Jökull - 01.07.2003, Page 19

A calibrated mass balance model for Vatnajökull
Figure 10. Clear-sky emissivity as a function of 
 . In plot a,  and  of the free atmosphere are used, which
are available twice for each day. In plot b, hourly values of  and  at screen-height (2 m) are used. In both
plots fits of equation 11 to the data are shown (solid lines), and in plot b a fit of equation 11 with a theoretical
acceptable value of 9 for is also shown (dotted line). – Geislunarstuðull frá andrúmslofti við heiðan himinn
sem fall af hlutfalli gufuþrýstings og lofthita (
 ).
APPENDIX: Parameterization for the
incoming longwave radiation
The incoming longwave radiation is given by:


!


  !




"#

   (10)
where !
 is the emissivity of a clear sky, the
cloudiness,  a constant (integer), !
the emissivity
of clouds, # the Stefan-Boltzmann constant,  the
longwave radiation received from surrounding upper-
hemisphere slopes and " a constant that is estimated
from the DEM for each measurement site. The emis-
sivity of a clear sky is written as
!
   


  (11)
where  and are constants. The integer is theoret-
ically expected to be not smaller than 7 (Konzelmann
et al., 1994). For all stations  and e are ob-
tained from the radio soundings that were made twice
a day near station U2. By doing so we assume that
the atmospheric profiles above U2 are also valid for
the rest of Vatnajökull. The parameterization contains
four constants (, , !
 and ) that need to be tuned
to the data. First,  and are determined by fitting the
parameterization to the clear-sky ( =0) measurements
of  . We use the hourly mean values of  that are
closest in time to the radio soundings. For all stations
we find comparable values of  and , with mean val-
ues of 0.438 and 9, respectively (Figure 10a). This
shows that the assumption of a horizontally homoge-
neous atmosphere is justified. The residual standard
deviation for !
 is 0.022. The value of  compares
well with those found by Konzelmann et al. (1994),
0.443, and by Greuell et al. (1997), 0.475 and 0.407.
The value of is, as theoretically expected, larger
than 7. Konzelmann et al. (1994), who used  and
 and not  and e in their calculations, found
a value of 8 for a location near the equilibrium line
of the Greenland ice sheet. There,  and e obvi-
JÖKULL No. 52, 2003 17