From: rmg3@grebyn.com (Robert Grumbine)
Subject: FAQ Sea Level, Ice, and Greenhouses 
Organization: Grebyn Timesharing
Date: Mon, 16 Nov 1992 21:18:00 GMT

  Last Revision: 7/92

  Please e-mail me corrections (with citation preferably) if you 
find one.  Sea level directly, rather than the role 
of ice in sea level solely is now the subject of the FAQ.  There is a 
factual revision (melting sea ice _can_, slightly, change sea level), 
and new material.  This FAQ does not contain everything relevant to the 
question of sea level.  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 to sci.geo.meteorology
and sci.environment.  Please edit your follow-up line 
accordingly.  Sorry for the long preamble.

Bob Grumbine
rmg3@grebyn.com

  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 warm-
ing 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 want 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 can 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 that 
matters is West Antarctica.

  First, why can 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 (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 (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.  Well, it turns out, not terribly 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 worry about).  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 also 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 
bergs.  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.  True, they 
can't.  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 (500 - 1000 meters) sea level.  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 where the ice shelf meets the ice sheet).  Ice flows
from the 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.  Effects can be 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
Thermal Expansion  10   cm per degree warming, per km of ocean warmed
                                   decades
Mountain Glaciers  10's cm         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.

Bob Grumbine
rmg3@grebyn.com

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.

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.
The Initiative was not funded.  "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.

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.
  
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.

Xref: sparky sci.environment:12961 sci.engr.civil:547 sci.engr.chem:589 soc.college.gradinfo:1691 phl.misc:322