reference point is sea level rising?

With satellites it presumably is some absolute diameter..and it should be possible to arrive at how much land levels are to that absolute level, falling.. but then of course that wipes out ice melt from icecaps..oh dear.

Jan 18, 2015 at 12:58 PM | Unregistered CommenterLeo Smith

There is also the effect of sequestration of water on land in reservoirs, about 10,000 km3, equivalent to 30 cm (1 foot) rise in sea level that would have taken place in the absence of water storage on land.

Impact of Artificial Reservoir Water Impoundment on Global Sea Level by B. F. Chao, Y. H. Wu, Y. S. Li

Offsetting the sequestration of water in reservoirs is the abstraction of fossil ground water, such as the Ogallala or High Plains aquifer and other aquifers in desert and steppe regions of Africa, Asia and Australia. Similar effects arise from drawdown of rechargeable aquifers in landlocked basins like Bandung in Indonesia and lakes such as the Aral Sea..

(Abstraction from coastal freshwater aquifers may have insignificant impact because sea water intrudes into the coastal aquifers.)

Jan 18, 2015 at 1:53 PM | Unregistered CommenterFrederick Colbourne

Sorry, I misplaced the decimal point.

There is also the effect of sequestration of water on land in reservoirs, about 10,000 km3, equivalent to 30 mm (a little over one inch) rise in sea level that would have taken place in the absence of water storage on land.

The calculation is 10,000 km3 of stored water and 361 million km2 of ocean surface.

10,000 km3 / 361,000,000 km2 * 1000 meters = 0.028 meter = 30 mm

Jan 18, 2015 at 2:41 PM | Registered Commenterfrederickcolbourne

As I look into the pot, stirring, many unknown elements rise gradually to the surface.

Jan 18, 2015 at 4:25 PM | Unregistered Commenterkim

There has been massive groundwater abstraction that is estimated to be (from memory) about 0.7mm/year for last 50 years. This would (I think) produce a net shift of water mass towards poles that would speed earth up.

Jan 18, 2015 at 6:29 PM | Unregistered CommenterRobL

As sea level rises, the earth slows down and leap seconds need to be inserted to keep Universal Coordinated Time (UTC) aligned with our annual orbit around the sun:

Twenty-six leap seconds have been inserted since 1972 (when the scheme was started); 22 were inserted between 1972 and 1998. Since 1998 only 4 leap seconds have been required, including the one which will be inserted on June 30th this year.

It would appear that the lack of leap seconds correlates extremely well with the 'pause'. Funny old thing. (Disclaimer: correlation does not equal causation)

Dr Nils-Axel Mörner does not agree with the IPCC with regard to sea levels. It is hard not to have some sympathy for his view: if the current supposed rate of increase in sea level is extrapolated back to the 11th century, sea level would have been some 2-3 metres lower. Does anyone believe this is likely?

Jan 18, 2015 at 7:41 PM | Unregistered CommenterBilly Liar

The oceans must be getting smaller and/or shallower.

Or is this far too simple?

Jan 18, 2015 at 9:41 PM | Unregistered CommenterJ Calvert N

Billy Liar: interesting. A recently-broadcast episode of Tony Robinson’s “Time Team” was about the Battle of Hastings. The most interesting thing about it was that the sea-levels appeared to be considerably higher then than now; so, it would appear that sea-levels have fallen during the past 1,000 years, and are now rising… Very interesting.

Jan 18, 2015 at 11:25 PM | Registered CommenterRadical Rodent

@RR: Nice idea; but unfortunately the environmental archaeological evidence indicates that most of the post-Roman coastal changes around East Anglia and South-east England are due to silting and/or erosion and not changes in sea level.

Jan 19, 2015 at 12:48 AM | Registered CommenterSalopian

The historical realities of Troy being inland when it was a port in the Homeric era, that silting, swamp/marsh draining, levee building, river way movement, local subsidence, erosion and silting are all far more significant than are the ~3mms per year in actual slr.
Yet in the age of climate obsession our efforts are nearly entirely focused on the ~3mms, and its putative control knob, CO2.

Jan 19, 2015 at 3:31 AM | Unregistered Commenterhunter

Alas they never seem to accept the simplest explanation:
Sea rise is less than imagined (as above).
There is no cooling masking the warming; just a lack of warming.
There is no missing heat.
There is no such thing as warming causing cooling anywhere.
There was no aerosol cooling from 1950 to 1975, just a (solar-induced) natural dip and recovery.
etc, etc.

Because there is no grant money in concluding that nothing unusual is happening!

Jan 19, 2015 at 9:01 AM | Unregistered CommenterJamesG

RadRod and salopian

Down here in Kent and Sussex, the seafron was irrevocably changed by huge storms in the 1250s. They destroyed Winchelsea and pushed the sea back leaving Dungeness with its moonscape and New Romney several miles inland ( where the sea used to come right up to the town).

These events and the afore mentioned silting, coastal erosion and of course manmade land reclamation have dramatically altered the face of the south coast over the last 1000 years.

Jan 19, 2015 at 3:52 PM | Unregistered Commenterottokring

I may have missed something, but surely mountains erode and fill the sea up.
Jan 18, 2015 at 12:58 PM | Unregistered CommenterLeo Smith

Leo - there was some discussion and analysis if this on a recent discussion thread. Turns out that sea level rise due to erosion is negligible - a fraction of a millimetre per year.

Jan 19, 2015 at 4:37 PM | Registered CommenterMartin A

Ironically, it was only last month that another paper came out, stating

The global mean sea level (GMSL) changes derived from modelling do not match actual measurements of sea level and should not be trusted. Compilations of individual tide gauges of sufficient quality and length provide much more reliable information.

They also find, as other studies have, that there is no sign of acceleration.

Somehow this paper did not seem to attract much media attention!

As I read the Hay paper, the normally accepted rise in sea levels during the 20thC of 180mm or so cannot be explained by the global temperature record, or assumptions about glacial loss.

Does this not suggest that in reality temperatures were higher in the early and mid 20thC (i.e what the record said before it was tortured) and that glacial loss was also much faster then, for which there is plenty of evidence from Alaska and elsewhere?

Jan 19, 2015 at 5:36 PM | Unregistered CommenterPaul Homewood

The level of my bath goes up when I get in it. I reckon there are just too many people mucking about in the sea. Get the swimmers out, and the level will surely go down. And all those bloody fat whales.

Jan 19, 2015 at 5:48 PM | Unregistered CommenterJames Evans

A few years old, but this shows how some dreadful work on sea levels can be done by academics (Univ. of Southampton and Tasmania); finding the answers they wanted by ignoring information, and just plain lack of common sense. Easy reading, and worth it. Lets hope subsequent work is better.

Jan 19, 2015 at 6:07 PM | Unregistered CommenterAllan M

ottokring , Radicla Rodent and salopian

It's quite a complicated situation even for the south coast of England. So apart from storms, erosion, and mankind messing around by dredging and all the other things we do there's the after effects of the Ice Age.

Southern England is slowly sinking while Scotland is rising up, according to a new map created by Durham scientists that shows how land and sea levels around the British coastline are rising or subsiding.

As the ice sheets melted at the end of the last Ice Age 20,000 years ago, the release of their enormous weight resulted in the landmass tilting up in the north and down in the south. The Coastland Map, which has produced the most accurate predictions to date of land uplift and subsidence in the UK, shows that the tilt is continuing.

Jan 19, 2015 at 6:22 PM | Unregistered CommenterSandyS

Thanks, Sandy S

What is interesting is Harlech Castle, which had steps down to sea in the Middle Ages, so that boats could be unloaded.

. Now the sea is about a mile away, and there is no evidence of silting. Harlech, according to the map, is in a neutral zone for GIA.

Certainly the idea that sea levels in the MWP were higher than the LIA was no surprise to the likes of HH Lamb. And given what we know about Greenland icecores, Alaskan glaciers etc, why would not they be?

Jan 19, 2015 at 7:19 PM | Unregistered CommenterPaul Homewood

Reconciliation of recorded sea level to the causes of that rise is something I have looked at - without much success for a while now. For instance my most recent comments on the discussion thread about thermal expansion made the error of looking at pure water, not salt water. However, as an ex-beancounter reconciling data is in my bones. For instance, the early measurements of ice mass loss from the GRACE data, showed accelerating ice loss. An extreme view from Rignot et al 2011 claimed that the contribution of ice melt to sea level rise had gone from 0 to 1.8mm a year between 1992 and 2010. The Satellite data showed no rise at all.
Less than two years later, most of the authors contributed to the Sheppard et al 2012 paper used in AR5, that virtually no acceleration at all in ice loss, and none in recent years.

Jan 19, 2015 at 11:26 PM | Unregistered CommenterKevin Marshall

James Evans re "...fat whales". Just got back from Maui where the humpback whales were leaping out of the water all the time. The sea level was going up and down like a yoyo. Expect a fight soon between the, " Save the Whales " and "Climate Alarmist" tag teams any time soon.

Jan 20, 2015 at 5:18 AM | Unregistered Commenterjohnbuk

Heh, halfway up a duck, and human civilization is an adaptable duck.

Jan 20, 2015 at 8:23 AM | Unregistered Commenterkim

But, but, but, is Monk's Enigma not inconsistent with Trenberth's Travesty? Or, more likely, do none of them have a real clue. When you cast the models in your own image it probably makes it harder to take on board someone else’s thoughts and problems.

Jan 20, 2015 at 11:17 AM | Unregistered Commentermichael hart

In 2013 Gregory et al. had a paper out that looked at sea level rise over the 20th century. There has been a problem in that the rise was greater than the sum of its parts. The paper includes the contribution from volcanic forcing and re-estimates glacier melting and groundwater contributions. The researchers achieve fairly good agreement with total sea level rise, thus 'solving' the problem.

They write about a lack of acceleration in sea level rise: "The reconstructions account for the approximate constancy of the rate of GMSLR during the 20th century, which shows small or no acceleration, despite the increasing anthropogenic forcing." and "...the implication of our closure of the budget is that such a relationship [between the rate of sea-level rise and global climate change] is weak or absent during the 20th century."

Twentieth-century global-mean sea-level rise: is the whole greater than the sum of the parts?

Jan 20, 2015 at 11:35 AM | Unregistered CommenterRobert Pollock

Bish: Figure 4 from this report by Morner (probably not a peer-reviewed publication) suggests that one can cherry-pick whatever rate of sea level rise one prefers from the historical tide gauge record. Uplift (glacial isostatic rebound) is clearly a problem at some locations, while subsidence probably biases the results at other locations. If one believes Morner, the field of Sea Level Rising may be as corrupt as paleoclimate reconstruction, but I haven't read enough to know.

Two things seem obvious:

1) Over millennia, sea level can be very sensitive to changes in temperature. It rose 120 m as the earth warmed about 5 degC as the last ice age ended. The remaining ice on land contains enough water for an additional 60 m of SLR. A sizable chunk of the ice cap in southern Greenland melted during the previous interglacial.

2) The 18 cm/century of sea level rise seen in the first half of the 20th century can not possibly be "normal" for the late Holocene. If sea level rose at this rate for the last five millennia, the total rise would have been 9 m - about ten-fold more than is consistent with the geological record. If the 18 cm/century rise reported by some tide gauges in the late 19th and first half of the 20th century is correct, it must have had some cause - presumably the end of the LIA.

Jan 20, 2015 at 4:16 PM | Unregistered CommenterFrank


The 18 cm/century of sea level rise seen in the first half of the 20th century can not possibly be "normal" for the late Holocene.

What needs to be remembered is that over the last few thousand years, there have been ups and downs in sea level, despite there being little overall change.

Certainly HH Lamb talks about bigger rises than the 20thC at various times in the last couple of thousand years or so, which would suggest there is nothing unusual at all about current rise.

Put another way - how much did sea levels fall during the LIA? We know that glaciers all around the world grew massively, so there must have been a significant drop.

Jan 20, 2015 at 4:38 PM | Unregistered CommenterPaul Homewood

Paul: I agree with everything you say. SLR could have fallen during the LIA and rose after it ended, with that rise stretching well into the twentieth century. However, the vast majority of SLR in response to the end of the last ice age ended at least 5 millennia ago. The relatively large changes in SLR seen in the tide gauge record must be CAUSED by climate change over the past few centuries or decades.

Over the past few millennia as the earth's orbital has changed, their has been less irradiation in the NH during its summer and more irradiation in the SH during its summer.

Jan 20, 2015 at 5:17 PM | Unregistered CommenterFrank

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