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Subject: Sea Level, Ice, and Greenhouses -- FAQ

This article was archived around: 19 Dec 1999 10:18:33 -0500

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Archive-name: sea-level-faq Version: Sea Level FAQ v 7.1 1997/10/23 19:35:00 rmg3
The relation between sea level, ice, and greenhouses (or more generally, climate change) is a recurring issue in these groups. Much of the underpinning, is alas misunderstood or garbled. This FAQ tries to bring a little coherence to the discussion. It does not address the matter of detailed predictions or attempts at predictions. Nor does it survey the detailed processes involved in observing sea level change. These are subjects for a different faq. What this FAQ _does_ address are the primary physical mechanisms which affect sea level. It does so with particular reference to those mechanisms which are either commonly mentioned, or which have the most potential for driving sea level changes. Since it is addressing relatively timeless issues, the references may appear a bit dated. This is not the case. The basic processes are well known, and haven't changed their spots in the years since I first issued the FAQ. This FAQ is archived and is available on the web at http://www.radix.net/~bobg/. Also at that directory and web site are some of Jan Schloerer's articles, which I strongly recommend to all. This article is copyright protected. Write me regarding further use of the material. Robert Grumbine bobg@radix.net Revision: October 1997 New introduction Some wording changes in text Revision: June 1994 Explicit copyright notice Minor wording changes Note of future modifications Please e-mail me corrections (with citation preferably) if you find an error. This FAQ does not contain everything relevant to the problem of sea level change. Consequently, you should not use this FAQ as the end of investigation on sea level. The basic principles are outlined, no more. This note has been cross-posted with the default followup set to sci.environment. Please edit your followup line accordingly. This article is copyright 1993, 1994, 1997 by Robert W. Grumbine. All rights are reserved. Begin, at last, the article: There are two ways of changing sea level on the human time scale. We can change the amount of water in the oceans, or we can make the water there is occupy more or less volume. The first corresponds to changing the mass of ice on land. The second can be done by warming or cooling the ocean. Colder water is denser, so the same mass of water occupies less space. In considering sea level changes, an important consideration is the rate at which they occur. 1 meter in 1 day is quite disastrous. 1 meter in a million years would be irrelevant on the human scale. Water has a small but nonzero expansion as it warms. The expansion is approximately 2E-4 per degree of warming, at the temperatures of the upper ocean. To convert that into a sea level change, we need to multiply by the amount of warming and the thickness of the ocean that gets warmed. The amount of warming is the subject of the climate modelling. Let's consider a warming of 1 K for simplicity. The central question for the oceanographers is then how deep a layer of the ocean gets warmed. This is a difficult question. The challenge lies in the fact that the atmosphere heats the ocean at the top. Obvious. Not obvious is that this impedes warming much of the ocean. Warm water is less dense, so tends to stay at the surface of the ocean. If this were all that happened, only the layer of ocean directly warmed by the sun would be affected, about the top 100 meters. There is mixing within the ocean, which tends to force some of this heat further down. Balancing that effect is the fact that water from the deep ocean (which is cold) generally rises through most of the ocean basin. So mixing brings down warm water, and upwelling brings up colder water. Let's assume that the thickness that gets warmed is approximately the same as that which is already warm. That is approximately 500 meters. For the 1 degree warming, we then have 500*2E-4*1 meters of rise, or 0.10 meters. The time scale over which this occurs is the length of time it takes to mix the upper ocean, and is on the order of decades. In terms of the ice, there are five identifiable reservoirs, only one of which is expected to be able to have catastrophic effects on sea level. They are sea ice, mountain glaciers, the Greenland ice sheet, the East Antarctic ice sheet, and the West Antarctic ice sheet. The one expected to be potentially catastrophic is West Antarctica. Catastrophic is taken to mean meters of sea level in a few hundred years or less. First, why can't the other four be catastrophic? Sea ice cannot change sea level much. That is can do so at all is because sea ice is not made of quite the same material as the ocean. Sea ice is much fresher than sea water (5 parts per thousand instead of about 35). When the ice melts (pretend for the moment that it does so instantly and retains its shape), the resultant melt water is still slightly less dense than the original sea water. So the meltwater still 'stands' a little higher than the local sea level. The amount of extra height depends on the salinity difference between ice and ocean, and corresponds to about 2% of the thickness of the original ice floe. For 30 million square kilometers of ice (global maximum extent) and average thickness of 2 meters (the Arctic ice is about 3 meters, the Antarctic is about 1), the corresponding change in global sea level would be 2 (meters) * 0.02 (salinity effect) * 0.10 (fraction of ocean covered by ice), or 4 mm. Not a large figure, but not zero either. My thanks to chappell@stat.wisc.edu (Rick Chappell) for making me work this out. Mountain glaciers appear to have already made their contribution. Further collapse of them seems unlikely, and they are too small to be major elements in sea level change (even should they double their size). The three ice sheets can change sea level significantly, depending on whether they grow or decay. Unlike the sea ice, they are _not_ floating on the ocean. They are grounded on land. Sometimes, which will be important in a minute, that land is far below sea level. So what makes the ice sheet grow or decay? As with bank accounts, it is income minus outgo. The income is from snow fall -- accumulation. The outgo (ablation) is primarily melting and the calving of icebergs. It is believed that in a warmer climate, the amount of precipitation would increase. This is not inarguable as precipitation depends on more than temperature. The mechanism for the increase is that warmer temperatures put more water into the atmosphere (inarguable) so that snow clouds could drop more snow on the ice sheets (arguable). But, Greenland is already quite snowy and quite warm. A warming is likely to increase the melting far more rapidly than the accumulation. A small bit of graphics would help here. Draw an arc that opens downward. This is the Greenland ice sheet. About three quarters of the way to the peak of the arc, draw a horizontal line through the sheet. This is the 'snow line'. Above this line, there is net accumulation through the year. Below the line, there is net ablation through the year. In a warming, the snow line moves upwards. Three things happen then. First, in the area that is melting increases. Second, the melting rate increases. Third, the area of accumulation decreases. The possible fourth is that the rate of accumulation may increase in the area that does have net accumulation. But we have definitely increased both the area that is melting, and the melt rate. Outgo definitely increases, and income probably decreases or at best holds even. These mechanisms set up the possibility for an accelerating collapse of the ice sheet. Namely, this excess ablation lowers the ice sheet in that region. Since the lower elevations are even warmer, the ablation rate increases further. In the mean time, the ice sheet tries to flow so as to fill in the depression (ice is a fluid). This lowers the top of the ice sheet and decreases the accumulation. Together, the accumulation is decreased and the ablation is increased. This is the elevation-ablation feedback. It is believed to be operating in Greenland already. Under present climatic conditions, the Greenland ice cap could not be regrown. It is simply too warm there. (Odd thought for Greenland, I know, but glaciologists have unusual standards). But, how fast would it melt away? This is our major question for human and ecosystem response. It turns out, probably not very fast. The Greenland ice cap is surrounded by mountains. These have the general effect of damming up the ice sheet (which is part of the reason it still exists for us to consider). So, according to simulations, the collapse would take on the order of several hundred years. The sheet represents 5 meters of sea level, so the rate of sea level rise would be several (10 if 500 year collapse) millimeters per year. This is well under the rates of sea level rise experienced during the end of the last ice age (around 20 mm/year), so is not ecologically unprecedented. Such rises have occurred several times in the last 2 million years. What about East Antarctica? The ice sheet there is extremely large, about 70 meters of sea level. Get a map for a minute. East Antarctica is the part of Antarctica that lies between 15 W and 165 E as you move clockwise. It is the vast majority of the Antarctic ice and land mass. It has no decent means of losing mass. Nor of gaining mass. East Antarctica is so cold already that a slight warming will not raise the snow line enough to put much if any of the region into the melting zone. East Antarctica is also ringed by mountains, so that the ice sheet has little opportunity to calve icebergs. The only sizeable mechanism of mass loss is for ice to flow through passes in the transantarctic mountains over to West Antarctica. Having little means to lose mass, East Antarctica would seem to be a good place to increase accumulation and lower sea level. A nice idea, but it runs into the problem that precipitation is also highly inefficient over the East Antarctic plateau (arguably the driest desert in the world). The best estimates place the rate of increased accumulation over East Antarctica at right about the same as the increased ablation on Greenland. That would be a wash for sea level. Some redistribution of water from north to south, but no net effect. West Antarctica is the joker in the deck. Sea ice we can ignore (for sea level that is). Greenland and East Antarctica seem to be inclined to balance each other's effects. But West Antarctica represents 6 meters of sea level that _can_ collapse rapidly as glaciologists measure things. The collapse mechanisms rely on the peculiar geometry of the West Antarctic ice sheet. The first major feature of West Antarctica is that it includes two large ice _shelves_. These are masses of ice approximately the size of France, approximately 500 meters thick. They float on the ocean, so cannot directly change sea level if they were lost. The peculiarity of having ice shelves is that ice shelves are dynamically unstable. The stable configurations are for the ice sheet to advance all the way to the edge of the continental shelf, or to collapse to include no ice shelf. Why should we worry about the presence or absence of the ice shelves? They can't change sea level if they disappeared. But the ice shelves serve another role in West Antarctica. The Filchner-Ronne (in the Weddell Sea) and the Ross Ice shelf (in the Ross Sea) act as buttresses to the West Antarctic ice sheet. Without these buttresses, the West Antarctic ice sheet will collapse into the ocean on a time scale of several decades to a few centuries. The ice shelves contribute to ablation both through melting (at their bases more than the surface) and through iceberg calving. Some notably large bergs have calved in the last few years, including a couple larger than the state of Rhode Island. So through either a warmer ocean providing more ablation or through an increase in calving (arguably observed), the West Antarctic ice shelves could collapse. That West Antarctica can collapse much faster than Greenland relies on another oddity of the West Antarctic geometry. Most of the ice sheet base rests well below sea level (500 - 1000 meters below). The important oddity is that as you move further inward, the land is further below sea level. So, consider a point near the grounding line (the point on land where the ice shelf meets the ice sheet). Ice flows from th e grounded part into the floating part. The rate of flow increases as the slope (elevation difference) between the two sections increases. Extra mass loss in the ice shelf means that the shelf becomes thinner (and lower) so more ice flows in from the ice sheet. This makes the ice sheet just a little thinner. _But_ at the grounding line, the ice sheet had just enough mass to displace sufficient water to reach the sea floor. Without that mass, what used to be ice sheet begins to float. Since the sea floor slopes down inland of the grounding line, the area of ice sheet that turns into ice shelf increases rapidly. More ice shelf means more chance for ice to be melted by the ocean. The collapse mechanism has a mirror-image advance mechanism. Should there be net accumulation, the ice sheet/shelf can ground out to the continental shelf edge. Go back to near the grounding point. This time add some excess mass to the ice sheet/shelf. This thickens the system to ground ice shelf. The grounded ice shelf takes area away from the ocean ablation zone, which makes the mass balance even more in favor of accumulation. So the advance can also be a self- acclerating process. The big question in all this is whether accumulation will go up faster than ablation. The problem is, we don't know how either of them occurs in West Antarctica at present to satisfactory detail. From experience in other polar regions, we would expect the ice shelves and central West Antarctica to have a fairly high accumulation rate. They are almost as dry as East Antarctica. The ablation from the base of the ice shelves relies on the mechanisms that get 'warm' water (the water is in fact near the freezing point, some subtleties are involved in the melting) from the open ocean to the ice shelf base. We don't know enough about how the transfer occurs to be able to say confidently whether this ablation would increase or decrease under a warmer climate. Iceberg calving, the other major ablation source, is also not terribly well understood. So, the proper answer to the question "Will sea level rise or fall in a greenhouse world" is yes. Warming the ocean will cause a sea level rise. Ice will act either to raise or lower the sea level. The major player for catastrophic change is West Antarctica, which is currently in an unstable configuration. It _will_ either advance or retreat. Current glaciological opinion favors a collapse. So far, observations of the major ice sheets (East and West Antarctica, Greenland) are inconclusive as to whether the ice sheets are currently growing or shrinking. It is true, though, that in the last century, sea level has risen. Note too that effects can be locally serious even without catastrophic sea level rise (which I've taken to be meters of sea level in under 500 years). The players Size (approx) Speed (approx) Sea Ice 0.4 cm years Mountain Glaciers 10's cm decades Thermal Expansion 20 cm per degree warming, per km of ocean warmed decades West Antarctica 500 cm a few centuries Greenland 500 cm several centuries East Antarctica 7000 cm several centuries to millenia My thanks to chappell@stat.wisc.edu (Rick Chappell), Ilana Stern, Jan Schloerer, neilson%skat.usc.edu@usc.edu (D. Alex Neilson), Kyle Swanson, and all others, whose comments (if not addresses) have helped improve this note. Robert Grumbine bobg@radix.net Further Reading: Climate Change - The IPCC Scientific Assessment Report Prepared for IPCC by Working Group I Houghton, J.T., G.J. Jenkins, J.J. Ephraums (eds.) Cambridge Univ. Press, Cambridge, UK 1990 ISBN 0-521-40720-6 paperback (approx. US$35) A look at thermal expansion and sea level: Wigley, T. M. L. and S. C. B. Raper Thermal expansion of sea water associated with global warming. Nature, 330, 127-131, 1987. The Role of glaciers Oerlemans, J. and J.P.F. Fortuin, Sensitivity of glaciers and small ice caps to greenhouse warming, Science 258, 115-117 , 1992 The mass balance of Antarctica: Jacobs, S. S.. Is the Antarctic Ice Sheet Growing? Nature, 360, 29-33, 1992. Sea level during the last 17,000 years: Fairbanks, R. G. A 17,000 year glacio-eustatic sea level record: influence of glacial melting rates on the Younger Dryas event and deep-ocean circulation. Nature 342, 637-642, 1989. Classic text on glaciology: Paterson, W. S. B. _The Physics of Glaciers_ 2nd ed, Pergamon Press, Oxford, New York, Toronto, Sydney, Paris, Frankfurt. 380 pp., 1981. ISBN 0-08-024005-4 (hardcover), 0-08-024004-6 (flexicover). Precipitation in Antarctica: Bromwich, D. H. Snowfall in High Southern Latitudes Reviews of Geophysics, 26, pp. 149-168, 1988. (This issue contains many Antarctic Science papers.) Proposed research plan for the West Antarctic Ice Sheet Initiative. "West Antarctic Ice Sheet Initiative Science and Implementation Plan" ed. by R. A. Bindschadler, NASA Conference Publication Preprint. 1991. NASA. Conference on the West Antarctic ice sheet, including an introduction to why West Antarctica is the focus: Van Der Veen, C. J. and J. Oerlemans, eds. _Dynamics of the West Antarctic Ice Sheet_ D. Reidel, Dordrecht, Boston, Lancaster, Tokyo. 365 pp., 1987. ISBM 90-277-2370-2. Greenland in a Greenhouse world: (also general reference) Bindschadler, R. A. Contribution of the Greenland Ice Cap to changing sea level: present and future. IN: Glaciers, Ice Sheets, and Sea Level: Effect of a CO2-induced Climatic Change. US Dept. of Energy Report DOE/EV/60235-1, pp. 258-266, 1985. Antarctica in a Greenhouse: Oerlemans, J. Response of the Antarctic Ice Sheet to a climatic warming: a model study Journ. climat. 2, 1-11, 1982. Instability of ice shelves: Weertman, J. Stability of the junction of an ice sheet and an ice shelf. Journ. Glaciol., 13, 3-11, 1974. An example of the elevation-ablation feedback, triggered by geology. Birchfield, G. E. and R. W. Grumbine "'Slow Physics of Large Continental Ice Sheets and Underlying Bedrock and Its Relation to the Pleistocene Ice Ages" J. Geophysical Research, 90, 11,294-11,302, 1985. -- Also my first paper, which is really the only reason it's mentioned. -- Robert Grumbine http://www.radix.net/~bobg/ Science faqs and amateur activities notes and links. Sagredo (Galileo Galilei) "You present these recondite matters with too much evidence and ease; this great facility makes them less appreciated than they would be had they been presented in a more abstruse manner." Two New Sciences