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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

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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

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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 69N 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.)

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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 72N 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

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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

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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 4C 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,

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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 10C 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,

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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 1.5C, 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~.

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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

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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 8C; 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 5C 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

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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.

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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 3C 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~. 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