Sea Level, Ice and Greenhouse Gases

Archive-name: sea-level-faq

  Last Revision: 6/93

  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.

Bob Grumbine

  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 (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

  But, how fast would it melt away?  This is our major question for
human and ecosystem response.  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.  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

  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 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
West Antarctica   500   cm         a few centuries
Greenland         500   cm         several centuries
East Antarctica  7000   cm         several centuries to millenia

  My thanks to (Rick Chappell), Ilana Stern,
Jan Schloerer, (D. Alex Neilson), Kyle
Swanson, and all others, whose comments (if not addresses) have
helped improve this note.

Bob Grumbine

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.

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

Bob Grumbine