Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 171
10
Role of Land Ice in Present and
Future Sea-Leve! Change
MARK F. METER
University of Colorado
ABSTRACT
Rising concentrations of CO2 and other greenhouse gases in the atmosphere will cause air tempera-
ture to increase and precipitation to change. This chapter reviews our present knowledge of the
response of ice sheets and glaciers to the changed climate, and the consequent effect on sea level,
from the present to the next 100 yr. Glaciers other than the two existing ice sheets are currently
wasting, and this has contributed about 0.46 + 0.26 mm/yr to sea-level rise since 1900. The
Greenland Ice Sheet appears to be close to a state of balance at present. The Antarctic Ice Sheet may
be growing at a rate equivalent to about 0.6 mm/yr of sea-level fall; on the other hand, the rate of
iceberg discharge may have been underestimated and it may be close to balance. Future growth or
wastage of mountain glaciers could be calculated if the changes in climate were known, because the
mass and energy balance variables are, in many regions, known functions of altitude. Calculation of
future changes of the Greenland Ice Sheet, the Arctic ice caps, and the marginal areas in Antarctica
requires study of the complex fluid mechanics/thermodynamics of subfreezing snow and firn sub-
jected to water percolation. Determination of changes in iceberg calving is difficult because little is
known about the rate-controlling processes: in addition, changes in the geometry of a glacier or ice
stream cause changes in the rate of basal sliding, a process that is still imperfectly understood.
Striking changes in calving and sliding of Columbia Glacier are occurring as it disintegrates. A
warmer climate may cause warmer ocean water to intrude under the floating ice shelves of Antarc-
tica, causing increased basal melt and ice shelf thinning. This may, in turn, reduce the back pressure
on the ice streams that flow into the shelves, causing the ice streams to accelerate. This process
could deplete the ice sheet, producing a sea-level rise of up to 0.3 m, or possibly more, by the year
2100. Complete disintegration of the West Antarctic Ice Sheet is not likely for many centuries or
millennia. Increased accumulation on Antarctica could contribute to sea-level fall by 0.1 to 0.5 m
in the next 100 years. Long-term questions include the rapid fluctuations in CO2 and other variables
observed in ice cores, the rapid deglaciation of North America at the end of the last ice age, and the
possible disappearance of the West Antarctic Ice Sheet due to present-day and near-future processes.
171
OCR for page 172
172
INTRODUCTION
Could wastage of the land ice of the world account for
the current rise in sea level? Will a CO2-enhanced atmos-
phere cause so much ice melt in the next century that the
sea will rise to cause major flooding? Thorarinsson ~ 1940),
in a comprehensive and seminal analysis, attempted to
answer the first question without the benefit of good maps
or sufficient data. Although more data are now available,
the question is not completely answered. The second
question is even more difficult, as it involves atmospheric,
oceanographic, and glaciologic processes that are not
completely understood and that are difficult to model.
The concentrations of CO2 and other "greenhouse gases"
in the atmosphere are currently rising (Figure 10.1), and
one consequence of this will be a rise in air temperature
(Carbon Dioxide Assessment Committee, 1983), which
might lead to increased wastage of land-based ice. An
1 .s
1.4
1.2
- 1.0
0.8
0.e , - . . .
z
o 1 SO
6
~- 340
z
~ 33C
i 320
o
310
300
290
7Rn_
CH4 ,:
<:3 it,...
,
. . . , . . ~ . . . . . . . . . . . . . . . . . . . . . . . . .
1 800 1 850 1 SOO 1 950
co2
£)
_~
1700 17S0 1800 1850 1900 1950 2000
FIGURE 10.1 Data from ice cores showing the increase in two
"greenhouse" gases since preindustrial times. The CO2 results
are from Neftel et al. (19851. The line represents a model-
calculated back extrapolation assuming only CO2 input from
fossil fuel. The CH4 results are from Stauffer et al. (1985). The
solid ellipses represent results from melt extraction; the dashed
ellipses, dry extraction. The plus signs represent atmospheric
measurements. In both diagrams the vertical ellipse axis repre-
sents gas measurement error, and the horizontal axis the uncer-
tainty in the dates of air bubble close-off.
MARK F. METER
other consequence will be changes in precipitation, which
may lead to ice buildup in some areas.
In this chapter, the physical processes involved in the
relation between climate, ice wastage, and runoff are
emphasized; existing modern data are analyzed; and the
glaciological problems involved in estimating sea-level
change during the next century are discussed. Finally, a
brief, longer-term perspective is presented.
Much of this chapter is derived from the results of a
1984 Workshop on Glaciers, Ice Sheets, and Sea Level:
Effects of a CO2-Induced Climatic Change (Committee on
Glaciology, 1985), to which the reader is referred for more
detail on the current state of knowledge. An earlier work-
shop examined what is known about the effect of CO2-
induced changes on the environment of the critical West
Antarctic Ice Sheet (Committee on Glaciology, 19841. The
subject of ice and sea-level change has been discussed in
several recent papers, including, for instance, Grossval'd
and Kotlyakov (1978), Hollin and Barry (1979), Oerle-
mans (1982), Revelle (1983), Barry (1984), Robin (1986),
and Thomas ~ 1987~.
ICE ON EARTH AT THE PRESENT
The amount of ice on land at the present moment is
huge, probably exceeding the sum of all other amounts of
water substance in and on land (Table 10.1~. A continuing
annual loss of only 0.001 to 0.002 percent of the land ice
volume would be sufficient to cause the observed change
of 1 to 2 mm/yr in global sea level. But is this happening?
Here we examine this question separately for small gla-
ciers and for each of the two large ice sheets.
Glaciers and Small Ice Caps
Observational data on glacier fluctuations include
measurements of advance or retreat, volume changes
(surface altitude and area), and annual and seasonal mass
balances (the difference between totals of mass accumula-
tion and loss such as by melt). Mass balances can be
measured directly on the glacier surface or derived from
study of ice cores; mass balance sequences can be ex-
tended by use of numerical models using long-term mete-
orologic and hydrologic records. Most of the available
glacier fluctuation data are concerned only with changes
in length; these data do not provide volume change infor-
mation directly and, over the short term, can be misleading
in sign. Measurements of balances in cores taken at single
locations in the accumulation area of a glacier are insuffi-
cient to infer the mass change of the entire glacier. Meas-
urements of mass balance made on the glacier surface are
confined to relatively short time sequences. Thus most of
the inferences about the long-term effects on sea level
OCR for page 173
ROLE OF LAND ICE IN PRESENT AND FUTURE SEA-LEVEL CHANGE
TABLE 10.1 Ice and Water on Earth (adapted from
Meier, 1983)
Volume (km3 x 106)
Oceans
Ice on land
Groundwater
Lakes, reservoirs, rivers, swamps
Water in the soil
Water in the atmosphere
1370.0
30.0
4.oa
0.13
0.06
0.01
aValues as high as 60 x 106 km3 have been reported for water
in pores deep in the Earth's crust. The amount of groundwater
that can participate in the hydrologic cycle at time scales of years
to centuries is probably about 4 x 106 km3.
must come from observations of long-term volume changes,
or from extensions of short-term balance measurements
using long-te~m meteorological and hydrologic data and
numerical models. When both kinds of info~-~ation are
brought to bear on the same glacier record for checking or
calibration, the results are considered especially trustwor-
thy (Figure 10.2~. The calibration is important because the
statistical relations between hydrometeorological variables
(e.g., precipitation, temperature, runoff) and balance
components (e.g., accumulation, melt) may not be station-
ary over long time intervals.
Glacier balance and volume change data for periods of
record exceeding 50 yr were found for 25 glaciers in 13
regions from reports of the Permanent Service on the
Fluctuations of Glaciers RASH (1967, 1973, 19771] and
other sources. The mean period of record for those gla-
ciers is from 1900.5 to 1961.7. The balance model se-
quences were pruned to the interval 1900 to 1961 to make
the data set more homogeneous. Almost all glaciers showed
long-term wastage, but the rates varied, depending largely
on location. The unweighted average of these 25 mean
balances is -0.40 m/yr (water equivalent) + 0.25 (standard
deviation), and the mean of the regional averages weighted
by quality of the data is -0.38 + 0.20 m/yr (Meter, 1984~.
The few glaciers with long-term data are, with one
exception, between 38° and 69°N latitude; none are at low
latitudes or in the Southern Hemisphere. Thus a method is
needed to transform results from this biased sample to an
estimate of the mass balance of the whole Earth's cover of
glaciers. Meier (1984) suggested that the magnitude of the
long-term balance may be related to the magnitude of the
seasonal mass fluxes (accumulation and ablation), and that
this may be used as a scaling factor to derive global esti-
mates. This way to scale results to a global average is
aided by the fact that values of the annual amplitude can
be calculated for most of the world's glacier areas from
~ 7O
data reported since 1965 and can be estimated for other
areas because they are primarily functions of the climato-
logical regime. The annual amplitudes are highest at tem-
perate to sub-Arctic (and sub-Antarctic) latitudes and lowest
near the poles, and they decrease with increasing continen-
tality (Meter, 1985~.
The 1900 to 1961 data, when averaged by region and
scaled to a global average, suggest that the wastage of the
world's glaciers and small ice caps contributed 0.46 + 0.26
mm/yr to the 61-yr rise in sea level (Meter, 1984~. This
result is similar to some previous estimates based on many
fewer data (Grossvaltd and Kotlyakov, 1978; Lambeck,
1980~. Unfortunately, the three major contributing re-
gions (the mountains bordering the Gulf of Alaska, the
mountains of Central Asia, and the Patagonian Ice Caps)
are also regions of meager observational data. Until more
observational data are obtained from these regions and the
scaling by annual amplitude rigorously tested, these re-
sults will have to be considered tentative.
Greenland and Antarctic Ice Sheets
These two large ice masses gain material mainly through
the accumulation of snow, and lose material through sev-
eral processes that include surface melt and the runoff of
meltwater, calving (discharge) of icebergs, melting of the
underside of floating ice shelves, evaporation of snow, and
erosion and transport of surface snow to the sea by wind.
The last two processes are considered to be negligible
items in the total mass balance for both ice sheets. Surface
-
`, 20
~ -20 I= = ~ _5tabrcen
>-40 ~,~ ~es
-60 I
South Cascade
-80
1880 1900 1920 1940 1960 1980
Men
Sarennes
South Cascade
FIGURE 10.2 Cumulative mass balance, in meters of water
equivalent, of Storbreen (Norway), Sarennes Glacier (France),
and South Cascade Glacier (Washington state). All values are
related to 1900. These curves were derived from numerical
models using long-term meteorologic and hydrologic data, cali-
brated with several decades of mass balance observations and
with long-term volume change information. (From Meier (1984),
with permission of the American Association for the Advance-
ment of Science.)
OCR for page 174
174
melt/runoff is also a minor item for the Antarctic Ice
Sheet, but it is important to the balance of the Greenland
Ice Sheet. Iceberg calving is an important loss term for
both ice sheets and is the predominant one in Antarctica.
Melting of the underside of ice shelves has no effect on sea
level, but it does control the speed of discharge of land-
based ice from Antarctica and is important for predicting
the behavior of that ice sheet in the next century.
The difficulty of estimating the surface mass balance of
the Greenland Ice Sheet can be illustrated by reference to
the concept of snow facies (Benson, 1962; Muller, 1962),
as shown on Figure 10.3. Most of the Antarctic Ice Sheet
and much of the Greenland Ice Sheet are in the dry snow
zone, where no melting occurs; some of the marginal areas
in Antarctica and an appreciable fraction of the Greenland
Ice Sheet reach the percolation zone, where surface melt-
ing occurs but the meltwater refreezes in that year's snow-
pack. Runoff of meltwater to the ocean cannot occur from
either zone. Runoff can occur from the wet snow zone,
where meltwater saturates the entire thickness of the snow-
pack. In order to calculate the net mass balance in this
zone, the amount of runoff (which is difficult to measure)
must be subtracted from the snow accumulation; alterna-
tively, one can measure density-depth profiles through the
snowpack and several underlying layers, at the beginning
and again at the end of the melt season, in order to detect
the amount of ice deposited by refreezing at depth. Unfor-
tunately, the wet snow zone covers a considerable area in
Greenland; so that precise determination of the net mass
balance is a formidable task. Similar problems arise in the
. .
superimposer . Ice zone.
equilibrium
line
dry snow I I
zone percolation
| zone | wet snow zone
:~:J.' ~W ~ 'l' ,'~ )! {! (~;1~ -
prewlous summer
surf ace
super
imposed
ice zone
_7rDllll~llllll~summer
no runoll -~ runoff possible Runoff occurs
MOST OF THE ANTARCTIC ICE SHEET
~GREENLAND ICE SHEET
MOST MOUNTAIN GLACIErIS
FIGURE 10.3 Diagrammatic section through a large ice mass
illustrating the concept of snow facies. Dotted areas are dry
(subfreezing) snow; areas with vertical wiggly lines are snow
into which meltwater has percolated; and areas with vertical
straight lines represent refrozen meltwater that has formed super
. .
1mposec . Ice.
MARK F. MEIER
Iceberg calving is also difficult to measure. Repetitive
high-altitude aerial photography or possibly satellite im-
agery can be used to measure calving speed as the differ-
ence between glacier speed and terminus advance, and the
iceberg discharge obtained by integrating the calving speed
over the area of the calving face (Brown et al., 1982~.
Unfortunately, aerial photography is expensive, and satel-
lite images generally do not have sufficient resolution to
measure glacier speed. Furthermore, most expeditions to
measure calving do so in the summer, and so it is not
known whether these data are representative of annual
averages. In Antarctica, major calving events can occur
infrequently in time, perhaps once in 100 yr. Major Ant-
arctic breakoffs, unprecedented in the historic record,
occurred from the Filchner and Larsen ice shelves (Jacobs
et al. 1986) and the Ross Ice Shelf in 1987. Iceberg
discharge can be estimated by iceberg counts coupled with
estimates of iceberg lifetimes (Orheim, 1985), but the lat-
ter are difficult to obtain, the sampling problem is forrni-
dable, and the episodic nature of ice-shelf breakoffs makes
it difficult to obtain a long-term average value. Thus
calving data for Greenland are insufficient, and for Ant-
arctica are extremely meager.
The difficulty of measuring the mass balance compo-
nents of the ice sheets can be circumvented partly by
considering the flow out of specific drainage basins. The
discharge through a cross section can be determined from
surface velocity and ice thickness measurements combined
with models to relate surface velocity to the depth-aver-
aged value. The surface mass balance, integrated over the
drainage basin upstream from the cross section, gives the
"balance flux," which can be compared with the total flux
through the cross section. The difference, the "thinning
flux," is a measure of the mass imbalance.
A future alternative is promising and exciting-direct
measurement of the thinning flux, through the use of re-
petitive satellite altimeter surveys to detect the rate of
change of the surface elevation. This requires a satellite in
a polar orbit equipped with an altimeter; a laser altimeter
would allow results to be obtained in a year or so, but a
radar altimeter might require many years before results of
significance were obtained. Preliminary results for that
part of the Greenland Ice Sheet south of 72°N latitude,
from a radar altimeter mounted in a satellite, are encourag-
ing and suggest ice-sheet thickening (Zwally, 1985~.
Estimates of the net mass balance of the Greenland and
Antarctic ice sheets are presented in Table 10.2. Most of
the information in this compilation (Committee on Glaci-
ology, 1985) was obtained in the late 1970s and early
1980s, but it is difficult to assign a discrete time to these
estimates, let alone to determine the time rate of change.
In spite of wide error bands, the results suggest that the
current rise in global sea level is not due to the melting of
OCR for page 175
ROLE OF LAND ICE IN PRESENT AND FUTURE SEA-LEVEL CHANGE
TABLE 10.2 Estimated Balance of Glaciers and Ice Sheets at the Present Time (from
Committee on Glaciology, 1985)a
Average
Mass Balance Effect on
Period of Area (water equivalent) Sea Level
Ice Mass Observation (106 km2) (m/yr) (mm/yr)
Glaciers and 1900 to 1960 0.54 -1.2 + 0.7 +0.5 + 0.3
small ice caps
Greenland 1929 to 1984b 1.73 +0.02 + 0.08C {).1 + 04c
Ice Sheet
Antarctic
Ice Sheet
1970 to 1984~
11.97
+0.02+0.02 ~.6+0.6
aError limits represent approximate bounds of estimation and cannot be defined statistically.
bObservations scattered in both time and space.
CCombination of (a) historical estimates, (b) extrapolation of modern ablation data from West
Greenland and accumulation data from Central Greenland, and (c) extrapolation of thickness change
data from Central Greenland..
Come observations talcen earlier are included.
the polar ice sheets. In fact, these published results sug-
gest that current growth of the Antarctic Ice Sheet is, at
least in part, canceling out the effect of small glacier
wastage, leaving even more of the sea-level rise to be
explained by ocean warming, loss of volume of the ocean
basins, or other such mechanisms, an alternative that seems
unlikely.
One way to test the meager glaciological results on
long-term mass balance is through study of the effect that
mass balance changes might have on the rate of Earth
rotation and the relative motion of the rotational pole
(Pettier, 1985, and Chapter 4, this volume). Pettier (1988)
applied Meier's (1984) model of small glacier wastage to
Earth rotation models, assuming no current change in the
major ice sheets and that a major ice sheet had existed on
the Barents Sea platform during the last glacial period (a
somewhat controversial point). His results correctly pre-
dict the observed changes in polar motion or rotation rate.
This further suggests that the Greenland and Antarctic ice
sheets are currently close to balance, and that the long-
term iceberg discharge has been underestimated (Orheim,
1985).
CHANGES IN ICE IN THE NEXT CENTURY
The increase in air temperature caused by a rise in
concentration of CO2 may cause increased snow and ice
melting, and some of this meltwater may run off to the
oceans, causing a rise in sea level. Increased air tempera-
ture and/or meltwater production may also cause some
outlet glaciers and ice streams to flow faster, transferring
land-based ice to the ocean and causing a further rise in
175
sea level. On the other hand, a rise in CO2 concentration
may, in some regions, lead to increased snow precipitation
on glaciers and ice sheets, which will have the opposite
effect on sea level. Predicting the effects of climate change
on ice growth and wastage is a complex problem because
several different, interacting processes must be consid-
ered.
Here we discuss five important processes that are in-
volved in potential impacts on sea level of future changes
in glaciers and ice sheets: (1) the variation of energy and
mass balance components with altitude, (2) the dynamic
response of ice masses to changes in thickness, (3) the
warming of cold firn to allow meltwater runoff, (4) in-
creased flow and iceberg calving of tidal glaciers due to
increased meltwater, and (5) the stability of ice-sheet/ice-
stream/ice-shelf systems. We restrict the time frame to the
next 100 yr, approximately the time of doubling of the
present level of CO2.
Energy and Mass Balances as a Function of Altitude
Mountain glaciers continuously move ice from an area
of high altitude where, on an annual basis, snow accumu-
lation exceeds snow and ice wastage, to an area at a lower
altitude where snow and ice ablation exceeds snow accu-
mulation (Figure 10.41. Thus the magnitude of these
processes is dependent on altitude, and consideration of
the attitudinal gradients in the mass and energy fluxes
allows one to generalize from measurements in one re-
stricted area to large regions (Kuhn, 1981~. Mass balance
components also vary, but more weakly, with latitude and
with distance along air mass trajectories as the airmass
OCR for page 176
MARK F. METER
176
2500
2400
2300
2200
2 1 00
2000
1 900
1800
7~
1 600
FIGURE 10.4 Snow accumulation, snow and ice melt, and net
balance for South Cascade Glacier, Washington, for the 196~1965
balance year. Also shown is the area at each altitude increment.
From Meter et al. (1971~.
moves from the sea across mountain ranges. The mass
balance of the Greenland Ice Sheet can be analyzed by
considering the attitudinal gradient as primary, although
the latitude and distance from the sea are also important
(Ambach, 19851. Such an approach is less useful in Ant
arctica, where iceberg discharge and subshelf melting are
the dominant processes causing ice loss to the sea.
Many of the energy fluxes that cause melting are known
or observable functions of altitude. The most sensitive of
these are the absorbed solar radiation and the precipitation
as snow. The first of these is critically dependent on the
albedo (reflectivity) of the surface, which in turn depends
on how long the surface is covered with high-albedo snow
during the course of the melt season. The persistence of
the snow cover depends, of course, on the amount of snow
and the intensity of melt processes, both of which also
depend on altitude. Kuhn (1985) and Ambach and Kuhn
(1985) estimated the attitudinal gradients in energy bat- ocean) is
ance components for an Alpine mountain glacier and for
the central western portion of the Greenland Ice Sheet,
respectively. Bindschadler (1985) used such information
to calculate the static response of the Greenland Ice Sheet
to doubled CO2. Such analyses should be done in other
parts of the world, as this information leads to a relatively
simple way to relate climate change due to a CO2 perturba
tion to a change in the mass balance of an ice mass. A rise
in the annual melt rate at the equilibrium line leads to a
rise in the altitude of that equilibrium line, displacing the
ablation/accumulation rates as functions of altitude, and
changing the size of the ablation and accumulation areas.
The attitudinal dependence of the mass and energy fluxes
leads to a potential instability, which is one of the reasons
for the sensitivity of glaciers to slight climate changes. A
rise in melting causes a lowering of the ice surface, which
AREA (km2) in turn may cause a further increase in melting or decrease
0 01 0203 04 0s 06
; i; ~in snow accumulation, leading to further changes accentu
ating the melting and vice versa (Bodvarsson, 19551. This
sensitivity/instability thus requires improved understand
snow ing of the exact magnitude of annual and seasonal changes
r: accumulation in precipitation, surface air temperature, and other vari
ice melts | ~ )snO ~> ables, on a regional basis, before reliable estimates can be
// net ~< ~ ~made of the changes to be expected as a consequence of a
~ 1 ~ · ~ r · ~ ·
J bat/ leear~dodilm ' J nse m cu2 concentration. 1nls IS a ronnlaaole task In
/' t:, ~, ,
-6 -5 -4 -S -2 -l ~ ~ ~ ~ ~S Time Scales of Ice Wastage and Dynamic Response
WATER EQUIVALENT (m)
Studies in the Alps (Kuhn, 1985) suggest that a 4°C rise
in temperature, caused by a doubling of CO2 in the next
100 yr, would lead to a negative mass balance change from
O to about 0.3 m/yr. If this wastage were to increase
linearly with time, the effect over time could be estimated
for a glacier of known initial dimensions. Assuming a
nonflowing, wedge-shaped glacier of length L(t), surface
slope ~ resting on a bed of slope 0, and having a constant
width W. the amount of thinning HI during the period O to
tl, for a mass balance scenario bitt is
tl
Hl=|b~t~dt. (10.1)
o
Assuming a linear decrease (more negative) with time in
the balance, bitt = kt,
H(t) = 0.5kt2. (10.2)
The glacial length L(t) is thus
kt2
() ° 2(tan oc-tan p)' (10.3)
and the loss of ice to increased runoff (and thus to the
R (t) = WL (t~b(t) = WL o kt - ~2(tan a - tan p) (10 4)
it(t) reaches a maximum at the time
tmaX = [2LO(tan a - tan p)/3k]° s, (10.5)
which is of the order of decades to centuries for typical
mountain glaciers. Under these assumptions, South Cas-
cade Glacier, Washington, will reach a maximum rate of
ice loss in about 70 yr, and be gone completely in about
130 yr, assuming a constant increase in the rate of wastage
of 0.03 m/yr2 (Figure 10.51.
This simplistic analysis needs to be modified, not only
to reflect a more realistic geometry, but also to incorporate
glacier dynamics and the change of balance with altitude.
The effect of thinning will be to decrease the rate of flow,
OCR for page 177
ROLE OF LAND ICE lN PRESENT AND FUTURE SEA-LEVEL CHANGE
causing a steepening of the longitudinal profile. The nor-
mal attitudinal balance gradient will tend to accelerate the
ice loss as the surface profile lowers, but the dynamic
steepening and the loss of ice at the lowest altitudes will,
in part, reduce this acceleration in wastage. For a moun-
tain glacier, the characteristic time for dynamic response
is of the same order of magnitude as the time for glacier
disintegration (Figure 10.6~.
On the other hand, for the Greenland and Antarctic ice
sheets, the characteristic time for dynamic response is one
or more orders of magnitude longer (Alley and Whillans,
1984; Bindschadler, 1985), with the possible exception of
ice-stream/ice-shelf interactions discussed later. Except
for this last possibility, the dynamic response to changes
in the two existing ice sheets due to altered climate in the
next century can be ignored.
The Warming of Cold Snow and Firn
Figure 10.3 illustrates the fact that most of the Antarc-
tic Ice Sheet and much of the Greenland Ice Sheet are not
likely to be affected by small rises in air temperature, such
sit
t4
111 ~ 2 ~ _
ILL /
6 O /
it
0 20
· . ~
glacier area
1 1 1 1
40 60 80 1 00
TIME (a)
\ \~\
120 140
FIGURE 10.5 Excess runoff from South Cascade Glacier pro-
duced a linearly increasing wastage rate of 0.03 m/yr2, assuming
a nonflowing glacier of simple wedge shape. Data on South
Cascade Glacier taken from Meier and Tangborn (1965J.
v
WE 7
;~' 6
C 5
to 4
As 3
if) 2
1 '
O
o
·. . .
. .
. .
. .
.
- !
!
20 40 60 80 100
T I M E ( a )
FIGURE 10.6 Thickness change at the terminus of South Cas-
cade Glacier in response to a 1-m balance perturbation for 1 yr.
From Nye (1965).
177
as those that might be caused by an increased CO2 concen-
tration in the next century. Increases in summer air tem-
perature cause no melting unless the increases exceed the
present (negative) surface air temperature. The more inter-
esting question, however, concerns the situation where an
increase of the summer air temperature brings the surface
snow up to the melting point. With an increase of mean
annual temperature of 5° to 10°C in the polar regions, as
suggested by many atmospheric circulation models for a
twofold enhancement of CO2, there would be a large shift
of the boundary between the dry snow, percolation, and
wet snow facies on the two ice sheets. But how long
would it take to develop enhanced runoff to the sea?
The transient response of infiltration into and warming
of snow and firn (consolidated snow that has survived at
least one summer season and has not yet become imper-
meable ice) is complex. The equations of flow through a
porous medium are complicated by heat flow considera-
tions and the physics of the freezing interstitial water.
Research on this problem is now under way (Illangasekare
et al., 1988; Meier et al., 1988~.
Flow and Iceberg Calving of Tidewater Glaciers
Much of the transfer of water mass from land to the
ocean is accomplished by the breakoff (calving) of ice-
bergs. This is the dominant process in Antarctica and is
also important in Greenland, the Arctic Islands, Alaska,
and Chile. Unfortunately, our understanding of calving
glacier dynamics is insufficient to predict how these gla-
ciers will react to an altered climate in the future.
The length of a calving glacier depends on the balance
between ice flow to the calving face and the discharge of
icebergs from the face,
ddL = V-V , (10.6)
where L is the glacier length, t is time, V is the speed of the
glacier at the terminus, and Vc the calving speed. Both V
and Vc are averages over the glacier thickness and width.
The calving speed (Vc) can be considered as the iceberg
discharge (in units of volume per time) divided by the area
of the calving face. Both V and Vc can vary, causing
changes in the length and volume of the glacier. These
changes in length may then affect V and Vc, and the ensu-
ing feedback can cause rapid disintegration of a calving
glacier (Post, 1975; Meier and Post, 1987~.
Studies of Columbia Glacier, Alaska, and other grounded
calving glaciers in Alaska suggest that
Vc = k'hW, (10.7)
where he is water depth at the terminus and k' is an empiri-
cal coefficient (Brown et al., 1982), or,
OCR for page 178
178
(W )
, (10.8)
where R is the liquid water runoff and hu is the thickness
of ice unsupported by buoyancy at the terminus (Sikonia,
19821. Although these two equations are very different in
form, they produce similar values of Vc over the range of
he, he, and R as measured at Columbia Glacier during the
period 1977 to 1980. Unfortunately, the generality of
these formulae for a wider range of variables is not yet
established.
No calving law has been established for a floating,
calving glacier, although Reeh (1968) and others investi-
gated the stresses in a floating ice tongue, and Fastook and
Schmidt ( 1982) analyzed the role of fracture in the calving
process. Obviously, a calving law for floating ice is needed
in order to predict future changes in glaciers and ice sheets.
Most calving glaciers flow rapidly, and most of this
flow is by basal sliding. No sliding law has been generally
accepted, but a relation of the form
b (Pi - P ~
where ~ is the shear stress on the bed, n is a constant (~3),
and Pi and Pw are the hydrostatic pressures in the ice at the
bed and in the subglacial water (Budd et al., 1979; Bind-
schadler, 1983), is commonly used for glaciers with Pi >
Pw (not floating). At the terminus, hu and Pi - Pw are
proportional. A grounded calving glacier with its bed well
below sea level slides faster than a similar glacier on land,
because Pw approaches Pi due to the pressurization of the
subglacial water system by the saltwater column at the
terminus.
The effect of CO2-induced climate change on calving
glaciers is complex; increased melt due to warmer tem-
perature might cause thinning of the ice. This thinning
would decrease t and P. if P. - P were small initially the
l; I w ~
decrease in P. - P could predominate and V would
~ w b
increase. Because hu would decrease, Vc would increase,
if the glacier were grounded.
Increased flow would cause further thinning, and an
unstable disintegration would ensue. Increased melt or
increased rainfall also might increase Pw, leading to more
rapid flow, and the increase in R (for a grounded glacier)
would lead to more rapid calving. Thus calving glaciers
could respond to slight increases of melting and rainfall by
rapid and dramatic disintegration (Meter and Post, 1987),
but it is difficult to calculate the rate of change because of
our insufficient knowledge of subglacial hydraulics, basal
sliding, and calving.
The rapidity of change in the dynamics of a calving
glacier is illustrated by the current disintegration of Co-
lumbia Glacier, Alaska (Figure 10.7~.
MARK F. MElER
Stability of Ice Streams and Ice Shelves
Mercer (1978) warned that a climatic change due to
increased CO2 in the atmosphere could lead to disintegra-
tion of the West Antarctic Ice Sheet, causing a 5-m rise in
global sea level. The discharge of ice from this ice sheet
is mainly through rapidly moving ice streams, which flow
into floating ice shelves (Figure 10.8~. Hughes (1973) and
Weertman ( 1974) pointed out that an ice sheet that rests on
a flat bed situated below sea level can be inherently un-
stable. If the climate in the future were to become warmer
and this caused warmer ocean water to intrude under the
ice shelves causing increased melting under the shelves,
then the back pressure exerted on the ice streams by the
shelves would be reduced and the ice streams would accel-
erate, draining the ice sheet itself. But how quickly could
this happen?
The interaction between an ice stream and an ice shelf
is illustrated in Figure 10.9. The ice stream pushes the ice
shelf past its margins and around shoals (ice rises). This
results in a compressive force (back pressure) F on the ice
(10.9) stream at the grounding line. The weight-induced spread
ing of the ice stream is resisted by F and by the shear along
the sides and base of the ice stream. If F is reduced due to
ice shelf thinning, the rate of extension of the ice stream
increases; the upper end flows at a very slow speed, and
the increasing extension rate is manifest in an increasing
velocity at the grounding line, and ice is moved from land
to sea at an increasing rate.
The critical questions then are (1) how much additional
heat will be delivered to the underside of the ice shelves in
an altered climate, (2) how will the changed conditions
affect calving rates and thus the dimensions of ice shelves,
and (3) how rapidly will the ice streams react to changes in
the back pressure?
The current basal melt rate for the ice shelves of Ant-
arctica has been estimated at about 0.4 m/yr (Jacobs et al.,
1985~. However, nearly undiluted circumpolar water, which
is several degrees above the in situ melting temperature,
intrudes onto the continental shelf of the Bellingshausen
Sea and causes about 2 m/yr of melt from the base of the
George VI Ice Shelf (Potter and Paren, 19851. One coupled
atmosphere-ocean circulation model (Schlesinger et al.,
1985) suggests that the ocean water 250 to 750 m below
the surface just north of the Ross Ice Shelf will be warmed
by 0.5° to 1.5°C, as a consequence of a doubled concentra-
tion of CO2. Such results, however, cannot be translated
into terms of ice-shelf melt, because our knowledge of
circulation under ice shelves is still incomplete (MacAyeal,
1984a,b; Jacobs, 1985~. It seems possible that, by the time
of doubled CO2, the basal ice shelf melt rate could increase
by as much as 1 to 3 m/yr (Committee on Glaciology,
1985~.
OCR for page 179
ROLE OF LAND ICE IN PRESENT AND FUTURE SEA-LEVEL CHANGE
o
.
80 _
l
1974
400 _
-300
E
v)
U)
z 200
Y
1
o
/ ~ j ~T H
SURFACE ELEVATION DECLINE
LU
O
Z
'1:
~ O
z
ID a
;),
-
67
_
I
_ 66
Z
rid \ \65
~200>
z
o
100 ~
o
z
(2) ~-~
(1)- \ ~
O C:
1976 1978 198019821984 ~
:c
l6
5
I At-:;-:::::--:-. :1: ::::.-;:::.::t: ::.::-::.::-.~.:::.:- ;::: -.-.1.:.-::.: ;--:.-:;:~:-X'--::::-:-:-:~:-.:-: :-.--: 1 o
1976 1978 1980 1982 1 984
Unfortunately, almost nothing is known on how the
calving rate, and thus ice-shelf dimensions, will be af-
fected by a warmer atmosphere and ocean. At this stage,
one can only make arbitrary guesses. This does not invali-
date but certainly limits the confidence one can have in the
results of ice-stream/ice-shelf modeling.
Ice-stream/ice-shelf interactions resulting from a CO2-
enhanced climate change have been explored by several
authors. Lingle (1984, 1985) modeled the evolution of Ice
Stream E, by assuming changes in the back pressure and
assuming no change in the ice-shelf dimensions. His re-
sults show a slight and very slow response to a 10 percent
179
FIGURE 10.7 Changes in Columbia Glacier,
Alaska, as disintegration begins. This
grounded, calving glacier resembles a small
4 ~e ice stream, but it does not terminate in a float
-ME ing ice shelf. The upper diagram shows the
3 ' ~ x acceleration in retreat, the decline in ice-sur
~ ~face altitude, and the decline in the ice thick
-
c: ~ness unsupported by buoyancy (hu); the val
2 ~ Z ues in parentheses represent the distances
tJ7 ~above the 1984 terminus in kilometers. The
lower diagram shows the declining ice thick
ness and accelerating velocity, as measured at
a point near the 1984 terminus, and the rise in
calving flux. From Meter et al. (1985~.
reduction in back pressure, but a dramatic and rapid disin-
tegration in response to a 50 percent reduction (Figure
10.101. Thomas (1985) made a simple calculation for Ice
Stream B in which various combinations of basal melt
rates and calving (change in ice-shelf dimensions) were
assumed.
Assuming that the model results from Ice Stream E are
representative of the whole West Antarctic Ice Sheet, Lingle
(1985) estimated that the contribution of this ice sheet to
sea-level rise by the year 2100 would be only 0.03 to 0.05
m. Thomas (1985), however, pointed out that most of the
discharge from Antarctica is through ice streams. He
OCR for page 180
180
FIGURE 10.8 Map of the Antarctic Ice
Sheet, with generalized flow lines (solid
lines) and ice divides (dashed lines). Ice
streams A and E in West Antarctica are
shown; floating ice shelves are stippled.
'it.
extrapolates the results from Ice Stream B to all of Antarc-
tica, and with his upper limit scenarios, predicts a probable
contribution to sea-level rise by 2100 of 0.2 to 0.8 m. This
represents a reasonable limit to the response, as there are
several processes that exert negative feedback that were
not taken into account. Bentley (1984) summarized a
number of reasons why disintegration of the West Antarc-
tic Ice Sheet will not happen in a few decades or centuries.
FIGURE 10.9 A typical Antarctic ice-drainage system. The ice
stream pushes the ice shelf seaward past its margins and around
the grounded ice rises, and there is a compressive force (F) at the
grounding line (X = L) between ice stream and ice shelf. This
compressive force is transmitted for some distance (L) upstream
of the grounding line, and there is an additional force due to
shear between the ice stream and its sides and bed. These forces
resist the extending flow of the ice stream. From Thomas (1985~.
/ ~_
MARK F. METER
no
1
~-- ~
Clearly, sea level will not rise catastrophically in the near
future due to the demise of this ice sheet; see Table 10.3.
Increased Accumulation on Antarctica
The Antarctic continent is large in area, but it is a
desert, with average annual precipitation of only 15 to 17
mm/yr, with a strong concentration of precipitation along
the coast. Greenhouse warming could lead to increased
precipitation because of two mechanisms: (1) reduction of
the surrounding sea ice allowing increased water vapor
exchange and transport to the continent, and (2) increased
water vapor content of the air due to increased tempera-
ture.
Oerlemans (1982) estimated a precipitation increase of
12 to 30 percent based on a temperature increase of 3° to
8°C; over a 100-yr period this would produce a sea-level
fall of 0.08 to 0.20 m. Warren and Frankenstein (in press),
using a simple relation of saturation vapor pressure to the
temperature of the inversion layer, suggest that a tempera-
ture rise of 5°C could lead to an increase in moisture of 60
to 90 percent, leading in 100 yr to a sea-level fall of 0.5 m.
They point out that the simple vapor pressure/temperature
model appears to be confirmed by the change in precipita-
tion observed at Dome C on the Antarctic plateau since the
last glacial period, but also that such a simple model might
not be valid when applied to the coastal regions.
The Committee on Glaciology (1985) report ascribed a
potential sea-level fall in their estimated range of only 0.1
OCR for page 181
ROLE OF LAND ICE IN PRESENT AND FUTURE SEA-LEVEL CHANGE
2OCO _
1530.
-
i: ~ OCC .
o
[_ S00.
IS
DISTANCE FROM ICE DIVIDE (km)
FIGURE 10.10 Thickness profiles for numerical mod-
els of Ice Stream E. In (a) the back pressure is reduced
by 10 percent from equilibrium back pressure; the pro-
files 1 through 5 are 0, 500, lOOO, 1500, and 2000 yr,
m in the next 100 yr (Table 10.3~. The study by WaITen
and Frankenstein suggests that this may be seriously under-
estimated. This is obviously a topic that deserves further
study.
A LONGER-TERM PERSPECTIVE
Fluctuations in CO2 Observed in Ice Cores
Recent studies of deep ice cores have shown rapid
fluctuations in climate during the last glacial period
(Dansgaard et al., 19829. These events, at time scales of
decades to a few centuries, appear to be paralleled by
similar changes in the CO2 content of the entrapped air
(Oeschger et al., 1984, 1985~. It is also clear that the CON
fluctuations do not lag the changes in climate; they may
lead them, but this is not well established. Although none
of these events has occurred so far in the Holocene (since
the last glacial age', they do indicate that a mechanism
involving CO2 exists that can cause rapid switches in cli-
mate over large regions, perhaps from one quasi-stable
mode to another (Broecker et al., 19851.
These results prove that changes in CO2, climate, and
ice are directly related. The ice core results do not indicate
directly how rapidly the ice masses responded to climate
changes. But these fluctuations represent changes in the
complex system involving the ocean, the ice, the atmo-
sphere, and the biosphere (Broecker et al., 1985~; so some
sort of rapid fluctuation in ice mass must have happened.
Rapid Deglac~ation in North America
The Laurentide Ice Sheet in North America covered
most of Canada and part of the United States as late as
20CO .
(b)
seo.
1 o00 .
soo .
O.
- se 0 .
-,coo. ,
a. _ ~;=7~
DISTA N CE FR O M ICE DIVID E (km)
respectively. In (b) the back pressure is reduced by 50
percent; the profiles 1 through 5 are 0, 39, 251, 487, and
664 yr. From Lingle (19851.
13,000 yr ago, but 7000 yr ago it was reduced to isolated
ice caps and Hudson Bay was opened (Andrews and Fal-
coner, 1969; Denton and Hughes, 1981; Andrews, 1988~.
Field evidence suggests that this retreat was not a smooth,
continuous meltback, but was accomplished by episodes
of rapid retreat, surrounded by periods of slower retreat or
advance. Field evidence (e.g., Prest, 1969) is not yet
sufficient to define the rates of retreat precisely, but the
evidence points to rates that can only be explained by
rapid calving disintegration. The rapid retreat in some
areas appears to have triggered rapid advances (surges?)
TABLE 10.3 Estimates of the Contribution to Sea
Level Rise by Ice Wastage in a CO2-Enhanced Environ
ment (from Committee on Glaciology, 1985)
Annual Probable Range of
Contribution to Estimated Contri-
Sea Level with button to Total
Steady-State 2 x CO' Sea-Level Change
Atmosphere (mm/yr) to Year 2100 (m)
Ice Mass
Glaciers and
small ice caps 2 to 5 0.1 to 0.3
Greenland
Ice Sheet
Antarctic
Ice Sheet
lto4 0.1 toO.3
-3 to 10 -0.1 to 1'
Note: Thermal expansion of the oceans and other nonglacial
processes that might cause additional sea-level rise are not in-
cluded here.
aValues in the range of O to 0.3 are considered most likely.
OCR for page 182
182
of ice into the recently deglaciated areas such as the Coch-
rane surges of southern Hudson Bay (Press, 1970~. There
is evidence that such rapid deglaciations occurred about
40,000 and 80,000 years ago as well as 8000 years ago
(Shills, 1982; Andrews et al., 1983~.
The rapid and complex deglaciation at the end of the
last ice age has obvious implications to understanding and
predicting the future of the marine-based portions of the
Antarctic Ice Sheet. The problem now is to obtain addi-
tional datable evidence of retreat, and to use these data in
ice-sheet models so that ice-sheet stability can be defined
more precisely.
Did the West Antarctic Ice Sheet Disappear During the
Last Interglacial?
During the last interglacial, global sea level stood, on
the average, 5 to 7 m higher than today. If the West
Antarctic Ice Sheet were to disintegrate, sea level would
rise 5 to 7 m. Mercer (1968) first suggested the connec-
tion. If this ice sheet disintegrated in the last interglacial,
then one would expect that it could do the same in the
forthcoming CO2-enhanced "super interglacial."
Soviet engineers have drilled an ice core from Vostok
in East Antarctica that penetrates ice from the last intergla-
cial, 116,000 to 140,000 yr ago. The results indicate that
the surface air temperature during the interglacial was
about 3°C warmer than during the Holocene (Lorius et al.,
1985~. But does this mean that the regional climate in
Antarctica was warmer during the last interglacial?
Robin (1985) suggested that the warmth was due to a
lower ice surface at that time, a suggestion that is sup-
ported by other evidence as well. Also, there is evidence
from other parts of the world that the climate of the last
interglacial was similar to that of the present. So, if the
climate were the same as that of today, the Vostok results
imply that the ice surface must have been 300 to 350 m
lower than today. If this were true over most of central
Antarctica, the lower ice volume would cause a higher sea
level during the last interglacial similar to that observed.
So the question is not yet resolved. A deep ice core in
West Antarctica penetrating interglacial ice, or penetrat-
ing the last glacial but showing no interglacial ice below,
is vitally needed if we are to evaluate the hypothesis of
rapid collapse of the West Antarctic Ice Sheet and the
dramatic effect on sea level that would ensue.
ACKNOWLEDGMENTS
I thank J. T. Andrews, C. R. Bentley, and T. J. Hughes
for helpful comments on the manuscript.
MARK F. METER
REFERENCES
Alley, R. B., and I. M. Whillans (1984~. Response of the East
Antarctica Ice Sheet to sea-level rise, J. Geophys. Res. 89,
6487~493.
Ambach, W. (1985~. Characteristics of the heat balance of the
Greenland Ice Sheet for Modelling, J. Glaciol. 31, 3-12.
Ambach, W., and M. Kuhn (1985~. The shift of equilibrium-line
altitude on the Greenland Ice Sheet following climatic changes,
in Glaciers, Ice Sheets, and Sea Level: Effects of a CO2-
lnduced Climatic Change, Committee on Glaciology, National
Academy Press, Washington, D.C., pp. 255-257.
Andrews, J. T. (19881. Climatic evolution of the eastern Cana-
dian Arctic and Baffin Bay during the past three million years,
Philos. Trans. R. Soc. London B318, 645~60.
Andrews, J. T., and G. Falconer (19691. Late glacial and postgla-
cial history and emergence of the Ottawa Island, Hudson Bay,
N.W.T.: Evidence on the deglaciation of Hudson Bay, Can. J.
Earth Sci. 6, 1263-1276.
Andrews, J. T., W. W. Shills, and G. H. Miller (1983~. Multiple
deglaciations of the Hudson Bay lowlands, Canada, since
deposition of the Missinaibi (last-interglacial?) formation, Quat.
Res. 19, 18-37.
Barry, R. G. (19841. Possible CO2-induced warming effects on
the cryosphere, in Climatic Changes on a Yearly to Millennial
Basis, N.-A. Morner and W. Karlen, eds., D. Reidel, Dor-
drecht, Holland, pp. 571~04.
Benson, C. S. (1962~. Stratigraphic studies in the snow and firn
of the Greenland Ice Sheet, SIPRE Research Report 70.
Bentley, C. R. (1984~. Some aspects of the cryosphere and its
role in climatic change, in Climate Processes and Climate
Sensitivity, J. E. Hansen and T. Takahashi, eds., Geophysical
Monograph 29, Maurice Ewing Vol.5, American Geophysical
Union, Washington, D.C., pp. 207-220.
Bindschadler, R. (1983~. The importance of pressurized subgla-
cial water in separation and sliding at the glacier bed, J. Gla-
ciol. 29, 3-19.
Bindschadler, R. (1985~. Contribution of the Greenland Ice Cap
to changing sea level present and future, in Glaciers, Ice Sheets,
and Sea Level: Effects of a CO2-Induced Climatic Change,
Committee on Glaciology, National Academy Press, Wash-
ington, D.C., pp. 258-266.
Bodvarsson, G. (1955~. On the flow of ice-sheets and glaciers,
Jokull 5, 1-8.
Broecker, W. S., D. M. Peteet, and D. Rind (19851. Does the
ocean-atmosphere system have more than one stable mode of
operation?, Nature 315, 21-26.
Brown, C. S., M. F. Meter, and A. Post (19821. Calving Speed of
Alaska Tidewater Glaciers, with Application to Columbia Gla-
cier, U.S. Geol. Surv. Prof. Paper 1258-C, 13 pp.
Budd, W. F., P. L. Keage, and N. A. Blundy (19791. Empirical
studies of ice sliding, J. Glaciol. 23, 157-170.
Carbon Dioxide Assessment Committee (19831. Changing Cli-
mate, National Academy Press, Washington, D.C., 496 pp.
Committee on Glaciology (19841. Environment of West Antarc-
tica, Potential CO2-Induced Changes, National Academy Press,
Washington, D.C., 236 pp.
1
OCR for page 183
ROLE OF LAND ICE IN PRESENT AND FUTURE SEA-LEVEL CHANGE
Committee on Glaciology (1985~. Glaciers, Ice Sheets, and Sea
Level: Effects of a CO2-lnduced Climatic Change, National
Academy Press, Washington, D.C., 330 pp.
Dansgaard, W., H. B. Clausen, N. Gundestrup, C. U. Hammer, S.
F. Johnson, P. M. Kristinsdottier, and N. Reeh (1982~. A new
Greenland deep ice core, Science 218, 1273-1277.
Denton, G. H., and T. J. Hughes (1981~. The Last Great Ice
Sheets, John Wiley, New York, 484 pp.
Fastook, J. L., and W. Schmidt (1982~. Finite-element analysis
of calving from ice fronts, Ann. Glaciol. 3, 103-106.
Grossvaltd, M. S., and V. M. Kotlyakov (1978~. Impending
climatic change and the fate of glaciers, Izv. Akad. Nauk SSSR,
Ser. Geogr. 6, 21-32.
Hollin, J. T., and R. G. Barry (1979~. Empirical and theoretical
evidence concerning the response of the Earth's ice and snow
cover to a global temperature increase, in Environment Inter-
national 2, Pergamon Press, pp. 437-444.
Hughes, T. J. ~ 1973). Is the West Antarctic Ice Sheet
disintegrating? J. Geophys. Res. 78, 7884-7910.
IASH (1967~. Fluctuations of Glaciers 1959-65, P. Kasser,
compiler, International Association of Scientific Hydrology/
Unesco, 52 pp.
IASH (19731. Fluctuations of Glaciers 1965-70, P. Kasser,
compiler, International Association of Scientific Hydrology/
Unesco, 357 pp.
IASH (19771. Fluctuations of Glaciers 1970-75, F. Muller,
compiler, International Association of Scientific Hydrology/
Unesco, 269 pp.
Illangasekare, T. H., M. F. Meier, R. J. Walter, and W. T. Pfeffer
(1988~. Modeling of water flow in sub-frozen snow to study
future sea level changes due to ice wastage, EOS 69, 366.
Jacobs, S. S. (19851. Oceanographic evidence for land ice/ocean
interactions in the Southern Ocean, in Glaciers, Ice Sheets,
and Sea Level: Effects of a CO2-Induced Climatic Change,
Committee on Glaciology, National Academy Press, Wash-
ington.D.C.,pp.11~128.
Jacobs, S. S., R. G. Fairbanks, and Y. Horibe (1985~. Origin and
evolution of water masses near the Antarctic continental mar-
gin: Evidence from H2'80/H2'60 ratios, in Oceanology of the
Antarctic Continental Shelf, Ant. Res. Ser. 43, American
Geophysical Union, Washington, D.C.
Jacobs, S. S., D. R. MacAyeal, and J. L. Ardai, Jr. (1986~.
Recent advance of the Ross Ice Shelf, Antarctica, J. Glaciol.
32, 464-474.
Kuhn, M. (1981~. Climate and glaciers, sea level, ice and cli-
matic change, in Proceedings of the Canberra Symposium,
December 1979, I. Allison, ea., IASH Publ. 131, pp. 3-20.
Kuhn, M. (1985~. Reactions of mid-latitude glacier mass bal-
ance to predicted climatic changes, in Glaciers, Ice Sheets,
and Sea Level: Effects of a CO2-Induced Climatic Change,
Committee on Glaciology, National Academy Press, Wash-
ington, D.C., pp. 248-254.
Lambeck, K. (1980~. The Earth's Variable Rotation, Geophysi-
cal Causes and Consequences, Cambridge University Press,
449 pp.
Lingle, C. (1984~. A numerical model of interactions between a
polar ice stream and the ocean: Application to Ice Stream E,
West Antarctica, J. Geophys. Res. 89, 3523-3549.
~3
Lingle, C. (1985~. A model of a polar ice stream, and future sea-
level rise due to possible drastic retreat of the West Antarctic
Ice Sheet, in Glaciers, Ice Sheets, and Sea Level: Effects of a
CO2-Induced Climatic Change, Committee on Glaciology,
National Academy Press, Washington, D.C., pp. 317-330.
Lorius, C., J. Jouzel, C. Ritz, L. Merlivat, N. I. Barkov, Y. S.
Korotkevich, and V. M. Kotlyakov (1985~. A 150,000-year
climate record from Antarctic ice, Nature 316, 591-596.
MacAyeal, D. R. (1984a). Potential effect of CO2 warming on
sub-ice-shelf circulation and basal melting, in Environment of
West Antarctica: Potential CO2-Induced Changes, Committee
on Glaciology, National Academy Press, Washington, D.C.,
pp. 212-221.
MacAyeal, D. R. (1984b). Thermohaline circulation below the
Ross Ice Shelf: A consequence of tidally induced vertical
mixing and basal melting, J. Geophys. Res. 89, 597~06.
Meier, M. F. (1983~. Snow and ice in a changing hydrological
world, Hydrolog. Sci. J. 28, 3-22.
Meier, M. F. (1984~. Contribution of small glaciers to global sea
level, Science 226, 1418-1421.
Meier, M. F. (1985~. Mass balance of the glaciers and small ice
caps of the world, in Glaciers, Ice Sheets, and Sea Level:
Effects of a CO2-Induced Climatic Change, Committee on
Glaciology, National Academy Press, Washington, D.C., pp.
139-144.
Meier, M. F., and A. Post (1987~. Fast tidewater glaciers, J.
Geophys. Res. 92, 9051-9058.
Meier, M. F., and W. V. Tangborn (1965~. Net budget and flow
of South Cascade Glacier, Washington, J. Glaciol. 5, 547-566.
Meier, M. F., W. V. Tangborn, L. R. Mayo, and A. Post (1971~.
Combined Ice and Water Balances of Gulkana and Wolverine
Glaciers, Alaska, and South Cascade Glacier, Washington,
1965 and 1966 Hydrologic Years, U.S. Geol. Surv. Prof. Paper
715-A, 23 pp.
Meier, M. F., L. A. Rasmussen, and D. S. Miller (1985~. Colum-
bia Glacier in 1984, Disintegration Underway, U.S. Geol. Surv.
Open File Report 85-81, 17 pp.
Meier, M. F., T. Pfeffer, and T. Illangasekare (1988~. The
behavior of liquid water in cold ice caps Initial results, EOS
69, 1211-1212.
Mercer, J. H. (1968~. Antarctic ice and Sangamon sea level, Int.
Assoc. Sci. Hydrol. 79, 217-225.
Mercer, J. H. (1978~. West Antarctic Ice Sheet and CO2 green-
house effect: A threat of disaster, Nature 271, 321-325.
Muller, F. (1962~. Zonation in the accumulation area of the
glaciers of Axel Heiberg Island, N.W.T., Canada, J. Glaciol.
4, 302-311.
Neftel, A., E. Moor, H. Oeschger, and B. Stauffer (19851. Evi-
dence from polar ice cores for the increase in atmospheric CO2
in the past two centuries, Nature 315, 45-47.
Nye, J. F. (1965~. A numerical method of inferring the budget of
history of a glacier from its advance and retreat, J. Glaciol. 5,
589007.
Oerlemans, J. (1982~. Response of the Antarctic Ice Sheet to a
climatic warming: A model study, J. Climatology 2, 1-11.
Oeschger, H. et al. (1984~. Late glacial climate history from ice
cores, in Climate Processes and Climate Sensitivity, J. E.
Hansen and T. Takahashi, eds., Geophysical Monograph 29,
OCR for page 184
184
Maurice Ewing Vol. 5, American Geophysical Union, Wash-
ington, D.C., pp. 299-306.
Oeschger, H. et al. (1985). Variations of the CO2 concentration
of occluded air and of anions and dust in polar ice cores, in The
Carbon Cycle and Atmospheric CO2: Natural Variations Arch-
ean to Present, E. T. Sundquist and W. S. Broecker, eds.,
Geophysical Monograph 32, American Geophysical Union,
Washington, D.C., pp. 132-142.
Orheim, O. (19851. Iceberg discharge and the mass balance of
Antarctica, in Glaciers, Ice Sheets, and Sea Level: Elects of a
CO2-Induced Climatic Change, Committee on Glaciology,
National Academy Press, Washington, D.C., pp. 210-215.
Pettier, W. R. (19851. Climatic implications of isostatic adjust-
ment constraints on current variations of eustatic sea level, in
Glaciers, Ice Sheets, and Sea Level: Effects of a CO2-Induced
Climatic Change, Committee on Glaciology, National Acad-
emy Press, Washington, D.C., pp. 92-103.
Pettier, W. R. (19881. Global sea level and Earth rotation, Sci-
ence 240, 895-901.
Post, A. (19751. Preliminary hydrography and historic terminal
changes of Columbia Glacier, Alaska, U.S. Geol. Surv. Hy-
drol. Invest. Atlas 559.
Potter, J. R., and J. G. Paren (19851. Interaction between ice
shelf and ocean in George VI Sound, Antarctica, in Oceanol-
ogy of the Antarctic Continental Shelf, Antarct. Res. Ser. 43,
American Geophysical Union, Washington, D.C., 1985.
Prest, V. K. (19691. Retreat of Wisconsin and Recent Ice in
North America, Geol. Surv. Canada Map 1257A.
Prest, V. K. (19701. Quaternary geology in Canada, in Geology
and Economic Minerals in Canada, 5th edition, R. J. Douglas,
ea., Department of Energy, Mines, and Resources, Ottawa,
Canada, pp. 676-764.
Reeh, N. (19681. On the calving of ice from floating glaciers and
ice shelves, J. Glaciol. 7, 215-234.
Revelle, R. R. (19831. Probable future changes in sea level
resulting from increased atmospheric carbon dioxide, in Chang-
ing Climate, Carbon Dioxide Assessment Committee, National
Academy Press, Washington, D.C., pp. 433~48.
Robin, G. de Q. (1985~. Contrasts in Vostok core changes in
climate or ice volume? Nature 316, 578-579.
MARK F. METER
Robin, G. de Q. (1986). Changing the sea level, in The Green-
house Effect, Climatic Changes, Ecosystems, B. Bolin, B. R.
Doos, J. Jager, and R. A. Warrick, eds., SCOPE 29, Wiley,
Chichester, Mass., pp. 323-359.
Schlesinger, M. E., et al. (1985). The role of the ocean in CO2-
induced climate change: Preliminary results from the OSU
coupled atmosphere-ocean general circulation model, in
Coupled Ocean- Atmosphere Models, J. C. J. Jihoul, ea.,
Elsevier, Amsterdam, pp. 447~78.
Shills, W. W. (1982~. Quaternary evolution of the Hudson/
James Bay region, in University of Guelph Symposium on
Hudson Bay, Can. Natur. 109, 309-332.
Sikonia, W. G. (1982). Finite Element Glacier Dynamics Model
Applied to Columbia Glacier, Alaska, U.S. Geol. Surv. Prof.
Paper 1258-B, 74 pp.
Stauffer, B., G. Fischer, A. Neftel, and H. Oeschger (1985~.
Increase of atmospheric methane recorded in Antarctic ice
core, Science 229, 1386-1388.
Thomas, R. H. (19851. Responses of the polar ice sheets to
climatic warming, in Glaciers, Ice Sheets, and Sea Level:
Effects of a CO2-Induced Climatic Change, Committee on
Glaciology, National Academy Press, Washington, D.C., pp.
301-316.
Thomas, R. H. (19871. Future sea-level rise and early detection
by satellite remote sensing, Prog. Oceanog. 18, 23~0.
Thorarinsson, S. (19401. Present glacier shrinkage and eustatic
changes of sea-level, Geogr. Ann. 22, 131-159.
Weertman, J. (19741. Stability of the junction of an ice sheet and
an ice shelf, J. Glaciol. 13, 3-11.
Warren, S., and S. Frankenstein (in press). Increased accumula-
tion on the Antarctic Ice Sheet due to climatic warming, ab-
stract for symposium on Ice and Climate, International Gla-
ciol. Soc., to appear in Ann. Glaciol.
Zwally, H. J. (19851. Mapping ice sheet growth by satellite
altimetry, paper presented to Symposium on Glacier Mapping
and Surveying, International Glaciological Society, Reykjavik,
Iceland, Aug. 26, 1985.
Representative terms from entire chapter:
antarctic ice
