SCOPE 29 - The Greenhouse Effect, Climatic Change, and
Ecosystem
7
|
Changing the Sea Level
|
|
Projecting the Rise in Sea Level Caused by Warming of the Atmosphere |
|
G. deQ. ROBIN |
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
atmospheric
ocean 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
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)
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
|
St
= aKt-t0+ b |
(7.1) |
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 bw is the winter balance and bs 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 HE 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 HE
» 100K with
HE in metres, and
K in °C. For comparison, Kuhn's (1981) detailed
assessment of factors governing HE used by Ambach (1985) with field data from
West Greenland gave HE/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 2HE/HG, where
HG is the elevation difference
from source to terminus of the glacier and HG / 2 is the estimated elevation
difference between the source and equilibrium line. The global change of sea
level is then given by
|
2 100K |
VSG |
|
|
SL = |
|
|
(7.3) |
|
 G
|
Ao |
|
G is the mean elevation span
of the world's glaciers (including ice sheets), VSG their total volume in water
equivalent (Table 7.3) and Ao 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 HE 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 VSG = 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:
-
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.
-
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.
-
Analysis of the temperature depth profile at Dome C (Ritz
et al.,
1982).
-
Accumulation of meteorites on ablation areas inland of mountains over
periods of 105 years or more.
-
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
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 t