Jökull - 01.07.2003, Page 11

A calibrated mass balance model for Vatnajökull
Figure 5. a: Average 2 m temperature () as a function of surface altitude, for different values of the temper-
ature in Kirkjubæjarklaustur (
); b: 2 m lapse rate () and 2 m temperature deviation at sea-level (
) as a
function of 
, both determined from the linear regressions in plot a. The data points for 
= 0ÆC are boundary
conditions. – a: Tengsl hita á Kirkjubæjarklaustri (
) og lofthita í 2 m hæð á Vatnajökli (). b: hitastigull
() og hitafrávik (
) við sjávarmál sem fall af hitastigi á Kirkjubæjarklaustri ().
mentum, heat and moisture. However, the dynamics
of the katabatic layer are very complex and external
effects such as advection further complicate the sit-
uation. On the other hand, when we analyzed the
data we found that  can be adequately described by
empirical relations that result in correct sensitivities.
 decreases linearly with altitude (Oerlemans et al.,
1999) and we found that this decrease changes with

(Figure 5a). We therefore write
 
  (4)
where 
is  at sea-level,  is the lapse rate of
 and  is the altitude. The dependence of both coef-
ficients in equation 4 upon 
is shown in Figure 5b.
For low temperatures hardly any katabatic flow exists
and  nearly equals . For higher temperatures,
 grows less negative and 
deviates more from

. For high values of 
,  approaches -2.5 K/km.
 is best described by an inverse tangent (Figure 5b):
 
  







(5)
When we impose the boundary condition that 

equals 
for 
= 0ÆC, we can describe the depen-
dence of 
upon 
with (Figure 5b):

 


(6)
So the higher T
, the less negative  and the more
negative the deviation of  from . These results
are not surprising because the katabatic layer, which
reduces  and , is better developed at higher tem-
peratures. Table 2 shows that mean observed and sim-
ulated values of  correspond reasonably well. The
parameterization of  produces mean errors between
0 and 1.2 K, but this error is much smaller than the
mean difference between  and . The sensitiv-
ities that result from the parameterization correspond
well with the observed sensitivities (Table 1).
JÖKULL No. 52, 2003 9