Thursday, June 17, 2010

Newton and sea level rise

By how much would sea-level rise if the Greenland ice sheet disappears ? Probably quite a lot, but not in Germany, or in North Western Europe for that matter. There, sea level would virtually unaffected. To formulate it a bit provocatively, Greenland is for Western Europeans irrelevant. They should be rather observing Antarctica more closely.

[Update: some other blogs referring to  this post present it as a new study of mine. This study is neither new nor mine. The figure caption in this post refers to some publications. You can also google  authors Milne, Tamiseia, Basset among others. ]

Global sea-level rise is caused about by several factors, among which the most important the expansion of the water column due to rising ocean water temperatures and the melting of the polar ice-sheets. Both effects are obvious and do not require further explanation. However, the shrinking of the polar land-ice masses does not lead to a sea-level rise uniformly distributed over the globe. Quite the contrary, its fingerprint is substantially heterogeneous. If the Greenland ice sheet melts, most of the  sea-level rise would occur in the southern Hemisphere. If, on the other hand, it is  the West-Antarctic Ice sheet that collapses, Nature's wisdom would produce a targeted maximum of sea-level rise right in front of the White House. This surprising effect is caused by very well-known physics - gravitational attraction - but it is seldom found in the public discussion of global sea-level rise.

The mechanisms by which this spatial distribution of sea-level response to the collapse of polar ice sheets is not difficult to understand either, albeit its magnitude may be surprising for many of us. Basically, sea-level in the Arctic, North Atlantic and North Pacific due to the additional gravitational pull of the large ice mass locked on top of Greenland, is a bit higher than it 'should be'. If this ice mass melts, the volume of the global ocean will increase accordingly and thus sea-level would tend to rise on average. But at the same time the gravitational pull that maintained the sea-leve in the Nordic seas will also disappear, and sea-level will tend to drop in those areas close to the present position of the ice-sheets.

The calculation of the final spatial distribution of this gravitational effect is somewhat complex, but it is possible. Other effects come into play as well, but their magnitude is just able to slightly modulate the overall fingerprint of the gravitational pull. For instance, melting of the polar ice sheets and the subsequent distribution of water masses over the the whole ocean changes the rotational speed of the Earth - in a similar way as an ice skater turns more slowly when he extends his arms away from his body. This in turn slightly affects sea-level as well

It turns out that for the Arctic Ocean, the gravitational effect overwhelms the increase in ocean volume; so that melting of Greenland ice causes a drop of sea-level in this ocean (see Figure). For Northern Europe, both effects roughly cancel (see the zero isoline separating the dark blue and light blue colors). Sea-level rises unabated in the Southern Hemisphere. In the case of Antarctic ice melting, we roughly find a mirror image, with sea-level dropping in the Southern Ocean and rising in the Northern Hemisphere. For the case of melting of ice sitting on the West-Antarctic peninsula, the maximum sea-level rise occurs in the Western North Atlantic.

Top: sea-level rise (in mm) caused by melting of an amount of Antarctic land-ice equivalent to 1 mm of globally average sea-level rise. Bottom: analogous calculation, but for Greenland land-ice. From Mitrovica et al, Nature 409, 1026 (2001). See also, Bamber et al. Science 324, 901 (2009).

Greenland glaciers and glaciers on the  Antarctica  Peninsula- the area in the Antarctic continent at greatest risk of melting, may react in different ways to overall warming. West Antarctic glaciers terminate below sea-level and thus are exposed to a much greater degree to ocean heat flux and warmer water temperatures. It is therefore possible that the West Antarctic Ice sheet may turn to be less stable to higher temperatures than Greenland. On the other hand, temperatures are projected to rise more in the Arctic region than over Antarctica, so that in this end it is not quite certain which one of the polar ice sheets will be the major contributor to the ocean mass. This introduces further uncertainties to sea-level projections at regional scales.


Anonymous said...

Interesting post, eduardo.

Two questions. Is it realistic to think that only an ice cap melts? What would happen if significant parts of both ice caps melt? (I guess the increase of sea level doubles in Equatorial areas)

Second one ... it seems to me that a significant change in the moment of inertia would appear. Consequences? Do you have any clue? The first obvious one has to do with angular speed of the Earth, but ... if the moment of inertia gets bigger in northern/southern latitudes, perhaps the structure of the inertia tensor changes, then, what about precession/nutation and so on? May be you know, may be you don't, I am just wondering about that. Precession is particularly important for solar irradiance ...



Anonymous said...

I do not think that Europeans/North-Americans can ignore Greenland mass loss yet (from a sea level perspective). There are other effects that you do not discuss. With an increasing melt water discharge there will be an associated slow-down of the overturning circulation. That can have large consequences for the spatial distribution of thermal expansion. There will also be transient effects. Consider these papers:

Yin et al. (2009) Model projections of rapid sea-level rise on the northeast coast of the United States. Nature Geoscience 2:262–266, doi:10.1038/NGEO462

Stammer (2008), Response of the global ocean to Greenland and Antarctic ice melting, J. Geophys. Res., 113, C06022, doi:10.1029/2006JC004079

Levermann et al. (2004) Dynamic sea level changes following changes in the thermohaline circulation. Climate Dynamics 24:347–354

KNMI, Exploring high-end climate change
scenarios for flood protection of
the Netherlands

Anonymous said...

isn`t it very unlikely, that eighter the west antarctic peninsula nor the greenland ice will lose a significant amount of ice due to the next few hundred years?
You need more than a few watts/m² increase in insolation over high latitudes to force massive melting, like in the EEM times, with about 40W/m² more radiativ forcing at 65°N.

Anonymous said...

Anonymous. Where do you get the 40 W/m2 data? From Berger's (and similar) papers? Then, you have a problem. 40 W/m2 at midday during summer is not the same as 1.6 W/m2 seven days a week 24 hours a day. You can convince yourself converting power to energy.


eduardo said...

@ 1

Hola Jon,
the paper states clearly that the effects are linearly additive - although my first thought would be that the gravitational interaction is non-linear. Maybe for small sea-level rise, both sources can indeed be simply added.

To your second point, the moment of inertia changes indeed. The length of day (LOD) would increase with melting, as more water mass is now located closer to the equator. Actually the lack of increase in LOD was what lead Munk to think that no much melting of polar land-ice could have occured during the 20th century (The sea-level enigma, PNAS 99, 6550).

My feeling is that precession would not be strongly - the reason is not that I know it for sure, but rather that the calculations of the orbital configuration in the last million years or so do not take into account the exact polar ice-volume, which is not accurately known.

eduardo said...

@ 3

Thank you for your comment and references. As I wrote, the statement about the relevance of Greenland was in 'provocative' mode.

I think, however, and correct me if I am wrong, that the effect that these papers are discussing is not the thermal effect of the slow down of the overturning circulation, but rather to the dynamical effect. The thermal effect would consist of a relative cooling of the north Atlantic linked to a diminished meridional heat transport, and therefore a more limited sea-level rise in this region.
The dynamical effect would on the other hand tend to cause an additional sea-level in the North Atlantic.
Could you give us some numbers about the expected magnitude when 1 mm of global sea-level equivalent melts ?

Anonymous said...


I have tried to estimate the dynamic MOC-influence of Greenland melt to European sea level rise. I've looked a sustained Greenland melt of 1mm/yr over a century. Note: 1 mm of sea level rise = 361 Gt = 0.01 Sv. (Not too far from present-day mass loss).

* A fresh-water forcing of ~0.01 Sv, could reduce THC strength by ~0.5 Sv (crude estimate based on fig2a, Stouffer Jclim 2006).

* A THC weakening of 0.5 Sverdrup could lead to a European sea level rise of ~0.02 m (based on Levermann 2004). This agrees pretty well with Yin 2009 (fig 3f).

So, to conclude I get ~20% of the global average rise in Europe due to a THC slowdown. To that we should add the small mass contribution of perhaps ~10%. So perhaps Europeans only need to worry about 30% of the Greenland melt.

eduardo said...


Thank you! I think this is a nice example of a constructive comment.

30% is not 100%, but it is not negligible indeed.

Lumo said...

Very interesting post, Eduardo! I will have to calculate it - at least approximately - by my own methods, otherwise I can't even uncritically buy the sign of the result you have obtained. ;-)

The simple well-defined question is what is the shape of the surface of a constant gravitational potential that has the desired volume inside it - in the presence of the point mass above the Greenland surface, and in the absence of it.

Yes, now I think you will be right but I will calculate it - to know how it depends on the height of the ice in Greenland, if it does, and so on.

Best wishes

Lumo said...

I just made the full-fledged calculation in Mathematica.

Indeed, if the average sea level rise is 7 meters, the rise of the sea level at the antipodal point would be around 8.3 meters.

However, near the center of Greenland, the sea levels would actually drop. Imagining the Greenland ice (today) as a mass point, the sea level rise would be zero about 1,700 kilometers from the center of this ice.

Below 1,700 kilometers, the elevation would be negative, and it would behave as -1/D for a very small distance D. The simple formula implies about 25 meters of sea level drop at the distance of 1,000 kilometers.

Of course, the point mass approximation can only be trusted if D is kind of greater than the actual radius of the ice – around 1000 kilometers.

However, it’s still clear that Iceland, which is only 1,000 kilometers from the center of Greenland, would see its sea level decrease. The Western European beaches which are about 3,000 km from the center of Greenland would experience about 4 meters sea level rise.

The full text with graphs will be completed at:

The Reference Frame: If Greenland melted, the sea level in Iceland would drop

Anonymous said...

This is very interesting.

Suppose that Greenland were to melt first (in our worst dreams of warming). This would make the Southern Ocean a lot higher, and therefore might cause much more melting of Antarctic ice than would otherwise occur. A teleconnection, perhaps?

I wonder -- a question for the experts on this blog -- if this differential in sea level increases by hemisphere might be one of the ways that the two hemispheres affect each other?

Ray Tomes said...

This is an insight, that (re)moving some mass changes the centre of gravity of the earth and has more effect somewhere else.

That is a first order effect. There is also a second order effect. The earth is approximately an ellipsoid which results from its rotation.

Additional effects come in from the weight of continents floating on the mantle. It is known that things only can stick up if they are less dense than in other places. Removing some mass from above will surely cause the local terrain to float higher on the mantle also.

Geoff Sherington said...

(This topic reminds me of trying to frolic on a water matress. Push down here, it pushes up there).

I presume that you have done a conservation of energy balance that shows that the global energy involved in the redistribution of mass is of the same order as the "causative" energy from sunshine over a nominated time.

IIRC, our early learning about isostasy etc did not include the component of shift of simulated "point" sources like the Greenland ice cap. Is there a point in the literature before which modelling of sea level changes onmitted the effect you describe; and therefore, are some reconstructions of past sea levels likely to be in error because of such an omission? There is a limit to any such error because there is a limit to the mass of global ice.

eduardo said...

First of all I should stress that I have not done any calculations by myself. I have just collated papers from the published literature. Note that some papers were published already in 2001. Sorry if I gave the impression that I had calculated anything.

@11. This is an intriguing possibility, although I think that the causes for that hypothetical Greenland melting would also have a large impact on Antarctica, at least West Antarctica.

@ 12,13 At the height of the last glacial maximum, Fennoscandia was depressed by roughly 400 meters under the weight of the ice sheet and it is still rebounding now, at a rate of about 10 mm/year in North Finland. The mantle is viscous and material is still slowly flowing north from Europe to Fennoscandia. The models of the mantle and lithospehere are able to reproduce this uplift quite accurately, which is clearly reflected in the dropping sea-level in the gulf of Finnland. These models, as I could learn recently, have to include not only the viscous rebound, but also the gravitational effects of the accumulating material below Fennoscandia. They are able to 'predict' the observed sea-level there drop with an accuracy of about 0.5 mm/year.