Jökull - 01.01.2009, Page 4

Guðmundsson et al.
Figure 2. Surface changes (a)
and total energy supplied for
melting (b) at G500 during
the summer 2001, displayed
as three-day moving averages.
The error is estimated as ±20
W m"2 for both Mm (Eq. 3)
and Mc (Eq. 4) in (b). – Sam-
felld mæling á leysingu í 500
m y. s., ásamt heildarorku til
leysingar reiknuð út frá veður-
þáttum og mældri leysingu.
is a formulation of the saturation vapour pressure in Pa
of temperature T (e. g. Buck, 1981; Murray, 1967).
METHODS
Melt energy derived from the sonic echo sounder
data
The observed melt rate derived from daily records of
the sonic echo sounder (as in m d"1 w. eq.) was used
to estimate the average daily energy supplied for ab-
lation (in W m"2), described as
Mm = Ll · ! · f · as (3)
where ! = 103 kg m"3 is the density of water,
Ll = 3.3 · 105 J kg"1 is the specific latent heat of
melting and f = 1/86400 d s"1.
Physical energy budget model
The energy budget on the melting surface of the
glacier can be written as
Mc = R + Hd + Hl (4)
whereR = Qi "Qo + Ii " Io = Qi(1"")+ Ii " Io
is the net radiation depending on the incoming solar
radiation, surface albedo (") and the long-wave ra-
diation balance, while Hd and Hl represent the verti-
cal turbulent fluxes of sensible and latent heat, respec-
tively. The heat supplied by rain is assumed to be neg-
ligible, as well as the sub-surface heat flux which is
appropriate under melt conditions. The water equiva-
lent (in m d"1) of the daily energy budget (in W m"2)
is calculated as
as =
#
$
%
Mc
Ll·!·f Mc # 0
0 otherwise
(5)
hereafter referred to as EBM. The effect of sub-
surface heat transport and refreezing is omitted.
Radiation components were measured directly
and the turbulent energy exchange calculated from
hourly mean values of the wind, temperature and rel-
ative humidity measured in the boundary layer of the
glacier. The Monin-Obukhov model can be adapted
for the single-level measurements as (e. g. Munro,
1989):
4 JÖKULL No. 59