Reeh (1985) attributed the thickening to the downward movement of harder Holocene ice as a result of lower impurity content than the Wisconsin (ice age) ice.
Snow and Ice Covers: Interactions with the Atmosphere and Ecosystems (Proceedings of Yokohama Symposia J2 and J5, July 1993). IAHS Publ. no. 223, 1994.
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Response of the Greenland ice sheet to ice age cycles and to recent climate changes AYAKO ABE-OUCHI Center for Climate System Research, University of Tokyo, Tokyo 153, Japan
Abstract The Greenland ice sheet is seldom in a steady state, because of climate change and transient ice dynamic response. Observations on elevation both by geodetic methods on the ground and by satellite altimetry suggest a slight change in elevation of about 10 mm per year at the centre part of the ice sheet. The aims of this work are to estimate the cause of the variation of the height in the interior part of the ice sheet and to predict future change due to global warming. Several numerical experiments were carried out using a two dimensional ice sheet model, which calculates the ice sheet surface and bed geometry, ice velocity, dating of the ice (isochrone) and ice temperature distribution time-dependently. It was applied along the EGIG flow line, where the data for the input and verification are the best documented for Greenland. It is suggested that the recent precipitation history is important for reconstructing and interpreting the present change in elevation. The present change of the height in the interior is mainly controlled by the decadal to millennial variation of precipitation; conversely the influence of the climatic transition from the glacial to interglacial condition is found to be much smaller. The future global warming may possibly lead the ice sheet edge to retreat, but lead the interior part to grow for the first centuries. The interior part will be influenced mainly by the increase of precipitation until the influence of the retreating edge reaches to the interior a few hundred years later.
INTRODUCTION To identify the influences of past climates and the recent climate on the Greenland ice sheet and to investigate the cause of the change of the ice-sheet mass are keys to understanding its present condition and to predicting the future influence of anticipated global warming. The change in the mass balance of glaciers and ice sheets will lead to a rise in sea level due to global warming: it is anticipated that further increase in the sea level, which occurs already at the rate of 0.001 m a"1 (m per year, Warrick & Oerlemans, 1990), will accelerate in the next century. At present, it is not conclusively known whether the Greenland ice sheet is growing or shrinking. However, there is some information on the height in the interior that suggests it is changing by the order of magnitude of 0.01 m a"1 as determined by geodetic surveys of the ice surface and topographic mapping using satellite altimetry (Van der Veen, 1991 ; Seckel, 1977; Reeh & Gunderstrup, 1985; Kostecka & Whillans,
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1988; Kock, 1993; Zwally et al., 1989). Reeh (1985) attributed the thickening to the downward movement of harder Holocene ice as a result of lower impurity content than the Wisconsin (ice age) ice. On the other hand, Zwally (1989) explains it as a result of a warmer polar climate in this century. Abe-Ouchi et ah (1994) discussed that the change must be due to recent climate change, although the cause-effect relationship was not yet clear due to the influence of the ice age. In this paper two important issues are addressed. One is to distinguish the influence of past climatic changes, such as glacial/interglacial transition, on the present ice sheet condition of Greenland from that of recent climate change. The other is to discuss the possible behaviour of the ice sheet in the near future. Since the response time of the ice sheet to climate change is as long as the climate change ( ~ 10 to 10 000 years), various time scales of climate change are taken into account and compared. After a brief introduction of the ice sheet model in this study and the climatic scenarios used in the experiments, the influence of the Wisconsin/Holocene climatic change on the ice sheet geometry is examined through 100 ka with a steady climate after the transition. The response of the ice sheet to a decadal to millennial variation is also examined, and finally the effect of global warming on the ice sheet is discussed.
METHOD 2-D ice sheet model For the present study, a model is used which permits calculation of the transient geometry, flow field, ice temperature, and the age of ice, taking into account a given climatic history. Both the long term effects of the glacial/interglacial transition and shorter term climatic changes such as variations during the Holocene are considered. For the presented case study, a cross profile of Greenland at about 70-72°N which corresponds approximately to the EGIG (Expédition Glaciologique International au Groenland) profile (Hofmann, 1974) is used. It is considered as a good representation of the middle part of Greenland including the Summit site. This profile is also well suited to the planeflow (2-dimensional) approximation due to the broad extension of the relatively uniform slopes, which ensure small transverse gradients (Abe-Ouchi, 1993). A time dependent numerical ice sheet model for the plane flow approximation was developed (Huybrechts, 1990; Abe-Ouchi, 1993). The model solves the equations of mass, momentum and energy conservation for a two-dimensional section following the flow field of the ice. It allows for an evolution of the free surface as a result of ice flow and mass flux and for an isostatic bed adjustment with a time lag. Ice was treated as an incompressible heat conducting, viscous fluid. A finite difference scheme was used to solve the equations for certain set of boundary conditions, which are bed topography and climate conditions. A brief description is given in the following. More details on the performance of the model can be found in Abe-Ouchi (1993) and Abe-Ouchi et al. (1994). The evolution of surface geometry was determined by applying the prescribed surface accumulation function as a boundary condition to the continuity equation for the ice thickness: !^ = - ^ +^ +^ dt dx p ; dt
(1)
Response of the Greenland ice sheet to ice age cycles
97
with the surface elevation hs, the vertically integrated horizontal ice velocity q, the bed elevation hb, the surface mass balance M, and the density of ice p7. The shallow ice approximation was applied (Hutter, 1983), thus horizontal heat conduction is neglected in the thermo-dynamic equation: dT , d2T dT ÔT Q — = k-—--u——w— + — Qz2
dt
dx
dz
n. (2)
PjC
where 7is the temperature, u and w are the horizontal and vertical velocity components, respectively, and Qlpf denotes the strain heating. As a boundary condition, the geothermal heat flux for Greenland was taken as 1 hfu (heat flow unit), which is 0.042 W nr 2 (Turcotte & Schubert, 1982, p. 136), at a depth of 3000 m below sea level. Ice is treated as a incompressible non-Newtonian fluid with a polynomial stressstrain relationship following the standard third-power Glen's-flow law (Paterson, 1981). Introducing the shallow ice approximation, the horizontal velocity component can be calculated by: -2
dhs
mA(hs-z'f dz'
(3)
with the gravity g. The temperature and velocity fields are coupled through the rate factor A = ACT), which shows a strong dependence on temperature (Paterson, 1981). The "softening" parameter m is introduced in order to take into account the impurity effect of the ice. In order to follow the different "impurity" effect, the particle track method was applied: d£ = X ^ (4) dt dz2 D is the date of the accumulation of an ice particle at the surface. On the right-hand side of (4) we introduced an artificial diffusion term in order to avoid numerical instabilities occurring near the base. The diffusion coefficient X was chosen small enough (X = 0.1) so that the overall solution of theD-field is not different from the solution with X = 0, except for the basal layer. Climate forcing An idealized climate model for the ice temperature and the mass balance at the surface was suggested by data collected along the EGIG profile (Ohmura, 1987; Reeh, 1989; Ohmura & Reeh, 1991, and references therein). The surface temperature 7^ was chosen as a linear function with a lapse rate a r and the temperature T0 at sea level: T, = T0-aTz
(5)
and the balance M as: M = mm[am(z-ELA),Ac]
(6)
where am denotes the melt lapse rate, ELA the equilibrium line altitude, z the altitude, and Ac is a given amount of annual snowfall (accumulation rate). As a first approxi-
Ayako Abe-Ouchi
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mation, am = 0.005 a"1 and aT - 0.008 K m were always kept at fixed values. Climatic conditions are defined through the three climatic parameters T0, ELA and Ac in equations (5) and (6), and additionally through the "softening" parameter m (enhancement factor) in equation (3). A change in the. ELA is mainly sensitive to summer temperatures (Ohmura et al., 1992), which strongly influence the melt. In order to examine the difference in the steady state of glacial and interglacial ice sheets and their transient behaviour, two different boundary climatic conditions are adopted which are (1) the glacial condition and (2) the interglacial condition. The parameters defining these conditions are given in Table 1. The glacial and interglacial accumulation rates Ac are estimated from ice core analysis, and it is believed that the precipitation rate during the last ice age was about half of that at present (Beer et al., 1984; Clausen et al., 1988; Reeh, 1990). The estimation of glacial and interglacial surface ice temperatures and equilibrium line altitudes are based on data provided by Reeh (1989) and Ohmura et al. (1992). The change of the softening parameter m (enhancement factor) was suggested by Paterson (1991). Cross sections of the calculated steady states are depicted in Fig. 1. The interglacial steady state ice sheet is slightly thicker than the glacial steady state ice sheet. The calculated highest point on the ice is not always at the same position: it migrates towards the centre during thickening of the ice. The elevation of "Summit", which is defined as a fixed point 600 km from the west coast and the mean thickness of the ice sheet are given in Table 2 for both steady states.
NUMERICAL EXPERIMENTS AND RESULTS The influences of ice age upon the present ice sheet condition The response of the ice sheet to a climatic change from glacial to interglacial conditions is first analysed. For simplicity, a step-change is assumed as a fair approximation for the sensitivity study. As an initial condition for the ice sheet a steady state under the glacial climate was used. In order to calculate this, the integration of the equations was started from "no-ice" conditions and continued for "glacial" climatic conditions for 500 ka. During the last 300 ka of this integration the distribution of the accumulation date D (equation (4)) of the ice was calculated to obtain its steady state representation. Then the climatic condition was set to the interglacial stage, by assuming an immediate Table 1 Numerical values for the four parameters defining the scenarios for "glacial" and "interglacial" climatic conditions: ELA denotes the mean equilibrium line altitude, Ac the accumulation rate, m is the softening parameter and T0 the ice surface temperature at sea level. Experiment
Parameters
"Glacial" condition
"Interglacial" condition
A
EL4(ma.s.l.)
100
1100
1
B
Ac (m a" ), accumulation rate
0.15
0.3
C
m, softening parameter
3
1
D
T0 (°C), temperature at sea level
—15
—5
99
Response of the Greenland ice sheet to ice age cycles 4500
_•
' ' • i ' ' • i i • ' ' • i i > ' ' i ' ' i > i • > ' i i • • ' ' i • i > > i > • ' ' i ' > ' '
; Steady State Topography "Glacial" condition in broken line 4000 1 ; "Interglacial" in solid line 3500 3000 Q-2500
2000 1500
1000 500 0 -500 -100
0
100
200 300 400 500 600 700 Distance from the coast (km)
800
900
Fig. 1 Cross sections of the calculated "glacial" (dashed line) and "interglacial" (solid line) steady state ice sheets.
Table 2 Summit elevation and mean ice thickness over the EGIG cross section for the calculated "glacial " and "interglacial" steady state ice sheets. "Glacial"
"Interglacial"
Summit elevation (m)
3185
3346
Mean thickness (m)
2031
2219
transition (which is referred to as "Full" scenario). For the following 400 ka the response of the ice sheet was calculated to obtain the new steady state. The transient response of the ice sheet to the climatic transition is shown by the curve labelled "Full" in Fig. 2. The volume and thickness changes occur in three phases with different time scales: (1) a rapid growth during the first 3000 years (3 ka) is followed by (2) a slower shrinkage for about 20 ka at most by the rate of 0.004 m a"1 and (3) a subsequent slow growth until a steady state is reached after 400 ka. If it is assumed that the model time span from 10-11 ka corresponds to the Wisconsin-Holocene transition, then the present ice sheet situation falls within the second phasei Although the elevation of the Summit at present is about 100 m higher than that at the end of the "glacial" stage, it is decreasing by 0.004 m a"1 during the second phase, mainly due to the increase in ice temperature. To study the contribution of each of the four climatic parameters to this complex behaviour, four different calculations were carried out, where each parameter in turn was switched to its "interglacial" value while leaving the others at their "glacial" values: this involved successive changes in ELA, accumulation rate, softening parameter, and
Ayako Abe-Ouchi
100 •
'
1
' ' ' '
-200
-
\
•
*• ! ;\
I -400
\ -600
-
:
-
: \V !
. •
-800 -••
i \
+3K +5K
: i
-1000 0
1000
.
2000
,
,
,
t
,
,
,
3000 4000 year
, , i , , . , i ,
5000
6000
7000
Fig. 4 Time sequence of the summit height (a) and the cross section volume change (b) of the ice sheet responding to a warming of 0.5 K, 3 K and 5 K of climatic change.
Acknowledgements This study was mainly done while the author was in the graduate course of ETH, Switzerland. The author is grateful to A. Ohmura, K. Hutter, H. Blatter and J. Jouzel for encouragement and valuable comments. The author is supported by the JSPS and Grant-in-Aid for Encouragement of Young Scientists.
Response
of the Greenland
ice sheet to ice age
cycles
105
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