11.2.2.4 Evolution of area

The above calculations all neglect the change of area that will accompany loss of volume. Hence they are inaccurate because reduction of area will restrict the rate of melting. A detailed computation of transient response with dynamic adjustment to decreasing glacier sizes is not feasible at present, since the required information is not available for most glaciers. Oerlemans et al. (1998) undertook such detailed modelling of twelve individual glaciers and ice caps with an assumed rate of temperature change for the next hundred years. They found that neglecting the contraction of glacier area could lead to an overestimate of net mass loss of about 25% by 2100.

Table 11.5: Current state of balance of the Greenland ice sheet (1012 kg/yr).
Source and remarks	A	B	C	D	E	F
	Accumulation	Runoff	Net accumulation	Iceberg production	Bottom melting	Balance
Benson (1962)	500	272	228	215		+13
Bauer (1968)	500	330	170	280		110
Weidick (1984)	500	295	205	205		± 0
Ohmura and Reeh (1991): New accumulation map	535
Huybrechts et al. (1991): Degree-day model on 20 km grid	539	256	283
Robasky and Bromwich (1994): Atmospheric moisture budget analysis from radiosonde data, 1963-1989	545
Giovinetto and Zwally (1995a): Passive microwave data of dry snow	461a
Van de Wal (1996): Energy-Balance model on 20 km grid	539	316	223
Jung-Rothenhäusler (1998): Updated accumulation map	510
Reeh et al. (1999)	547	276	271	239	32	± 0
Ohmura et al. (1999): Updated accumulation map with GCM data; runoff from ablation-summer temperature parametrization	516	347	169
Janssens and Huybrechts (2000): recalibrated degree-day model on 5 km grid; updated precipitation and surface elevation maps	542	281	261
Zwally and Giovinetto (2000): Updated calculation on 50 km grid			216b
Mean and standard devation	520 ± 26	297 ± 32	225 ± 41	235 ± 33	32 ± 3c	-44 ± 53d
a Normalised to ice sheet area of 1.67610 6 km 2 (Ohmura and Reeh, 1991). b Difference between net accumulation above the equilibrium line and net ablation below the equilibrium line. c Melting below the fringing ice shelves in north and northeast Greenland (Rignot et al., 1997). d Including the ice shelves, but nearly identical to the grounded ice sheet balance because the absolute magnitudes of the other ice-shelf balance terms (accumulation, runoff, ice-dynamic imbalance) are very small compared to those of the ice sheet (F=A�B�D�E).

Dynamic adjustment of glaciers to a new climate occurs over tens to hundreds of years (Jóhannesson et al., 1989), the time-scale being proportional to the mean glacier thickness divided by the specific mass balance at the terminus. Since both quantities are related to the size of the glacier, the time-scale is not necessarily longer for larger glaciers (Raper et al., 1996; Bahr et al., 1998), but it tends to be longer for glaciers in continental climates with low mass turnover (Jóhannesson et al., 1989; Raper et al., 2000).

Table 11.6: Current state of balance of the Antarctic ice sheet (10 12 kg/yr).
Source and remarks	A	B	C	D	E	F
	Accumulation over grounded ice	Accumulation over all ice sheet	Ice shelf melting	Runoff	Iceberg production	Flux across grounding line
Kotlyakov et al. (1978)		2000	320	60	2400
Budd and Smith (1985)	1800	2000			1800	1620
Jacobs et al. (1992). Ice shelf melting from observations of melt water outflow, glaciological field studies and ocean modelling.	1528	2144	544	53	2016
Giovinetto and Zwally (1995a). Passive microwave data of dry snow.	1752a	2279a
Budd et al. (1995). Atmospheric moisture budget analysis from GASP data, 1989 to 1992.		2190b
Jacobs et al. (1996). Updated ice-shelf melting assessment.			756
Bromwich et al. (1998). Atmospheric moisture budget analysis from ECMWF reanalysis and evaporation/ sublimation forecasts, 1985 to 1993.		2190b
Turner et al. (1999). Atmospheric moisture budget analysis from ECMWF reanalysis, 1979 to 1993.		2106
Vaughan et al. (1999). 1800 in situ measurements interpolated using passive microwave control field.	1811	2288
Huybrechts et al. (2000). Updated accumulation map.	1924	2344
Giovinetto and Zwally (2000). Updated map on 50 km grid.	1883c	2326c
Mean and standard deviation.	1843 ± 76d	2246 ± 86d	540 ± 218	10 ± 10e	2072 ± 304
a Normalised to include the Antarctic Peninsula. b Specific net accumulation multiplied by total area of 13.9510 6 km 2 (Fox and Cooper, 1994). c Normalised to include the Antarctic Peninsula, and without applying a combined deflation and ablation adjustment. d Mean and standard deviation based only on accumulation studies published since 1995. e Estimate by the authors. The mass balance of the ice sheet including ice shelves can be estimated as B�C�D�E=�376 ±38410 12 kg/yr, which is �16.7 ±17.1% of the total input B. Assuming the ice shelves are in balance (and noting that the runoff derives from the grounded ice, not the ice shelves) would imply that 0=F+(B �A) �C �E, in which case the flux across the grounding line would be F=A �B+C+E =2209 ±39110 12 kg/yr.

Meier and Bahr (1996) and Bahr et al. (1997), following previous workers, proposed that for a glacier or an ice sheet in a steady state there may exist scaling relationships of the form V µ Ac between the volume V and area A, where c is a constant. Such relationships seem well supported by the increasing sample of glacier volumes measured by radio-echo-sounding and other techniques, despite the fact that climate change may be occurring on time-scales similar to those of dynamic adjustment. If one assumes that the volume-area relationship always holds, one can use it to deduce the area as the volume decreases. This idea can be extended to a glacier covered region if one knows the distribution of total glacier area among individual glaciers, which can be estimated using empirical functions (Meier and Bahr, 1996; Bahr, 1997). Using these methods, Van de Wal and Wild (2001) found that contraction of area reduces the estimated glacier net mass loss over the next 70 years by 15 to 20% (see also Section 11.5.1.1).

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