The primary input, besides the bedrock topography, is the mass balance at
each node. In modeling existing ice sheets measured values of accumulation
rates can be used. However, if experiments dealing with changing climate
are desired, some self-consistent mass-balance relationship that accounts
for changes in the ice configuration is necessary. In the ideal we would
couple such an ice sheet model with a global circulation model (GCM), so that
changing topography and albedo would be able to affect the ice sheet's own
climatic conditions. With GCMs too expensive and complicated, a simpler
parameterization of the ice sheet's affect on local climate is required
for efficient experimentation.
We developed a mass-balance relationship based on empirically fitting to
present Antarctic accumulation rates. This relationship depends on surface
elevation, surface slope, and latitude. Complementary ablation rates
are based on South Greenland mass-balance data, and are appropriate
for modest warming of the Antarctic climate. The climate is adjusted by
varying the mean annual sea-level air temperature, 
, which
provides a starting point for all temperature calculations at present
sea level. We understand the limitations
of this very simplified model of the mass balance, but feel that it is
an appropriate approximation to the actual situation.
The mass-balance relationship follows Fortuin and Oerlemans [] with modifications suggested by Jourzel and Merlivat [] and Braithwaite and Olesen [].
Basically this involves a surface temperature derived from a lapse rate and modified for distance from the pole.
From this a free atmosphere-isothermal layer temperature is obtained.
This temperature is used to calculate the saturation vapor pressure from a standard meteorological relationship.
Finally the accumulation rate is obtained from a fit of accumulation versus saturation vapor pressure and surface slope.
Ablation is modeled by calculating the number of positive degree days based on assumptions of the seasonality as a function of latitude. We calculate a seasonality factor
and a monthly mean temperature
and then sum up the positive degree days
from which we calculate the ablation rate.
Finally, the net mass balance is the difference between these two.
Fortuin and Oerlemans [] estimated parameters for the various fitting equations from available Antarctic data. We have used the Scott Polar map as digitized by Budd []. This data provides surface elevation, ice thickness, bedrock elevation, surface temperature, accumulation rate, and balance velocity for a 20 km grid centered on the South Pole (241X241 grid).
The following are the values obtained for the monthly seasonality factors.
For 
we use 960, 1036, 1200, 825, 330, 90, 150, 600,
1200, 1020, 930, and 850.
For 
we use 0.667, 4.6, 11.667, 9.167, 3.667, 1.0, 1.667, 6.667, 12.0,
6.333, 0.333, and -3.333.
Other fitting parameters obtained include 
,
, 
, 
, 
,
and 
.
