Jökull - 01.01.2004, Page 19

Glaciological application of InSAR topography data of W-Vatnajökull
Vatnajökull, northern Mýrdalsjökull, Eyjafjallajökull,
Tindfjallajökull and Torfajökull (Figure 1). The In-
SAR data were used to create a DEM, with 5x5 m
resolution, of the whole scene (Dall, 2003). The DEM
was adjusted using differential GPS tracks along al-
most every road and path within the survey area and
western Vatnajökull. Relatively small but noisy ar-
eas on the glacier were also filtered. The outcome is a
DEM with resolution, which exceeds the resolution of
all prior DEMs of large uninhabited areas in Iceland,
and with an accuracy on the order of 1 m (Magnússon,
2003).
Here, we present maps, derived from the new
DEM, of the current ice-divides between the out-
let glaciers of W-Vatnajökull and water-divides of
the rivers draining them. By comparing them with
older maps we note significant changes, especially
the water-divides, most likely generated during re-
cent glacier surges within W-Vatnajökull and the 1996
Gjálp eruption, north of Grímsvötn (Figure 2). The
new DEM was also used to delineate pathways of sub-
glacial watercourses and calculate the area distribu-
tion of the outlet glaciers of W-Vatnajökull. Further-
more, the new DEM revealed several features, pre-
viously unrecognised, on the glacier surface, for in-
stance a cauldron near the margin of the Köldukvísl-
arjökull outlet glacier which has probably been gener-
ated by geothermal activity.
APPLICATION TO GLACIER
HYDROLOGY
We used the EMISAR DEM data to model the
basal water drainage and basal water potential of W-
Vatnajökull. A DEM of Skeiðarárjökull, generated in
1997 by Münzer et al. (1999) was also included in our
study (Figure 2).
The water potential at the glacier base is
φ = ρwgzb + Pw (1)
where ρw is the density of the water, g the acceler-
ation of gravity, zb the sub-ice elevation and Pw the
water pressure. Typically, the water tends to flow in
tunnels under the glacier. The water pressure in such
tunnels may be approximated for a steady state flow
as (Paterson, 1994)
Pw = Pi − kQ
1
12 (2)
where k varies only with the local slope, Q is the wa-
ter discharge rate and
Pi = ρigH (3)
is the ice overburden pressure. H is the ice thickness
and ρi is the density of ice. At water divides where
Q ∼= 0 and Pw ≈ Pi we get
φ = gρizs + g(ρw − ρi)zb (4)
where zs is the elevation of the glacier surface.
Even though a low discharge condition is not ap-
plicable to all of W-Vatnajökul this simple model
was used to calculate a static potential for all of the
area, using the basal DEM from the Science Insti-
tute (Björnsson et al., 1988a, 1992a; Magnús T. Guð-
mundsson, pers. comm., 2003) and a sub-sampled
100x100 m EMISAR DEM of the glacier surface.
The surface DEM was filtered prior to calculation
using 2-dimensional Gaussian filter with the width
from −σ to σ equal to the ice thickness at each place.
The filter is clipped at ±2σ rounded to a multiple of
200 m since the filter dimension always corresponds
to an odd number of pixels, which means that the
length between the centres of the edge pixels is always
a multiple of 200 m. The filter ignores pixels where
the ice thickness less than half the ice thickness at the
centre pixel.
Using this surface filtering we assumed that sur-
face features had considerable effects on the basal wa-
ter pressure over an area of the same length and width
as the ice thickness.
Location of water divides
The water divides of all major glacial rivers from W-
Vatnajökull were delineated applying the water poten-
tial calculated from Equation 4. The water divides
(Figure 2) where derived by digitizing streamlines,
which lie perpendicular to the water potential con-
tours, starting at the water divides between the rivers
at the glacier margin and following the reverse direc-
tion of the potential flow vectors.
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