Jökull - 01.12.1955, Síða 8

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Figure 2. Section through Brúarjökull, a glacier in the northern Vatnajökull in Icelancl. Thh is
approximately a central section ivith H = 600 m and L = 20 km. The velocity v and floiu F are
theoretical values from equations (21) and (22).
above equations is not constant but varies with
the length of the glacier L, that is, the longer
glacier can dissipate more ice. This means that
the glacier is more stable, ancl it can in special
cases be expected that the glacier can be stable
for a whole interval of lengths L. An outward
slope is consequently a stabilizing factor where-
as an inward slope has the reverse effect.
Another stabilizing factor is the spreading
of the lower parts of the glaciers as in the case
of piedmont-glaciers. By the spreading the
ablation area increases rapidly with the length.
It is consequently to be expected that actual
glaciers are in most cases more stable than the
theoretical case treated here, but the stabilizing
factors can be taken into account by a more
elaborate treatment.
RESPONSE TO CLIMATIC VARIATIONS
A further factor interfering with the stability
is the variability of the meterological factors
especially of the height of the firn line H.
These variations cause fluctuations of the height
and movement of the ice-sheets and glaciers.
The fluctuations present one af the most inter-
esting problems of glaciology and the present
paper will therefore be concluded by a short
investigation of the influence of climatic varia-
tions on the ice-sheets described by the equations
above. The method to be used is the method
of small perturbations which is much used in
other branches of mechanics and physics.
By the treatment of this problem it becomes
necessary to treat the ice-sheet as a whole, that
is, look for the perturbations of the combined
accumulation and ablation areas.
We will again turn to equation (17) and ask
for solutions for the combined accumulation
and ablation areas, that is, extend the above
solution (18) above the firn line. It is then as-
sumed that the total net accumulation above
tlie firn line is a(h—H), which is a rather
natural relation although other relations may
apply in many practical cases, but this will not
interfere with the main results.
The solution of (17) for the total thin linear
ice-sheet moving on a horizontal plane is very
simple:
A. = -(±J*J . (23)
where L0 is the total length of the accumu-
lation and the ablation areas, that is, the length
of the stable ice-sheet situated as in Figure (3).
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