Jökull - 01.01.2009, Page 11

Langjökull, energy balance and degree-day models
is above all evident during periods when melt was
primarily varying with the incoming solar radiation
(July in Figure 4), which suggests that temperatures
above the low-albedo surface away from the glacier
better signify the incoming radiation than the damped
boundary layer temperatures over the melting glacier.
Good consistency is indicated between the degree-
days models and the total energy supplied for melt-
ing when correlating all available daily values at both
G1100 and G500 (Table 4 and Figure 6a). However,
this consistency varied significantly within the abla-
tion season and values from 0.9 and down to 0.2–0.4
were obtained when the correlation for the daily val-
ues was calculated separately for each month (Figure
4c). Thus, the lumped degree-daymodels are not fully
reliable for estimating daily ablation. Typically, the
best performance of the degree-day models was dur-
ing periods when the total energy for melting corre-
lated strongly with the turbulent eddy fluxes (Figure
4c-d). Exceptions to this appeared when eddy fluxes
fluctuated due to variations in wind speeds rather than
temperatures. Both DDM1 and DDM2 predicted high
September melting in 2001 and 2002, however, more
accurately on daily basis at G1100 than G500.
The melting calculated with the EBM and degree-
day models include snow that falls and melts during
the summer. This melting is included in the sonic echo
sounder observations, but not in the measured total
summer balance at stakes (bS). When using DDM1
and DDM2 to predict the observed summer balance at
stakes (Figure 7), the ddf -parameters in Table 3 were
applied up to 1100 m a. s. l., ddf 1snow and ddf 2snow
at G1100 assumed to be valid within the accumulation
area (above 1100 m a. s. l.) and the observed winter
balance (bW ) was used to identify the transition from
snow to ice/firn. The boundary layer temperature TG
was assumed to vary linearly with elevation and calcu-
lated by interpolation of the temperatures observed at
G500 and G1100. The annual variation of bS consid-
ering all stakes is better described with DDM2 than
DDM1 (lower % values in Table 5), but the DDM1
model provides more accurate prediction on average
in the accumulation area where too much summer bal-
ance is predicted with DDM2 (Figure 7 and Table 5).
This can be explained with snowfall within the
ablation season that was frequently observed by the
sonic echo sounder at G1100 (!15–20 cm w. eq. a"1
during the years of observations) but hardly ever at
the lower G500. By using sonic echo sounder and
mass- and energy balance data, Guðmundsson et al.
(2005) found the amount of snow falling and melt-
ing during the ablation season 2004 at the northeast
Vatnajökull ice cap (Figure 1), to gradually increase
up-glacier from !15 cm w. eq. a"1 at 1100 m a. s. l.
up to 1 m w. eq. a"1 at 1525 m a. s. l. Thus, the 36 cm
w. eq. a"1 higher ablation predicted with DDM2 than
observed at the 1200–1300 m stake locations (Table
5) may be more realistic than the close fitting of the
DDM1 model.
Table 5: Mean (µ) and standard deviation (%) of the
predicted minus the stake observed summer balance
(bS) in Figure 7. The summer balance estimated with
DDM1 and DDM2 includes snow that falls and melts
within the summer that is not detected by the stake
observations. – Meðaltal og staðalfrávik mismunar
milli reiknaðra og mældra gilda í 7. mynd.
DDM1 DDM2
(cm w. eq. a"1) (cm w. eq. a"1)
Ablation area
µ -4 4
% 60 41
Accumulation area
µ 0 -36
% 23 21
DISCUSSION
Time and elevation dependency of the degree-day-
parameters
As a practical approximation, scaling parameters of
temperature index models are generally assumed to
be both time and elevation independent, only vary-
ing with the surface type (e. g. Jóhannesson et al.,
1995). The model DDM2, using temperature away
from the glacier, comes closer to be elevation inde-
pendent than DDM1 (Table 3). Annual sensitivities
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