Jökull - 01.07.2003, Síða 5

A calibrated mass balance model for Vatnajökull
10 km. Balloon soundings were made frequently near
U3 and near I6 to probe the lowest 500 m of the atmo-
sphere. Cloud observations were made approximately
every 3 hours near station U2 and irregularly near sta-
tion R5. The set-up of the experiment and the data are
discussed in more detail in Oerlemans et al. (1999).
ENERGY BALANCE
PARAMETERIZATIONS
Surface melt occurs when the energy balance at the
surface ( ) is larger than zero. is given by


      (1)
where
is the surface albedo,  the global radiation,
 the incoming longwave radiation,  the outgo-
ing longwave radiation, H the turbulent flux of sen-
sible heat and H the turbulent flux of latent heat.
Global radiation
Global radiation is computed according to the pa-
rameterization given by Greuell et al. (1997) which
is based on Meyers and Dale (1983). This param-
eterization is valid for horizontal surfaces. Most of
the surface of Vatnajökull slopes very gently, so we
apply a first order approximation to take the surface
inclination into account. The surface inclination only
influences the direct solar radiation, so we distinguish
between direct and diffuse shortwave radiation:

 
    

 (2)
where  

    and  
 . 
denotes the solar irradiance at the top of
the atmosphere,  is the solar zenith angle, and is the inclination of the surface in the direction of the
sun.  can be easily calculated from standard astro-
nomical theory (e.g., Walraven, 1978). For clear skies
 is 0.9 and  is 0.1 while for entirely overcast skies
 is 0 and  is 1. 
, ,  and 
 are trans-
mission coefficients that account for Rayleigh scatter-
ing and absorption by other gases than water vapor,
absorption by water vapor, aerosol extinction and ab-
sorption by clouds, respectively. The first three coeffi-
cients can directly be calculated from meteorological
variables.  and 
 are tuned to the data in the same
way as described in Greuell et al. (1997). The coeffi-
cients ,  and  account for the amplification
through multiple scattering at the surface, amplifica-
tion through directly reflected radiation at the surface
and attenuation by horizon obstruction. These three
coefficients can be obtained from the DEM. Figure 2a
displays hourly means of the observed and simulated
global radiation for the stations for which cloud ob-
servations are available.
Albedo
Snow albedo (
 ) depends on several climatological
and surficial quantities and thus changes in time and
space. These quantities are grain size, impurity con-
tent, cloudiness, solar inclination, liquid water content
and surface roughness (e.g., Warren, 1982). The in-
fluence of most of these quantities on
 is not well
understood and some simplifications have to be made
when
 is parameterized. We use a parameteriza-
tion that describes the daily albedo as a function of ag-
ing of the snow and snowdepth (Oerlemans and Knap,
1998). We calibrate this parameterization to the data
measured on Vatnajökull.
The ice albedo displays large spatial variations
over Vatnajökull which cannot be described with a
simple parameterization. In the north and northwest
(U8, U9 and R2) the mean ice albedo is very low
(<0.10). As has been confirmed in situ, these low val-
ues are caused by black volcanic deposits, tephra. The
tephra melts out and accumulates in the ablation zone.
To the south and to the east, the ice is cleaner, but the
albedo has not been measured on all major outlets and
it varies a lot in some areas. For example, the albedo
values measured at the stations A4, A5, I6 and R4
are most likely not representative of their surround-
ings (Reijmer et al., 1999). We therefore use satel-
lite reflectance images to determine the ice albedo of
different parts of Vatnajökull. We do not study the
snow albedo in this way, because the snow albedo is
more homogeneous on a horizontal scale than the ice
albedo. Furthermore, there are too few usable satellite
images to resolve changes in snow albedo. We use
NOAA-AVHRR images which have a resolution of
1.1 km at nadir. The retrieval method is described by
De Ruyter de Wildt et al. (2002). Figure 3 shows one
JÖKULL No. 52, 2003 3