Jökull - 01.07.2003, Síða 13

A calibrated mass balance model for Vatnajökull
culated values are too high, so for these stations the
mean cloudiness and/or the optical thickness must
have been higher than at U2. R3 was located near
the Grímsvötn depression and was often surrounded
by fog. R6 was located near Hornafjörður, where the
mean cloudiness was higher than at U2 (Table 3). For
U9, U10 and R1 no other indications of a low cloud
factor are available. Note, however, that U10 and R1
were not located on but close to the ice cap.
We force the model with daily values of cloudi-
ness, and it seems best to use values measured in KIR.
This is expected to introduce errors over the lower-
most ablation zones in the north, the southeast (not
over Breiðamerkurjökull) and perhaps in the west.
Precipitation and tuning of the model
Because the albedo depends upon the number of days
since the last snowfall, it is important to simulate the
time between subsequent snowfalls correctly. When
we assume that precipitation falls every 5 day, and
define days with snowfall as days with precipita-
tion and a daily mean temperature below 3ÆC (in
the free atmosphere above the katabatic layer), the
mean albedo in the accumulation area is simulated
correctly. The exact amount of annual precipitation
is only known at a few locations near the coast and
we will have to use it for final tuning. We assume that
the precipitation gradients are fixed in time, and for all
sites where has been measured regularly, we cali-
brate  so that the modeled annual mean is equal to
the observed annual mean (over the years 1993 to
1999). The resulting precipitation field must be inter-
polated to the model evaluation sites, but the measure-
ment sites are irregularly distributed over the ice cap
and do not resolve many of the altitudinal gradients.
Hence, we make a distinction between horizontal and
vertical gradients. Precipitation is often found to dou-
ble in a certain altitude interval so we write:
  


(7)
where 
is the mean annual precipitation at a ref-
erence altitude and  is a constant (e.g., for a dou-
bling per 1000 m,  has a value of 2). We fit this
equation to the winter mass balance data, which are
available for the years 1993 to 1999 (Björnsson et al.,
1997, 1998a,b,c, 1999; Gudmundsson, 2000; Sigurds-
son, 1997). These data were mainly obtained over the
northwestern part of Vatnajökull, including most of
the accumulation area. For Öræfajökull (the south-
ernmost dome of Vatnajökull) we also use precipita-
tion data from the permanent weather station in Fag-
urhólsmýri. When we correct the data for the small
amounts of ablation and rainfall that occur during the
winter season (both corrections are calculated with
the mass balance model), we find a value of 2.3 for
. At each measurement site, we can now reduce 
to its value at sea-level. The resulting values vary
smoothly over the ice cap and we can interpolate them
to the model evaluation sites with Kriging interpola-
tion (e.g., Cressie, 1993). This interpolation technique
is suitable for smooth interpolation of unevenly dis-
tributed data such as the mass balance observations
that we use. At each model evaluation site we then
calculate  with equation 7.
RESULTS
Energy balance
Observed and modeled components of the energy
balance are displayed in Figure 7. All components
change with altitude and this is simulated by the
model.  and
logically increase with altitude,
whereas the net longwave radiation and the turbulent
fluxes decrease with altitude. For station U9, and to
a lesser extent for A4, A5 and I6, the modeled cloud
factor is too low and hence the calculated global radia-
tion is too high. Significant differences in the percent-
age of reflected shortwave radiation are present for
A4, A5, and R2. For A4 and A5 this is caused by the
ice albedo which is not representative of the surround-
ing ice. The model uses a more representative value.
In the model results the snow disappears too soon at
station R2 so the modeled mean albedo is too low.
This is a consequence of tuning the model precipita-
tion with mass balance data from several years. Errors
in the turbulent heat fluxes mainly result from errors
in the calculated meteorological variables at screen-
height. Note that for U9 and R2 part of the available
energy is not used for melting due to insulation.
JÖKULL No. 52, 2003 11