Jökull - 01.01.2009, Page 6

Guðmundsson et al.
G500 and G1100, respectively, which is well within
the errors of !35 W m"2 of Mc and 40 W m"2 of
Mm, calculated by using the instrument errors given
in Table 1.
Empirical ablation models
Two degree-day models were used to relate the spe-
cific ablation rate (as in m d"1 w. eq.) at an elevation
hG on the glacier to degree-days, either as observed
on the glacier (DDM1, Eq. 9) or estimated at a base
station outside the glacier (DDM2, Eq. 10):
as = ddf1
t2&
t1
T +G (9)
as = ddf2
t2&
t1
!
TS " $(hG " hS)
"+
. (10)
The sums are computed over the period from day t 1
to t2 of the ablation season, ddf1 and ddf2 are degree-
day factors that remain constant with time but are dif-
ferent for snow and ice/firn. The number of degree-
days calculated for each day is the mean daily tem-
perature above the melting point, 0 !C, + stands for
degree-days over a threshold of 0 !C, TG is the ob-
served temperature 2 m above the surface at elevation
hG on the glacier, TS is the observed temperature at a
weather station of elevation hS away from the glacier
(here S475) and the constant $ = 0.6%10"2 !Cm"1
approximates the adiabatic lapse rate. The tempera-
ture TG is damped by energy exchange processes near
the melting ice surface but (TS " $(hG " hS)) is typ-
ically representative for the atmosphere temperature
at an elevation hG above the off-glacier weather sta-
tion S474, and not influenced by a melting ice surface.
Hence, (TS " $(hG " hS)) is not an estimate of the
damped boundary layer temperature TG, but rather an
estimate of the temperature at height hG in the free
atmosphere surrounding the glacier.
The ddf -parameters of DDM1 and DDM2 (Table
3) were scaled to fit the water equivalent of the daily
energy supplied for melting (Eq. 5), using: a) a com-
bined 2001–2005 energy budget calculations at the
two AWSs (G500 and G1100), and b) the 2004 energy
budget at three mass balance stakes at 700 to 1000 m
a. s. l. (Figure 1), inferred by assuming the parame-
ters TG, e, u, Qi and Ii of Eqs. (4–7) to vary linearly
with elevation between the observation sites G500 and
G1100, and setting Io equal to 315Wm"2 (for a melt-
ing surface) and Qo = Qi · " with albedo (") esti-
mated by combining information from the stake ob-
served winter balance (bW ; for snow/ice transition),
the observed daily albedo at the two AWS sites and
three optical SPOT5 satellite images (5x5 m spatial
resolution) acquired on August 12, 17 and 19, 2004.
When fitting the ddf -parameters, the energy bal-
ance data-sets were divided into periods with melting
of snow and ice/firn, respectively. The timing for the
exposure of ice/firn was estimated when an abrupt re-
duction in albedo took place as the summer surface
of the previous year was exposed, as well as consider-
ing the melting needed to remove the measured winter
accumulation (bW ). Albedo changes due to new snow
that was deposited on an ice/firn surface and melted
was also easily detected from the albedo profiles. The
uncertainty of the ddf -parameters was estimated at
G1100 and G500 (Table 3) as one standard deviation
of the annual variance of ddf -parameters fitted sepa-
rately to each year.
RESULTS
Energy budget during the ablation seasons 2001 to
2005
The ablation seasons under investigation started at
the end of April/beginning of May and terminated in
September/early October.
Net radiation was typically the main contributor
to the total energy supplied for melting during the
months of June through August but was equalled or
surpassed by turbulent fluxes during occasional spells
of high temperatures and strong winds (Figure 3a-b).
Throughout the ablation seasons, the albedo and the
global radiation were the main factors determining the
net radiation (Figures 3c-d) as the long-wave net radi-
ation was fairly constant; slightly negative, with radia-
tion emitted from the melting glacier hovering around
315 W m"2 (Figure 3c). Daily variations in the en-
ergy budget were, however, generally highly related to
turbulent eddy fluxes (Table 4), especially during the
6 JÖKULL No. 59