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peripheral to the Antarctic ice sheet (28 % of the global estimate), where large temperature
sensitivities, temperature trends, and glacier area combined to yield large mass losses. In
contrast, the Gardner et al. (
2013
) ICESat analyses found very little mass loss for the
Antarctic periphery during 2003-2009.
3.2 Models of surface mass balance
This approach directly models the evolution of surface mass balance in time by simulating
surface melting and accumulation using climate data. Melt is most commonly modeled by
so-called degree-day models, mainly because of their simplicity and the fact that the positive
degree days are shown to be good indicators for glacier melt (Ohmura
2001
; Hock
2003
).
Raper and Braithwaite (
2006
) were the first to perform global-scale projections of glacier
mass balance based on a degree-day model. Resulting mass-balance gradients were regressed
against annual precipitation and summer temperature from gridded climatology, and the
relation applied to all 1 9 1 grid cells with glaciers (Cogley
2003
). Based on the initial,
calibrated equilibrium line altitudes (ELAs), upscaled glacier size distributions for each
glacier grid cell, and derived vertical extent for each glacier, the model was run by perturbing
the ELAs according to summer temperature anomalies. The resulting changes in total area
and area-altitude distribution were computed annually with a simple glacier geometry model
assuming a generic area-altitude distribution triangular in shape between its minimum and
maximum altitude. Driven by climate data from two GCMs with A1B emission scenario, the
projected sea-level rise for all glaciers, but excluding the glaciers peripheral to the Antarctic
and Greenland ice sheet, was 46 and 51 mm for 2001-2100 (Table
2
).
Hirabayashi et al. (
2010
) used a degree-day model specifically designed to feed into a
global hydrological model. Consistent with the resolution of the latter model, the mass-
balance model was run with daily time steps and on a 0.5 9 0.5 grid, treating each grid
cell's glacier area as one large glacier, but allowing for sub-grid elevation bands. The
model was initially used for the reconstruction of mass balance for the period 1948-2004,
where gridded datasets of daily precipitation and near-surface temperature (Hirabayashi
et al.
2005
,
2008
) were used as forcing. The modeled parameters were tuned to maximize
the match between modeled and observed mass balance from 110 glaciers (Dyurgerov and
Meier
2005
); thus, the modeled global mass balance of 0.42 ± 0.15 mm SLE almost
replicated the consensus estimate from Kaser et al. (
2006
). Recently, the model has been
refined and run with the new Randolph glacier inventory (Arendt et al.
2012
) to project
glacier mass changes in response to the more extreme climate scenario (RCP8.5) from 10
GCMs prepared for the IPCC AR5 (Hirabayashi et al.
2013
). They projected global glacier
mass loss, excluding glaciers peripheral to the ice sheets, to be 73 ± 14 mm SLE for the
period 2006-2099 (Table
2
).
Radi´ and Hock (
2011
) developed a global-scale mass-balance model for the elevation-
dependent mass balance of each individual glacier in the world glacier inventory by Cogley
(
2009a
). The inventory comprised * 120,000 glaciers, covering 40 % of the total global
glacier area. A degree-day model was calibrated using in situ mass-balance observation
from 36 glaciers. The parameter values for all other glaciers were derived from established
relationships with climate variables. Projections were made in response to downscaled
monthly temperature and precipitation scenarios of ten GCMs from IPCC AR4 based on
the A1B emission scenario. For the regions with incomplete glacier inventories, the pro-
jected volume changes were upscaled with a scaling relationship between regional ice
volume change and regional glacierized area. The multi-model mean suggested sea-level
rise of 112 ± 37 mm for the period 2001-2100. In a follow-up study, Radi´ et al. (
2013
)
