SCOPE 29 - The Greenhouse Effect, Climatic Change, and Ecosystem

 7.1 INTRODUCTION 

This chapter discusses the effects of atmospheric warming on sea level. We draw on results in other chapters for the possible rise in atmospheric temperatures caused by the increasing atmospheric concentration of CO₂ and other radiatively active gases.

Changes of global temperature affect components of the global hydrological cycle in different ways and with different response times. Higher temperatures increase the amount of water vapour in the atmosphere. Precipitation patterns alter and affect runoff from rivers and glaciers into the sea. Ocean waters expand. Catastrophic collapse of ice sheets has been suggested as another consequence of rising temperatures that might cause a rapid rise of sea level.

Although components of the hydrological cycle have been studied for some time, it is only during the past few years that quantitative attempts have been made to integrate all relevant data. So far, most studies related to rising sea level have been directed at positive components that together could explain the observed rise of sea level. Negative components that could extract water from the oceans for long periods, such as increases in the mass of the Antarctic ice sheet and of the level of groundwater, have received less attention.

Our approach is to interpret observational data and to emphasize correlations and physical models that involve the minimum of assumptions. The more assumptions involved, the more easily can models be tuned to fit existing data but this does not necessarily improve resultant forecasts.

Discussion in Sections 7.3, 7.4 and 7.5 on components of the hydrological cycle shows so many deficiencies in our knowledge of factors affecting mean global sea level that we make use of a simple linear correlation between changes of mean global temperature (K) and of mean global sea level (SL). Ideally we should use a correlation such as SL = a K + b (K )² + c(K)³ + ..., where a, b, c ... are constants determined from correlations of existing data. The overriding factor that limits correlation to the linear is that data scatter is too large to determine higher order terms. A further weakness of this approach is extrapolation from global temperature changes of a few tenths of a degree to several degrees. This is only justified if the processes involved are known to be linear over the greater range.

Several processes involving an approximately linear response to temperature help to justify our use of linear correlation. These include the thermal expansion of sea water (except near 0 °C) and the change of height of the equilibrium line on glaciers, that is the line separating the accumulation zone from the ablation zone. The change of saturation water vapour pressure with temperature is approximately linear over a small temperature range (less than 5 °C, say) and is one factor that determines transfer of water mass from oceans to land. Other factors, such as those involving atmospheric and ocean dynamics, are unlikely to involve linear correlations and in some cases we are not sure whether correlations are positive or negative.

Another problem is the time responses of different processes. If these are small compared to the period considered, say 100 years, then the response will be approaching completion within 100 years and the correlation reasonable. If response to K is long compared to the analysis or forecast period, then SL will be given by the product of the rate of change (e.g. mass) and the time. Use of the same period (100 years) of data analysis and of forecasting helps to eliminate the time factor correction for the (unknown) proportional effect of processes with long response times.

Processes with response times short compared with 100 years include warming of upper layers of the ocean, adjustment of small glaciers to climatic change and runoff of water from land. Response times of the order of 100 years are associated with deeper oceanic layers and larger glaciers while melting of continental ice sheets and resultant adjustment of the Earth's crust to changing ice loading continue over some millennia.

Two other factors related to melting glaciers are the non-linear relation between melting rate and temperature and the apparent polar amplification of global temperature change. During summer months when glacier melting occurs, global circulation models of Manabe and Stouffer (1980) and Washington and Meehl (1984) show the polar amplification over Greenland and Antarctica to be small or negligible and barely significant in relation to melting. Climatic data from some polar regions do show a higher variability than those of lower latitudes, but as with models this is likely to be due to winter rather than summer phenomena that do not affect melting. These include the strength of cold surface inversion layers and delays in oceanic freezing.

This report is concerned with changes of mean global sea level (SL). By this we mean changes of mean level in relation to bench marks on the shore recorded by tide gauges operated over long periods. Global or regional changes of sea level refer to the mean value of such changes at many locations over the globe or region. Finally, we should emphasize that damage done by high sea level usually results from storm surges at the time of high tides. We do not attempt to discuss the problems of surges or tides. The former may well be influenced by dynamic factors involved in atmosphericocean interactions that are also related to climatic change. These are, however, local and regional problems that require separate study to that of changing global mean sea level.

7.2 OBSERVED CHANGES OF SEA LEVEL AND GLOBAL TEMPERATURE OVER THE PAST CENTURY

7.2.1 Sea Level 

Sea level changes at any location are affected by a combination of local, regional and global factors. In addition to the quality and length of records, variations between stations are caused by changes of meteorological, oceanographic and tectonic conditions. To determine global changes of the water mass we need mean values from instruments spaced in a regular network over the world's oceans. Instrument locations where disturbances are likely to be high should be avoided. Mid-oceanic sites rather than continental coastlines may be more stable tectonically. Unfortunately, the distribution of available records is far from meeting the above criteria. Europe and North America provide many of the records, but often are not tectonically ideal. The Southern Hemisphere is poorly represented.

Analyses of global sea level changes are summarised in Table 7.1. There is some variation in the period covered and in the methods used. The earlier estimates and those covering the whole period »18801980 give values from 10 to 15 cm/century while the more rapid rise since 1920 is shown in analyses of post-1930 data.

The last four studies made special efforts to avoid regional and other bias. Statistically Barnett's (1984) analyses were rigorous, but presentations of Gornitz et al. (1982) and Klige (1982) are more convenient for discussion of global changes of mean sea level (SL) and their relation to physical processes over the past century. Their global curves are shown in Figure 7.1. The three authors agree that there are large variations between regions, but that over large sections of the world's coastlines, changes of sea level are spatially and temporarily coherent. Barnett does not present a global curve. He considers that the data from 1881 to 1920 indicates a time of little change and that the period 1920 to 1980 was a time of steady increase of SL. Klige and Gornitz et al. show the most rapid changes of SL from around 1925 to about 1955, after which SL stayed about the same level until 1975 (Figure 7.1).

Table 7.1 Estimates of mean 'global' sea level increase

Author	Rate (cm/century)	Method
Thorarinsson (1940)	> 5	Cryologic Aspects
Gutenberg (1941)	l l ± 8	1937 (many stations)
Kuenen (1950)	1214	1942 Different Methods
Lisitzin (1958)	11.2±3.6	Sea Level (six stations)
Fairbridge and Krebs (1962)	12	19001950 (selected stations)
Emery (1980)	30	19351975 (selected stations)
Gornitz et al. (1982)	12	18801980 (many stations)
Klige(1982)	15	19001975 (many stations)
Barnett (1984)	14.3± 1.4	18811980 (many stations)
Barnett (1984)	22.7±2.3	19301980 (many stations)

Prior to 1920 data were scarce and derived SL changes may be questioned, but after 1950 data were selected from over 500 stations. Barnett considers it inadvisable to fit other than a linear equation to his 193080 data, so he does not confirm the 195575 levelling off shown by Gornitz et al. Nevertheless, visual inspection of Barnett's six regional curves shows little change in SL between 195575 over three regions, two show a marked rise and one a marked fall. Although variable, Klige's SL decreases after 1955 but levels off in the 1960s. We attach some significance to the change of slope shown in SL curves around 1955, since such a change is linked by physical processes with independent data also shown in Figure 7.1. In particular, comparison of slope changes of the SL and temperature curves indicates that processes involving time constants of around one to three decades have had a major influence on sea level changes over the past century. 

The analysis of Gornitz et al. (1982) also helps this study by correcting recent SL changes for long-term trends over the past 6000 years, that is since the ice sheets of the last glaciation finally melted. They used ¹⁴C dating of measured elevations of past shore line indicators, such as molluscs, corals and brackish water peats to calculate mean trends. Details of the corrections are not given, but in principle the approach supplies the information needed for this assessment. Figure 7.2 shows the corrected trends for the 10 out of their 14 regions for which corrections were available. Table 7.2 gives numerical details. Column (4) was added to the original table to show the difference between column (2) and column (6), so is not a true mean of actual corrections applied to individual station records. The mean of column (4) of 2 cm/century, is therefore a rough estimate of slow changes due to combined effects of movement of material in the Earth's mantle and of any slow long-term changes in volume of ice sheets. Klige (1982) suggests a figure of around 1 cm/century for the slow rise of SL over the past 6000 to 7000 years, half the value shown in Table 7.2, but does not apply this figure as a correction. This is one reason for the smaller change of SL by Gornitz et al. in Figure 7.1 compared with Klige's data; other possible reasons are the different time spans covered and greater weight given to North Atlantic data by Klige.

Figure 7.1 

K	Global mean temperature, 5 year running mean from Hansen et al. (1981) Gornitz Sea level. Global mean-from Gornitz et al. (1982)5 year mean Klige Sea level. Global meanfrom Klige (1982), annual values
O.E.	Ocean Expansion to thermocline-from Gornitz et al. (1982)median estimate based on K and constants Keq = 2.8 °C and K = 1.2 cm2/sec.
	GI. Glaciers melting. Effect of small glaciers and ice caps melt on sea level. From Meier (1984)
C.S.	Caspian Sea level changes multiplied by 6.6 and expressed in equivalent sea level changes less 2 cm. Data from Micklin (1971) to 1965 and other sources

Figure 7.2 Regional mean sea level trends. The heavy lines are 5year running means. Long-range (6000-year) trends have been subtracted (after Gornitz et al., 1982)

Table 7.2 Sea level trends, 1880 to 1980 including correction for long-term (6000-year) trends (based on Gornitz et al., 1982)

Region	Sea level trend  1880 to 1980								Corrected sea level trend  1880 to 1980
	(1)  Number of stations		(2)  Linear trend (cm/100 years)		(3)  95% confidence limit (cm/100 years)		(4)  Mean station trend (up to 6000 years) (cm 100 years)		(5)  Number of stations		(6)  Linear trend (cm/100 years)		(7)  95% confidence limit (cm/100 years)
West coast, North America	16		10		2		2		1		8		3
Gulf coast and Caribbean	6		23		4		7		4		16		5
East coast, North America	32		30		2		15		30		15		2
Bermuda	1		26		16		6		1		20		16
West coast, South America	8		19		31		22		2		-3		3
East coast, South America	5		4		11		+12		2		16		11
Africa	2		32		31				0
Southern Europe	15		32		2		25		7		7		2
West central Europe	7		13		2		9		5		4		2
Southern Baltic	21		4		2		+1		14		5		2
Scandinavia	47		-37		3		+47		10		10		3
Asia	9		4		3		+18		2		22		4
Australia	9		13		3				0
Pacific Ocean	15		19		3		13		6		6		4
Global mean	193		12		1		(2	)	86		10		1

The global mean values of uncorrected trends given by Gornitz et al. appear to exclude the two regions for which corrected trend data were not available, while including Scandinavia. If uncorrected trends for all 14 regions are included without weighting by numbers of stations or areas, the global mean is 14 ± 5 cm/century where 5 is the standard error of the mean. The corresponding mean of the corrected trends is 10.5 ± 2.5 cm/century. Avoidance of regional bias by combining adjacent zones in Europe and of the other forms of bias by excluding areas with less than 70 years of data or Bermuda because it has only one record made little difference to the rate of 10.5 ± 2.5 cm/century which is based on data from 75 stations.

7.2.2 Station Trends

Corrections for trends of station elevation in relation to sea level over the past 6000 years have halved the spread of sea level trends between regions in Table 7.2. This justifies the assumption that long-term trends may be extrapolated over the next few centuries to correct for vertical movement of the Earth's surface. Isostatic adjustments and tectonic movement associated mainly with plate crustal boundaries were shown to be the main cause of this vertical movement by Newman et al. (1981). They analysed 3000 dated sea level determinations spanning 12,000 years to provide maps of elevation changes from the present sea level for 1000 year periods, each including 100 to 300 data points. The analysis also revealed a persistent Holocene equatorial bulge which they suggest could be due to changes in the Earth's rotational speed following deglaciation, but its (small?) magnitude is not specified.

Theoretical studies such as Clark et al. (1978) show that the response of  world oceans to the disappearance of a major ice sheet will not produce a uniform rise of sea level over the whole globe. A changed gravitational field due to removal of ice plus elastic and isostatic rebound due to removal of ice and increasing ocean loading produce viscous flow of material below the crust. Papers in 'Earth Rheology, Isostasy and Eustasy' Nils-Axel Mörner (ed, 1980) show no consistent agreement over details of viscous flow in the aesthenosphere and mantle, but provide possible explanations for the mean 6000 year trend of around 2 cm/century in Table 7.2 and of variations from that mean due to changes of the shape of the Earth with time.

7.2.3 Sea Level, Salinity and Oceanic Circulation

In addition to expansion of ocean waters with rising temperatures, its density is also strongly dependent on salinity. The surface salinity of the ocean is affected by evaporation and precipitation at the sea surface, by input of fresh water from rivers and melting ice and by salt rejection during sea ice formation. These processes in turn govern convection or the lack thereof in different regions and thus affect the dynamic circulation of the ocean in addition to its response to the global pattern of wind stresses.

The density of the stable mixed layer of 50 to 100 m deep produced by solar heating from around 45° N to 45° S is determined mainly by temperature rather than salinity effects, so we assume that here, the density changes are mainly a function of temperature changes. In high latitudes with lower sea temperatures, salinity changes could have more effect, but where deep convection takes place during winter relative changes of density will be smaller. Around the Arctic Ocean, where river discharge forms a lower density layer 200 m deep at temperatures little above freezing one would expect variations of river discharge with climate to affect sea level by a few centimetres or at most by a few tens of centimetres but its global significance would not be large.

The major effect of salinity changes is likely to be on the circulation of deep ocean waters (see Duplessy and Shackleton, 1985), but knowledge is not sufficient to predict the resultant changes of sea level. Ocean circulation changes driven by wind stresses and oceanic eddies produce surface elevation changes of up to several tens of centimetres that may persist for weeks or months as in the El Niño event of 1982 (Wyrtki, 1985).

Local and regional changes of sea level are smaller and less persistent than global changes. The former include seasonal changes of salinity in estuaries and adjacent regions due to variable discharge from rivers. On the longer time scale, the inverse barometric effect from long-term pressure trends at meteorological stations was investigated by Barnett (1983). The maximum change from 19001970 was about 2 mbar, equivalent to a change of relative sea level between stations of 3 cm/century. Major changes of oceanic circulation over long periods, such as the shift of position of the Gulf Stream in the Atlantic since the last glacial maximum will produce relative changes of up to one metre or more while the stream moves across any region.

7.2.4 Temperatures 

Similar problems to those of sea level occur in determining mean global trends of temperature due to non-uniform distribution of data and a paucity of records extending back to 1880 in the Southern Hemisphere. These problems are discussed in Chapter 6. Fluctuations of global mean changes of temperature determined by Hansen et al. (1981) incorporating Southern Hemisphere data, which are compared with sea level data of Gornitz et al. (1982) in Figure 7.1, are very similar to the three Northern Hemisphere analyses of Figure 6.1. The latter show a mean change of around +0.4 °C over the same period as Hansen et al. (1981).

7.2.5 Correlation Between Sea Level Changes and Global Air Temperatures

Gornitz et al. (1982) tentatively fitted a linear relation between their sea level curve and Hansen et al.'s (1981) global temperature trend using

where S and K are 5 year means of global sea level and temperature changes respectively and t is time. Parameters a and b were obtained by least squares linear regression and the time lag t₀ was chosen to minimise the variance between sea level curve and temperature. The results were a = 16 cm/°C, b = 0.3 cm, and t₀ = 18 years with a correlation coefficient of 0.8. We can also obtain the coefficient a by equating the average global rise of sea level from 1880 to 1980 of 10.5 cm (corrected for local trends) to the mean rise of 0.4 °C of global air temperature from the same sets of data to give a = 26 cm/ ^°C. Barnett's (1984) value of 14.3 cm for sea level rise 18811980 and the global temperature rise of 0.5 °C of Chapter 6 would give a = 29 cm/°C or the use of 0.4 °C and subtracting 2 cm/century to allow for longterm trends would give a = 31 cm/°C. There is no point in using shorter term data after 1930 in this way. There is little net temperature change over this period to match the large sea level rate of change possibly because the time lags involved are then too large. In round figures we therefore suggest limits for a as 16 and 30 cm/century and apply these figures to the estimate of 3.5 ± 2 ^°C for the response of global temperature to a doubling of CO₂ over the next century. This gives sea level changes using a = 16 cm/°C of SL = 56 ± 32 cm and for a = 30 cm/°C of SL = 105 ± 60 cm which indicates that the sea level rise should be in the range 25165 cm. We again draw attention to the limitations of this type of linear extrapolation set out in the introduction 7.2.1. It is the only type of estimate that can be made without a full evaluation of the contributions of all physical processes involved. These are now discussed in more detail. Only by their use will we develop a firmer base for forecasting future sea level changes. However, our present state of knowledge is insufficient for this purpose. Linear correlation thus provides a simple forecast that is better than no forecast.

7.3 RESERVOIRS AND EXCHANGE RATES WITHIN THE HYDROLOGICAL CYCLE

 7.3.1 Distribution of the Global Water Mass

Figure 7.3 from Woods (1984) based on data in Baumgartner and Reichel (1975) presents a simplified but very useful general picture of the main storages and exchanges within the Earth's hydrological system. Figures for exchanges are based on available data adjusted to produce global balances between precipitation and evaporation and between runoff to the oceans and the excess of precipitation over evaporation on the continents. Residence times are simply the reservoir mass divided by the exchange rate.

 Table 7.3 Present global water mass distribution

Reservoir	Area		Water		% fresh		Sea level	Annual Exchange		Residence time
	(106km2)		equivalent (106km3)		water		equivalent (mm)	Volume (km3)	Sea level equivalent (mm)	(volume/annual exchange) (years)
Antarctic inland ice	12	.0	26	.5	70	.9	73.2 .103	1,800	6	16,200
Greenland ice sheet	1	.8	2	.46	6	.6	6.8.103	500	2	5,400
Other glaciers	0	.54	0	.12	0	.3	330	661	2	180
Permafrost	(»12	)	0	.03	0	.1	8	0	0
Total ice on land			29	.1	77	.8	80.4.103
Lakes, rivers, soil			0	.225	0	.6	0.62.103	37,600	104	6.0
Groundwater			8	.06	21	.6	22.3.10 3	?	?	0 to 104
Atmosphere	504		0	.013	<0	.1	35	496,000	1,370	9.6 days
Continents  Total freshwater	142		37	.33	100		103.1 .10 3
Oceans	362		1,354				3,750

Figure 7.3 The global water balance shown schematically on the basis of data in Baumgartner and Reichel (1975). The residence time of water in the ocean is 3000 years, in the soil one year, and in the atmosphere ten days (after J. D. Woods, 1984) 

Table 7.3 shows similar details, with data on ice volumes and exchanges from other sources. Also shown in Table 7.3 are areas, volumes instead of masses (10²⁰₇ = 10⁵ km³) and equivalent sea level thicknesses to the volumes. 

7.3.2 Oceans

These contain around 97.3% of the water mass on Earth and provide the major reservoir and the primary source of water via the atmosphere to continents. 86% of global evaporation comes from the oceans and 78% of global precipitation falls directly into the ocean, the remainder returning as runoff of water or ice from the continents. Changes of ocean temperature, radiation and atmospheric circulation will change the rate of precipitation over the continents. The resultant effect on mass distribution between land and sea clearly depends on the reservoir characteristics of other parts of the hydrological cycle as discussed in the introduction (7.1). We regard the ocean as the prime reservoir in which mass changes are evaluated from the response of other reservoirs to changes of climate. We must also consider effects on sea level of thermal expansion of ocean waters caused by climatic changes.

Thermal Expansion

Rising surface temperatures decrease the density of sea water and hence raise sea level. Propagation of temperature changes in the North Atlantic has been discussed by Roemich and Wunsch (1984) and Roemich (1985) using a time series of deep oceanographic observations from 1955 to 1981 at a fixed location off Bermuda. They also compared results of  IGY transects of the Atlantic Ocean from the USA to Spain in 1957 that were repeated in 1981. Seasonal temperature variation in the mixed layer about 100 m deep caused variations of around ±8 cm in mean sea level. This layer varies from 70 to 100 m or more in depth between 45°N and 45°S approximately and the thickness response to warming of this layer can be calculated readily. A 3 °C rise of temperature will increase the thickness of a 100 m layer of sea water in low latitudes by around 9 cm.

The next layer extends to a thermocline at around 6 °C with depth of around 1000 m between 45° N and 45°S. This is formed by cooling of surface waters polewards of these latitudes. This water then slides almost horizontally towards lower latitudes beneath the warmer but more saline surface waters. Temperature changes of this layer will be due primarily to changing heat advection from higher latitudes rather than to vertical conduction and diffusion of heat from the surface. Between Bermuda and Spain, the layer was up to 0.6 °C colder in 1981 than in 1957. A mean cooling of around 0.4 °C over the period would thin the layer by around 4 cm (100 m to 1000 m depth). However, in contrast to the above trend, off Bermuda temperatures increased by around 1 °C between 500 and 1000 m depth from 1970 to 1978.

Below 1000 m the Atlantic water warmed by up to 0.2 °C at a fairly uniform rate from 1957 to 1981 down to a depth of 3000 m or more. A 0.2 °C rise would produce an expansion of a 2000 m layer of around 4 cm. This layer is probably fed from Arctic regions and may have been responding to surface warming in northern latitudes in the first half of this century, while the layer above the thermocline may have responded to post-1940 cooling.

The above figures indicate the order of magnitude of expansion effects of layers on sea level. Roemich found that variations of sea level on the east coast of the USA at Charleston were less than at Bermuda some 1000 km offshore, but the trends were similar. This suggests that sea level on continental coastlines follows density changes in the deep ocean, at least partly.

It is clear that oceanographic theory is not yet sufficiently well developed to give an adequate dynamical explanation of existing data on deep sea density distribution, let alone provide forecasts of its response to climatic change. This could involve large changes of circulation and thicknesses of intermediate and deep layers. However, some estimates have been made assuming the pattern of density distribution does not change. Revelle (1983) finds the increase of sea level due to expansion of water above the thermocline to be at least 30 cm over the next century for a global warming averaging about 4.5 °C. He uses a steady state model for the ocean circulation above the thermocline and makes no estimate of temperature changes below this level.

7.3.3 Atmosphere

The mean water vapour content of the atmosphere is equivalent to a layer of water 25 mm thick over the whole Earth, or 35 mm over the ocean surface. If we assume that relative humidities do not change, a rise of equatorial temperature of 3 °C and of double that at higher latitudes would lower sea level by around 7 mm due to additional water vapour in the atmosphere.

7.3.4 Continents

7.3.4.1 Surface Water: Lakes, Rivers, Soil

Residence times of water on land vary widely, depending on the path from the point of precipitation to the ocean including its passage through lakes. However, seasonal variations of river flow indicate that in most areas the average runoff time is a fraction of a year. Over a period of a decade or a century, significant changes of surface water will be due mainly to changed volumes of inland lakes, both natural and man made. Golubev (1983) puts the volume of man-made reservoirs at not less than 5500 km³, equivalent to subtracting a layer 1.5 cm thick over the ocean surface. Man also extracts around 3500 km³ per year for use in irrigation and other projects, equivalent to a 1.0 cm ocean layer, but much of this soon rejoins the river systems and oceans by drainage and through evaporation and precipitation. There is, however, no agreement on how conversion of land to agricultural use affects the global water balance.

Overall, man's management of water stocks by storage and depletion of groundwater may lower sea level by around one cm per century, a negligible amount.

In comparison with man's usage, natural runoff from land is an order of magnitude greater while atmospheric transfer is over two orders of magnitude greater (Table 7.3). It is difficult to estimate effect on sea level from natural variability of water transport and storage on continents due to changes of the balance between precipitation, evaporation and runoff, but if global temperatures increase, some changes can be expected. This applies especially to the 25% of continental areas which return no runoff to the sea and to drier areas where runoff is small. Quantitative data from such areas are scarce.

Global variability of precipitation is discussed in some detail in Section 6.2.5. Some coherence in precipitation over regions of 10⁶ km² or more is found, along with time scale variability (order 10 years) and a few significant long-scale trends (order 100 years). It is suggested that there is no evidence of any overall global mean trend, or if there was, it would almost certainly fail to reach statistical significance. Corresponding data on variations of evaporation are still more limited.

The above lack of data makes variations in the level of the Caspian Sea more significant. This is fed from a watershed of 3 x 10⁶ km² comprising 2.3% of all non-glaciated lands. This is the largest basin not returning water to the oceans by river flow and it includes both arid and better-watered temperate lands. We therefore use data from the Caspian Sea to suggest the possible magnitude of variations of continental storage rather than assuming that increases and decreases of precipitation and evaporation patterns over all continents will be in balance and so have no effect on sea level. We multiply the observed volume changes of the Caspian Sea by the square root of the ratio of non-glaciated continental areas to that of the Caspian basin as a suggested estimate of changes of continental storage. The changes are inverted in Figure 7.1 to show the effect on sea level.

We note that Caspian Sea levels changed relatively little from 1880 to 1920, followed by decreasing storage (raising sea level) from 1920 to 1960, then by smaller changes since 1960. This follows a similar pattern to the sea level record.

Since changes in Caspian Sea level correspond closely to the cumulative flow deficit of the Volga River at Volgograd over the same period (Micklin, 1971), they should reflect the precipitation/evaporation balance over the whole basin. Related changes of groundwater storage within the basin are also likely.

7.3.4.2 Groundwater

Although the volume is several times larger than the water equivalent of the Greenland ice sheet, the total volume of groundwater and its residence times are quantitatively the least known part of the hydrological cycle. Nevertheless, some estimates of its importance have been made.

Decreases in groundwater levels in central and western USA during this century are estimated at around 390 km³ (1.1 cm SL) in Meier (1983). Falls are attributed mainly to extraction by man. Meier suggests global depletion would be four to six times the above figure, that is a rate of 20 to 30 km³ per year. During this century this would amount to about one half of the volume of water impounded in reservoirs.

Recharging of groundwater reservoirs comes from rainfall not returned to the sea, and so will contribute to extraction of water from the sea. Neither this nor the amount of direct runoff into the sea below sea level is adequately known on a global scale.

7.3.4.3 Smaller Glaciers and Ice Caps

Variations in volume of 25 glaciers measured during 1900 to 1961 were used by Meier (1984) to estimate the contribution to sea level from melting of all small glaciers and ice caps. Antarctica and Greenland were excluded and are discussed later. Many more glaciers have been monitored since 1965, the start of the International Hydrological Decade.

Meier used his long-term data to estimate regional changes of the average mass balance ()-that is the annual mean deficit (or surplus) expressed in water thickness equivalent over the whole glacier. He then applied this figure to the total area of all glaciers in each region, taking the total mass deficit to be proportional to the annual mass amplitude (a) defined by

where b_w is the winter balance and b_s the summer balance (normally negative) averaged over each glacier. The correlation coefficient between and a over his 13 regions was 0.55 and the average fraction /a was 0.23 (S.D. 0.12). The errors in the total contribution of all small glaciers and ice caps to sea level (Figure 7.1) are therefore large, but show that melting of all small glaciers and ice caps could contribute from 1/3 to 1/2 of the observed sea level rise during this century. Meier also notes that small glaciers and ice caps were approximately in balance from 1960 to 1975, the effect is approximately in phase with observed sea level changes. Meier's results suggest that the total addition to sea level from these smaller glaciers due to a CO₂-induced temperature rise of 1.5 °C to 5.5 °C over the next century would be from 9 to 31 cm.

Although Meier's extrapolation of the fraction /a over all glaciers of a region is the best available for small temperate glaciers, its use on larger cold glaciers may be questioned. We therefore make an independent estimate of volume changes in terms of the change in height of the equilibrium line H_E with temperature. This line separates the accumulation zone from the ablation zone of glaciers. Its elevation change with temperature approximately follows the dry adiabatic lapse rate, that is H_E » 100K with H_E in metres, and K in °C. For comparison, Kuhn's (1981) detailed assessment of factors governing H_E used by Ambach (1985) with field data from West Greenland gave H_E/K = +77 m/K for constant cloudiness and 4 m per 1/10 cloudiness at constant temperature.

We now make the crude assumption that glacier volumes change in proportion to 2H_E/H_G, where H_G is the elevation difference from source to terminus of the glacier and H_G / 2 is the estimated elevation difference between the source and equilibrium line. The global change of sea level is then given by

_G is the mean elevation span of the world's glaciers (including ice sheets), V_SG their total volume in water equivalent (Table 7.3) and A_o the area of the world oceans. _G = 1320 m was estimated from the mean elevation span of the 67 glaciers around the world studied during the IGY. For comparison with Meier's extrapolation equation (7.3) gives values of 8 and 28 cm for K = +1.5 °C and +5.5 °C respectively.

Our crude figure is likely to overestimate changes because it neglects time constants and uses the dry adiabatic lapse rate rather than Ambach's smaller figure. The neglect of thickness changes with glacier length leads to underestimation. The assumption that the height range of the accumulation zone is half the height from source to terminus could be in error in either direction and is in any case inferior to Meier's calculations related to total areas and mass balance of both accumulation and ablation zones. While close agreement with Meier's figures is somewhat fortuitous, it helps to support his figures. Furthermore, extrapolation from Meier's figures can be criticised, since melt rates do not bear a linear relation to global temperature change K, or to summer temperatures rather than, say, to (K)³. However, the assumption of a linear relation between K and H_E as a basis for calculations is reasonable.

In any case it appears likely that both the above figures are an overestimate. If the figure of V_SG = 120,000 km³ in Table 7.3 is correct, melting of all small glaciers would add only 33 cm to world sea level, and according to equation (7.3), all small glaciers would disappear if K = 6.6 °C. We need to allow for a realistic spread of glacier elevation ranges to rectify this.

7.3.4.4 Ice Sheets

Although the ice sheets of Greenland and Antarctica contain around 99.5% of land ice shown in Table 7.3, their annual exchange rate amounts to only 78% of glacier iceocean exchange, compared with 22% from smaller glaciers. This does not imply that these ice sheets dominate sea level changes due to glacier ice by a factor of 3.5, since once ice is discharged across the flotation line, its subsequent melting history does not change the total oceanic water mass (liquid and frozen) or sea level (minor density effects excepted). Meltwater runoff from Antarctica is low. As no reliable estimates are available, we assume it to be 2% of the total discharge, a similar or slightly larger figure than the fraction of the surface area covered by the ablation zone. This suggests a total discharge around 36 km³ per year of surface meltwater from Antarctica compared to estimates of Greenland melting ranging from 179 to 315 km³/yr (Table 7.4). The total surface melt-water discharge from these two sources is therefore put at around half all that from small glaciers. The latter figure should be increased by ten per cent to allow for melting of local glaciers on Greenland, not included with these ice sheet estimates or in Meier's figures. These local glaciers are about 5% of the area of the ice sheet and with an ablation area around 10% of that of the ice sheet.

Table 7.4 Annual mass balance of greenland ice sheet in km³

	Bader  (1961)	Benson  (1962)  (summary)	Bauer  (1967)	Weidick  (1984)	Reeh  (1985)
Accumulation	+630	+500	+500	+ 500± 100	+487
Melting	120 to 270	272	330	295±100	169
Iceberg discharge	240	215	280	205 ± 60	318
Net balance	+270 to +120	+13	110	0	0

If surface melting of ice sheets has varied with global temperature in the same way as that of smaller glaciers during the past century, we should add 50% to Meier's figures in the previous section to allow for variations of melting of polar ice sheets. This neglects any contributions from basal melting or from variations in the rate of discharge of solid ice across the flotation line due to global changes of temperature.

Penetration of surface temperature changes into cold ice sheets to depths where they could affect flow takes from centuries to millennia or tens of millennia, depending on ice thickness and surface accumulation rates (Robin, 1970; Budd and Young, 1983; Young, 1981; Oerlemans, 1982). For forecasting changes over the next century or two the assumption of constant flow, or of flow changing linearly with time appears satisfactory. Similarly, basal melting which is due to geothermal heat and frictional heat of ice motion but not to surface melting, should not change significantly over our forecast period.

Although we may assume that flow changes are too slow to affect forecasts for the next century, changes in the rate of surface accumulation as well as surface melting resulting from global warming cannot be neglected as they involve immediate mass exchange with the ocean. A 10% increase of accumulation over the Antarctic ice sheet would require extraction of 180 km³/yr of water from the ocean, lowering sea level by 5 cm/century, while increased melting would have an opposing but probably smaller effect. We therefore discuss polar ice sheets in more detail.

Greenland. Estimates of the mass balance of the Greenland ice sheet over recent decades are shown in Table 7.4. These are affected by poor distribution of data, and do not agree on whether the mass is increasing or decreasing. 

Measurements of change of elevation of the ablation zone of central West Greenland from 194859 by Bauer showed a general lowering of 0.3 m/year. Seckel (1977) found a mean lowering in the same area of 0.24 m/year from 195968 and a thickening in the accumulation zone of around 5 cm per year. Reeh and Gundestrup (1985) interpret data from Dye 3 near the southern dome of the ice sheet as due to thickening of around +3 cm/year with 95% confidence limits of 3 and +9 cm/year. Both changing climate and changing ice flow have been suggested as the reason for central thickening and marginal thinning. Bauer's net balance of 110 km³/year is a similar proportion of the total mass exchange as Meier's (1984) value of /a for small glaciers and we use this figure later, although the consensus among results suggests a mass balance around zero with an uncertainty of ± 100 km³/year (sea level ±2.8 cm/century).

Antarctica. Since Antarctic inland ice covers an area of one thirtieth of the world oceans, any small imbalance between the total mass accumulation rate of inland ice and the total rate of discharge of ice across the grounding line will have a marked effect on sea level.

Budd and Smith (1985) reviewed available evidence from mass balance studies. Earlier estimates of mass outflow had possible errors of a factor of two and indicated that accumulation over the ice sheet exceeded the outflow of ice to the sea by a factor of up to two. A series of field studies over limited regions using Doppler satellite position fixing has now provided a greatly improved quality of data. Budd and Smith conclude that the total influx of about 2 10³ km³/year of ice is nearly balanced by the outflow with a discrepancy from 0 to +20%. This corresponds to a sea level fall from 0 to 11 cm/century.

Present accumulation rates over East Antarctica vary with location in proportion to the mean annual air temperature above the surface inversion and suggest that accumulation rates during the 'Last Glacial Maximum' (LGM) were from 30 to 50% lower than at present (Robin, 1977). However, greater winds indicated by increased dust in an ice core at Dome C dated by isotopic events led Lorius et al. (1984) to estimate the accumulation was reduced by only 25% during the LGM. More recently, studies of an ice core from Vostok dating back to 160 ka BP by Yiou et al. (1985) and by Lorius et al. (1985) provide good evidence that during the last ice age precipitation was around half its present value. These figures indicate that a global warming of 3.5 °C should increase Antarctic accumulation by at least 10% and probably by more than 25% above the present level.

7.3.4.5 Global Warming

If global warming does not cause a catastrophic change of flow of the major ice sheets during the next century, we may assume that their form and flow does not change significantly in this time. Their effect on sea level can then be estimated in terms of changes of ablation and accumulation over the ice sheets. The problem is summarised schematically in Figure 7.4 from Oerlemans and van der Veen (1984). This portrays profiles of the Greenland and Antarctic ice sheets in relation to a simplified mass balance field. This is highly negative at lower levels in Greenland, rises to a maximum then decreases at greater elevations. To a first approximation a climatic warming implies an upward shift in the mass balance field. This would decrease the mass balance of the Greenland ice sheet but that of Antarctica would increase for a limited warming. The net effect on sea level would depend on which ice sheet is dominant and here estimates vary.

Figure 7.4 Height profiles of ice sheets of Greenland and Antarctica in relation to a simplified mass balance distribution

Oerlemans (1982) estimates that a doubling of CO₂ will increase precipitation over Antarctica by 12% and over the next 250 years this would lower sea level by 30 cm. This would be countered by a rise of 20 cm due to melting of Greenland ice according to his use of figures from Ambach (1980). A more detailed estimate is now described.

A warming of 3.5 °C around Greenland would raise the equilibrium line of the ice sheet by around 300 m. This would increase the area of the ablation zone from 16 to 20% of the whole area. If the ablationelevation relationship remained similar to that at present, ablation near the icerock margin in West Greenland would rise from around 3 m/year to perhaps 4.5 m/year, increasing the average rate by 50%. Together these two factors would increase melting by 70 km³ /year. The accumulation zone would decrease in area from 84 to 80% of the ice sheet, but if accumulation rates stay constant or increase by 10% (see Figure 7.4) total accumulation would change by 24 or +24 km³/year leaving a net budget decrease of 94 or 46 km³/year respectively.

Over Antarctica, increases of accumulation rate of 10 or 25% due to a 3.5 °C global warming would require 180 or 450 km³/year respectively of water from the ocean while doubling ablation over twice the area would return 108 km³/year to the ocean, leaving net budget increases in Antarctica of 72 and 342 km³/year.

The combined effect of the above changes on Greenland plus Antarctica ranges from 22 to +296 km³/year equivalent to a sea level change of +0.6 to 8.2 cm/century with the latter figure giving the preferred value.

These very rough estimates indicate that changes of sea level due to global warming affecting Greenland and Antarctica during the next century could be small and cancel each other. However, we may have underestimated changes of ablation or of accumulation associated with global warming on both ice sheets. The net effect of mass balance changes of the two ice sheets on sea level is therefore estimated to be within ±10 cm for a global warming of 3.5 °C over the next century (see Table 7.5).

The broad conclusion of this section is that while changes in the mass of polar ice sheets during the next century might have a significant effect on sea level, it may not be the dominant effect.

7.3.4.6 Global Cooling

The large volumes of ice extracted from the ocean to form ice sheets of the Northern Hemisphere during the Pleistocene period lowered sea level by between 100 and 200 m. This caused some expansion of Antarctic ice over the deeper continental shelf, followed by retreat during interglacials as sea level rose again. Models, such as those of Denton and Hughes (1981) and Drewry and Robin (1983) suggested that lower sea levels would also cause inland ice to thicken to a varying extent. However, Oerlemans (1982) and Alley and Whillans (1984), when incorporating lower accumulation rates during ice ages into their models, suggest that inland ice elevations may be smaller during ice ages. The latter also included the effect of changing sea level on their ice flow model which acts in the opposite direction by increasing the grounded area during ice ages. It is only recently that Lorius et al. (1984) have found evidence that ice in Central Antarctica may have been thinner during the last ice age. The contrast with the Denton and Hughes (1981) model is shown in Figure 7.5. They suggested an increase of Antarctic ice volume during the last ice age around 10 x 10⁶ km³ whereas Figure 7.5 suggests the increase could not have been greater than 3 x 10⁶ km³ and could have been much less.

Recent evidence indicating that ice levels were lower in Central Antarctica during the last ice age includes:

1. Studies of total gas content of ice cores, equivalent to a recording aneroid barometer. Raynaud and Whillans (1982) and Lorius et al. (1984) used this to show that the surface in the region of Byrd Station was around 200 m lower during the last ice age than at present and around Vostok it may have been 100 m lower at that time. 

2. Comparison of isotopic ¹⁸O profiles at Byrd, Vostok and Dome C stations suggests that a similar lowering of surface elevation occurred at all stations, with lowering at Dome C and Vostok being somewhat more than at Byrd.

3. Analysis of the temperature depth profile at Dome C (Ritz et al., 1982). 

4. Accumulation of meteorites on ablation areas inland of mountains over periods of 10⁵ years or more.

5. Glacial geological evidence of greater flow of ice into McMurdo Sound dry valley during interglacial periods shows that ice inland of mountains was higher at that time (Drewry and Robin, 1983).

One feature that would increase thinning of inland areas while coastal areas thickened would be if ice streams and trunk glaciers through mountains continued to drain inland ice with little change from their present elevation. At present they drain an estimated 80% of the area of the ice sheet, comprising almost all discharge from areas more than 200 km inland of the flotation line. Until the sliding mechanism governing the flow of such ice streams is understood and incorporated in models, the results from other modelling studies cannot be fully effective. Conclusions need to be drawn from the types of field evidence listed above.

Table 7.5 Changes of water storage affecting the sea level from 1900-1975

Storage type	Klige (1982)		This survey			Source
	km3/yr	SL effect (mm/year)	km3/yr		SL effect (mm/year)
Lakes	63	+0.17	72		+0.20	Caspian SL x 6.6 in Figure 7.1
Underground water	136	+0.38	25		+0.07	Meier (1983) mean value due to
						man's extraction
Antarctic	315	+0.87	+100		0.28	Mean from Budd and Smith (1985)
Greenland	82	+0.23	110		+0.30	Bauer (in Table 7.4)
Arctic Islands	12	+0.03	145		+0.40	Meier (1984)
Mountain Glaciers	3	+0.01
Man-made reservoirs	+69	0.19	+69		-0.19	Golubev (1983)
Total	542	+1.50	183		+0.50
Ocean expansion					+0.38	From Gornitz et al. (1982)
						k = 1.2 cm2/sec
Observed		+1.50			+1.01	Gornitz et al. (1982)

Figure 7.5 Estimated ice-thickness changes over Antarctica since last ice age

7.4 LONG PERIOD AND CATASTROPHIC CHANGES 

7.4.1 Climatic Stability

In contrast to the growth and retreat of vast ice sheets over continents in the Northern Hemisphere during the last 1.5 million years, the ice sheets of Antarctica and Greenland appear to have undergone relatively small changes. Once an ice sheet covers an entire continent or island, including the continental shelf, excess accumulation is returned to the ocean in icebergs and iceshelves without melting. Once afloat, melting of ice has no further effect on sea level.

As temperatures increase over such ice sheets, effects will differ between Greenland and Antarctica as seen in Figure 7.4. On Greenland, as the proportion of surface melting to iceberg discharge increases, ice flow will be diverted from the large outlet glaciers to the large ablation zones. When surface melting and the remaining iceberg discharge exceed accumulation, the ice sheet will no longer be stable in relation to climate and it will diminish in size. Our estimate from mass balance sums along the lines of the previous section suggests that this will occur for a temperature rise of 6 °C. Verbitsky (1982) gives a corresponding figure +5 °C. Even if the melting rate increases still further to an excess of 600 km³/year above the accumulation, sea level would rise only 20 cm/century. We use half this figure as our upper limit for possible warming over the next century.

Antarctica

Similar arguments to the above applied to Antarctica suggest that a major climatic retreat of the inland ice of East Antarctica due to surface melting would require a temperature rise of around 10 to 12 °C (Verbitsky, 1982) or around 15 °C (Robin, 1979).

It is useful to relate Figure 7.4 to the development of Antarctic glaciation on the geological time scale. The Antarctic crustal plates drifted to near their present position around 38 Ma BP (Kennett, 1978; Drewry, 1976). Mountain glaciation was followed by development of an ice sheet on East Antarctica some 12 to 14 Ma BP. This ice sheet would have been plotted on Figure 7.4 in a similar position to present-day Greenland. Gradual cooling that started around 22 Ma BP, presumably on a global scale, let this ice sheet expand over West Antarctica by around 4 to 6 Ma BP, at which stage the ice sheet was probably at its maximum volume covering the entire continental shelf. This would take place when the bulk of the accumulation zone of the Antarctic ice sheet lay within the zone of maximum accumulation of Figure 7.4. Further lowering of temperature would be matched by a lowering of the mass balance field on Figure 7.4 and correspond to the formation of the Greenland ice sheet after 3 Ma BP, as shown by studies of marine cores (Berggren, 1972; Shackleton and Opdyke, 1977). This continued global cooling would eventually decrease accumulation on the Antarctic ice sheet and lead to some diminution in its size. It is worth noting that although the global temperature was apparently warmer than today around 4 to 6 Ma BP, melting by warm ocean waters apparently did not prevent the growth of the West Antarctic ice sheet. Kennett's (1978) review suggested that some sea ice was present around Antarctica at 38 Ma BP. He notes ice rafting of debris again at 22 Ma BP which then increased around 1214 Ma BP, around 46 Ma BP and after 1.8 Ma BP during the Quaternary. Microfossil evidence in marine cores indicates that pack ice, if not the source of icerafted debris increased along with the debris. These observations suggest that current global circulation models that result in early removal of Antarctic sea ice cover with rising CO₂ should be viewed with caution.

The time constants involved in changing ice levels of Antarctica are important. Rising sea levels after glacial periods led to the disappearance of thicker coastal ice at much the same rate as the ice sheets of the Northern Hemisphere receded, according to both field evidence and model studies by Alley and Whillans (1984). In coastal regions, ice thicknesses that are in equilibrium with the present climate have changed little in several localities since 6000 BP. Further inland time constants must be much longer, probably several tens of millennia. An increase of accumulation of l cm/year (20%) would take 20,000 years to raise the ice level of central regions by 200 m if ice flow was unchanged, and longer if allowance for flow changes is included. Evidence that the ice surface may be rising by this amount 18,000 years after the last glacial maximum, as suggested by Budd and Smith (1985), is consistent with such a long time constant. The central Antarctic ice sheet is therefore unlikely to reach a thickness in equilibrium with the climate during an interglacial period of only 10,000 or 20,000 years. 

Although glacial periods tend to be several times longer than interglacials, the same comment applies in relation to lowering of ice levels as a result of lower accumulation. We may therefore expect the amount of lowering to vary with the length and severity of the glacial period.

The glacial period from around 200 ka BP to 135 ka BP preceding the last interglacial was both colder and had a more prolonged cold period than that from around 70 ka BP to 15 ka BP as shown by evidence from glacial deposits in the Northern Hemisphere (Flint, 1971) and suggested by marine core data such as those of Shackleton and Opdyke (1973). Greater lowering of the ice of Central Antarctica before the last interglacial than before the present one, together with the long time constant for recovery would then result in the ice of Central Antarctica being lower during the last interglacial than at present. A difference of 200 to 300 m between these levels during the last and present interglacial would explain one major problem of the last interglacial period (Robin, 1985).

7.4.2 The Last Interglacial

Considerable attention has been given to the possible instability of the West Antarctic ice sheet during the last interglacial for two reasons. The first is evidence of a rise in sea level of 7 m in equatorial regions around 125 ka BP, together with some early marine core data that suggested temperatures may have been some 3 °C warmer at that time. If the sea level rise were worldwide, this would require adding an additional volume of water to the oceans equivalent to the volume of the present Greenland ice sheet or to the volume of water above sea level in West Antarctica today. Because much of the ice rests on rock well below sea level, disappearance of the West Antarctic ice sheet due to instability has received much attention. This is the second reason for interest in this period, so we consider both problems.

The best information on climatic condition during this period is given by 23 well-known research workers in a report 'The last interglacial ocean, CLIMAP', Ruddiman (1984). The main evidence comes from detailed oxygen isotope analyses and biotic census counts in 52 cores across the world ocean. Their summary states 'The first order conclusion about last interglacial climate is that it was extremely similar to the current climate. The total volume of ice was probably equal to or slightly less than today's with any decrease due to calving of West Antarctic ice and atmospheric ablation of Greenland ice'.

Although major changes of ice volumes are deduced from isotopic data from marine cores, the noise level in the ¹⁸O signal was 50% or more above that of a possible signal corresponding to a worldwide sea level 7 m above the present level during the last interglacial. There is therefore no isotopic evidence of ice sheet retreat. The report states that the strongest evidence for an ice volume difference during the last interglacial is from dated coral reefs.

Effects discussed in Section 7.2.1, such as the persistent equatorial bulge during the Holocene and the non-uniform changes of sea level over the world proposed by Clark et al. (1978), might help to explain the 7 m high sea level on tropical coral reefs during the last interglacial without requiring much change from our present ice volume.

Other reasons for doubting that the West Antarctic ice sheet was greatly reduced in volume during the last interglacial are:

1. There is no evidence from marine cores around Antarctica of any hiatus in sediments due to ice sheet collapse and associated changes of ocean circulation.

2. The greater extent of the Antarctic ice sheet around 4 to 6 Ma BP when global temperatures were still higher is discussed in Section 7.4.1.

3. Antarctic bottom water production during the last interglacial was higher than today according to ¹³C studies of marine cores by Duplessy et al. (1984). This suggests that sea surface freezing and the thickness of ice shelves were then no less than at present.

At both Camp Century in Greenland and Byrd station, Antarctica, ¹⁸O values in near-basal ice indicate surface temperatures were similar or slightly above (+2 to +3 °C) present temperatures. This could be due to a lowering of surface elevations by 200 to 300 m or to a slightly warmer climate or to a combination of both factors (Robin, 1977). These small changes are incompatible with the collapse of either ice sheet. A third possibility is that ¹⁸O ratios in ice near bedrock have been changed by isotopic differentiation during the basal melting and refreezing that occurred at both sites.

Results from the first ice core (to 2083 m depth) to span the last interglacial and recover ice from the preceding glacial period are presented in Lorius et al. (1985). The ¹⁸O values at Vostok, where the core was obtained, were around 2 ‰ higher during the last interglacial than at present. The authors, on the evidence from Lorius et al. (1984) discussed in Section 7.3.4.6, assume the surface elevation has undergone little change and interpret the data as indicating the regional climate at the present elevation at Vostok was about 3 °C warmer than now. An alternative interpretation is that since global climate was very similar to the present, the ¹⁸O change at Vostok was due to a change of surface elevation rather than temperature. The warming of 3 °C would then indicate that the ice surface was then around 300 to 350 m lower. This interpretation fits the suggestion at the end of Section 7.4.1 that the mean surface was 200 to 300 m lower than at present at the end of the last interglacial.

Surface lowering of the above amount over the area of around 8 x 10⁶ km² shown in Figure 7.5 would mean that the volume of ice of central Antarctica was some 1.6 to 2.4 x 10⁶ km³ less than at present. Then if glaciers in Antarctic coastal regions and elsewhere were of similar volume to the present under a very similar climate, the ocean volume would be greater by an equivalent amount. This would provide sufficient water to explain sea level some 5 to 7 m higher during the last interglacial. This hypothesis avoids the difficulty of having to melt large sections of the Greenland and Antarctic ice sheets or having the West Antarctic ice sheet collapse to provide water needed to raise ocean levels by up to 7 m at a time when the climate was similar to the present. Furthermore, the higher sea level during the last interglacial need not be interpreted as an indication of higher temperature (Robin, 1985).

The question of how much the surface elevation and/or the climate around Vostok differed from the present may be answered when total gas content measurements on the ice core become available. This should help to settle the question of whether a catastrophic collapse of the West Antarctic ice sheet took place during the last interglacial period. If the answer is not clear, the controversy is likely to continue since glaciologists', opinions differ widely. Field research on the problem continues.

7.4.3 Dynamic Stability of West Antarctic Ice Sheet

We now consider the problem of stability of marine ice sheets such as West Antarctica against climatic change. It is suggested that ocean warming will greatly increase the rate of bottom melting of ice shelves, such as the Ross and Filchner-Ronne Ice Shelves, and lead to lowering of frictional restraint by grounded ice and ice boundaries, and hence permit rapid deglaciation to take place. Although advances over the past decade have increased our understanding of the problem, a precise answer is not possible because of our lack of understanding of oceanic heat transport as much as that of ice dynamics.

Beneath the Ross and Filchner-Ronne Ice Shelves, it is clear that much melting is due to circulation of continental shelf water at a temperature of the freezing point of sea water. As salt is rejected during freezing at the ocean surface, the denser water sinks so that the whole column of sea water of around 500 m depth over the continental shelf is cooled to 1.9 °C (Figure 7.6). It appears that it is this water that is responsible for melting ice at still lower temperatures governed by the depth (pressure) of the ice-water interface (2.2 to 2.8 °C or more) beneath the inner parts of the Ross and Filchner Ice Shelves. Such ice shelf water emerges from beneath the front at 2.0 °C or colder (Figure 7.7.). Seasonal warm water of the top 100 m is mainly at too shallow a depth to penetrate far beneath ice shelves, but a core of warmer waterAntarctic circumpolar deep waterpenetrates beneath part of the ice front of the Ross and Ronne Ice Shelves (not Filchner) and contributes to melting beneath some outer parts of these ice shelves (Figure 7.7). The same water, at temperatures up to + 1.0 °C, dominates melting beneath the ice shelf of King George VI Sound (Potter et al., 1984) and has also been observed on the continental shelf of the Amundsen Sea. This matches the absence of extensive ice shelves where the Pine Island Glacier and Thwaites Glacier discharge into the Amundsen Sea.

Figure 7.6 The observed temperature (q) and salinity (S) profiles below the Ross Ice Shelf at the J9 drill camp (from MacAyeal, 1984)

Figure 7.7 Summertime temperaturedepth distribution off the front of the Filchner-Ronne Ice Shelves, Antarctica. Also shown is the approximate depth to the base of the ice shelf 20 km south of the ice front (dashed line) and the depth of ice at the ice front (dotted line) estimated from the height of the floating ice cliffs. (Oceanographic data from Gammelsrød and Slotsvik, 1982. Glaciological data from Robin et al., 1983)

The suggestion that rapid collapse of the West Antarctic ice sheet has already started due to discharge of these glaciers into the Amundsen Sea can be countered. McIntyre (1983, 1985) has pointed out that a sharp surface slope around the head of Antarctic ice streams and large glaciers seen on Landsat images at a number of locations indicates the line across which ice transport changes from dominant internal deformation to basal sliding. The line on Landsat images corresponds closely to a sharp increase of bedrock depth in the flow direction seen in radar depth profiles. In deglaciated countries, this corresponds to the steep slope found at the head of many fjords as slopes change abruptly from elevated upland plains. The onset of sliding results from sudden steepening of basal slopes and is stabilized in position where the bottom slope changes. Both Pine Island Glacier (Figure 7.8) (Crabtree and Doake, 1982) and Thwaites Glacier (McIntyre, 1983, 1985) show these features.

Any change of location of the line where rapid sliding starts is unlikely to occur until bottom melting increases sufficiently to bring the ice base above the bedrock scarp. This requires a rise from around 1300 to 1000 m at the flotation line of Pine Island Glacier and 1100 m to 750 m beneath Thwaites Glacier. Crabtree and Doake estimate that a change of thickness of 10% would require an increase of bottom melting of 2 m/year beneath Pine Island Glacier. To decrease thickness at the grounding line to above the scarp level on this basis would require an increase of melting of 3.5 m/year above the present rates. Present melting may already approach the 2 m/year found from salinity and isotopic data beneath the northern part of ice shelf of King George VI Sound by Potter et al. (1984). Once melting raises the grounding line to the scarp level, rapid sliding of grounded ice could commence. The time taken to affect sea level is then a function of ice sheet dynamics.. Bentley (in Revelle, 1983) estimates a minimum of 200 years for the West Antarctic ice sheet to collapse through Pine Island and Thwaites Glaciers. Other estimates for collapse of the West Antarctic ice sheet range from under 100 to many hundred years, but the many estimates available are tentative because of lack of knowledge of the dynamics of sliding of fast ice streams.

Figure 7.8  Pine Island Glacier, Antarctica. (a) Longitudinal profiles of surface and base obtained by airborne radio echo sounding flight on 6 February (dashed line) and 9 February (solid line), 1981. (b) Landsat image showing flight lines. The grounding line is shown by linked arrows. Here downslope sliding leads to floating ice of decreasing thickness showing stream lines (due to varying thickness across glacier) in contrast to the dimpled appearance of inland ice moving over an irregular bedrock. (Based on Crabtree and Doake, 1982)

Other problems to which an answer is needed include: How much warmer will the Antarctic circumpolar deepwater become due to effects of rising CO₂? What time lag will be involved in this warming? Will circulation of this water beneath ice shelves increase or decrease due to changes of wind stresses on the sea surface and the changing density distribution with depth in the ocean? When may rising CO₂ effects be sufficient to prevent extensive formation of pack- ice and of shelf water at 1.9 °C over continental shelves of Antarctica?

The complexity of effects of changing ice loads on the Earth's crust beneath West Antarctica, of increased accumulation rate accompanying CO₂ warming and of increased melting by oceanic waters is such that a precise answer is not possible at this time.

7.5 COMPARISON

To illustrate lack of knowledge of factors governing global sea level, Table 7.5 compares estimated quantities from this report adjusted to cover the period 19001975 with corresponding figures given by Klige (1982).

The emphasis given to ocean water expansion and melting of small glaciers in Figure 7.1 is missing or almost negligible in Klige's paper. The biggest differences come when considering the two largest storage reservoirs. This paper largely neglected natural variations of underground storage, partly due to lack of knowledge and partly because mechanisms causing such large variations of storage are not understood. Agreement over figures for Greenland is not significant as other investigators differ greatly from these figures. Assessment of recent changes of the Antarctic ice mass shows the greatest difference. This paper suggested increased storage equivalent to sea level falling at up to 8.2 cm/century while Klige suggested decreased storage equivalent to a sea level rise at a rate of 8.7 cm/century.

Clearly much research needs to be carried out to obtain a satisfactory knowledge of factors affecting sea level. In this situation use of the simple linear correlation between global sea level and temperature records during the past century to predict future changes appears the only practical basis for a forecast. While such extrapolation is valid for some processes, it is not valid for all. 

7.6 CONCLUSIONS

• It is estimated that the prediction of global warming of 3.5 °C ± 2.0 °C due to CO₂ doubling would lead to a sea level rise of 80⁺⁸⁵_-60 cm. This figure is based on the correlation between past changes in sea level and temperature in Section 7.2.

• To predict future changes of sea level at any location, sea level trends over the past few thousand years at that location should be added to the figures above predicted from global warming.

• Over the next century major physical factors affecting sea level due to a postulated global increase of atmospheric temperature of 3.5 °C are likely to be

1. Thermal expansion of ocean waters could expand the top 100 m of tropical water by 10 cm and the next 900 m by at least 20 cm, and eventually by 50 cm or more. Below that level we would expect cold deep water to continue to flow from polar regions, perhaps at a slightly higher temperature involving a slow expansion of 10 to 20 cm with little effect during the next century. Changes in the depth of the thermocline and hence of the vertical distribution of temperature could, however, produce larger changes than the simple expansion figures given above. 

2. Melting of smaller glaciers and ice caps could produce a rise of around 20 cm ± 12 cm of sea level.

3. Changes of melting and accumulation of the ice sheets of Greenland and Antarctica will tend to counterbalance each other. Due to uncertainty of opposing trends, the effect on sea level should be within ± 10 cm/century and may well be negative (i.e., contribute to a lower SL).

4. Changes of water storage on land in lakes, rivers, reservoirs and groundwater are very difficult to predict and while unlikely to exceed ±10 cm/century (Table 7.5) will probably be a fraction of this value.

5. A catastrophic collapse of the West Antarctic ice sheet is not imminent, but better oceanographic knowledge is required before we can assess whether a global temperature rise of 3.5 °C might start such a collapse by the end of the next century. Even then it is likely to take at least 200 years to raise sea level by another 5 metres. 

ACKNOWLEDGEMENTS

Special thanks for provision of relevant material are due to Dr C. S. M. Doake and Mr R. D. Crabtree of the British Antarctic Survey, Dr M. F. Meier of the U.S. Geological Survey, Dr T. M. L. Wigley of the Climatic Research Unit of the University of East Anglia, Dr J. Oerlemans of the Institute of Meteorology and Oceanography of the University of Utrecht, Dr N. J. Shackleton of the Quaternary Research Laboratory, University of Cambridge, and Dr T. Hushen of the U.S. Academy of Sciences.

Detailed constructive and critical reviews of the first draft of this chapter have been received from Dr M. F. Meier, Dr T. M. L. Wigley, Dr J. Oerlemans, Dr V. Kotlyakov, and Dr B. R. Döös. Further helpful comments from a wider and less specialised review group have come from: Dr R. Bindschadler, Dr A. Berger, Dr H. W. Ellsaesser, Dr H. L. Ferguson, Dr R. M. Gifford, Dr J. Goudriaan, Dr G. McBean, Professor A. S. Monin, and Professor J. D. Woods.

With our lack of knowledge of certain aspects of the hydrological cycle and of the dynamics of the oceans and of polar ice sheets, forecasting of global changes of sea level involves considerable extrapolation and speculation. While comments by referees have resulted in considerable improvement both in the content and in the presentation of this chapter, it has not been possible to incorporate or sometimes to reconcile suggestions from different reviews. The article does not therefore reflect the views of all referees and responsibility for the contents lies with the author.

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