In this article, we present a simple modelling approach for the simulation of waves on glaciers. The concept of Forel showed how the traditional kinematic wave theory due to Boussinesq can be used to describe the behaviour of glaciers. In glaciological modelling, this concept has not yet been investigated. The traditional wave theory reproduces the continuous flow while energy is conserved. Despite the stage of scientific validation the wave pulse of the flow has seldom been validated. A pulse that maintains its uniform shape. The design concept of Forel & Richter can be used in order to investigate the behaviour of glaciers under more specific conditions induced by low-frequency (rare) variations in the supply rate and the surface accumulation by winter snowfall. This is done by Glacier des Bossons’ application (Mont-Blanc, France, 1997) inspired by references of Lliboutry. The classical zeroth-order can explain the observed relaxation-recovery time-function t [yr] meaning that the application itself cannot be rejected. Although, the fact of its shortest relaxation-recovery time was well-known indicating that the zeroth-order, the physical approximation-mechanism by which it occurs, remains uncertain. On the other hand, detection and visualization of a wave-front itself are difficult. A new point of view, historical snow records reanalysis (1995, 1951, and 1879) can be used to investigate glaciers under the specific conditions: in doing so, a delayed glacier-front variation due to the observed change in the supply rate can be simulated. The localized snowiest range of accumulation will be denoted by λ [m]. In this study investigated, expressed in one of the driest decades with short time and abrupt record-breaking supply rates studied by Einhorn and Chaix (“Climate change in the Alps’’, 2008), likely with anthropogenic influences on the climate forcing (1995) studied by Reichert, Benqtsson, and Oerlemans (2001). As the result of validation, we show in Bossons’ Experimental Results how the combined Boussinesq Navier-Stokes theory (poorly know) may be used to describe the evolution of the supposed wave along the transition zone as located in a sérac zone. We expect to develop a theory of solitary wave phenomena in the characteristic of non-linear behaviour which result from an unusual increase in snowfall with altitude. To activate the triggering mechanism, the signal from the meteorological climate pulse with a short-lasting time, t << 1 [yr], is defined as a low-frequency phenomenon due to the seasonal resilience of glaciers with the assumption of an unknown tipping point. The time-dependent motion for a triggering impulsive snow load is studied by superimposing the Boussinesq Navier-Stokes solution (1D) on a steady-state glacier (1D). Boussinesq presented the translator solitary wave theory in which an impulse is transmitted. The solution is carried out with the aid of the method of characteristics. A methodology used prior to the

1. MST-symposium,
23-24 March 2017,
Open University of the
Netherlands
ir. ing. L.F.C. (Loek) Van der Leek
Mont-Blanc Summit, France, Journal Paper
Glacier’s Resilience and Climate Change
new challenges

2. anthropogenic intensification
winter-time North Atlantic
Oscillation index
climate shift
1995
a return to
normality
snowiest
record-breaking
rate of winter
accumulation,
since 1894

3. the following two slides show the Mont Blanc area and
the historical front-variations of three French glaciers
namely de Argentiere, Mer-de-Glace and des Bossons
Glaciers of
Mont-Blanc
ice-velocity variations: - 25% < U0 /Ū0 < + 40% (+ 80%)
due to summer and winter

4. historical front-variations
1990s (mild, dry)
retreat -40 m/yr.
2000s (mild, wet)
retreat -25 m/yr.
winter
accumulation
2,750 m a.s.l.
1994/95 280%
2001/02 230%
2004/05 100%
2006/07 100%
2010/11 100%
100 m
advance
retreat
University of Grenoble by Louis Reynaud 1870-2007, and by Christian Vincent 1994/95.

5. GLACIER DES BOSSONS
summit/front
flowline/
gravity flow
steady-state/
retreat-advance
net ablation/
net accumulation
Increasing/
decreasing
compression/
extending flow
acceleration/
deceleration
direct response/
indirect response
(transition zone)
LCI
ELA
snowiest record-breaking winter (accumulation ≠ ablation)
Keywords:
annual part that melts away (accumulation = ablation)

6. the response of a glacier to a surface disturbance can have one
of the three different underlying mechanisms as the cause:
Forel, 1881, the Theory of the Continuous Flow (TCF),
the impulse/gravity wave
Richter, 1883, the Theory of the Intermittent Flow (TIF),
the pressure gravity wave
Theory of Albedo Feedback Flow (short summer)
these theories can be triggered or activated by snowiest
record-breaking rates of the winter accumulation

7. Observed Continuous Flow by Vallot, 1893
after climate change
corrections, University of
Grenoble by Lliboutry,
1958
change in the surface
elevation along four
cross-profiles over a
measured total period
of 10 years
the image shows the surface wave with an amplitude of 2-
6 m, a wavelength of about 3 km, and a wave velocity of
800 m/yr., the surface velocity itself increased from 125 to
155 m/yr., simultaneously over the entire ablation
Mer-de-Glace

8. Forel’s Theory of the Continuous Flow
Bossons’ limit ice wall speed, 1995
gravity wave

9. high-frequency low-frequency
2003
supra-, sub- or englacial manner
Forel’s Traditional Kinematic Wave:
gravity wave
Based on the idea of Lliboutry, 1958,
the methodology laid down by Fowler,
1980.
Based on the idea of Nye, 1958,
the methodology laid down by
Finsterwalder, 1907, and by
Fowler, 1980.
Forel’s General Kinematica Wave:
gravity flow and wave

10. resilience of glaciers
anthropogenic intensification
new challenges
since the Little Ice Age, the gravity waves as a low-
frequency phenomenon in combination with
satellite radar, that being developed with glaciers,
and nowadays climate change are challenges that
deserve more attention
learning
innovation
new challenges
MST-symposium,
23-24 March 2017,
Open University of
the Netherlands
L.F.C. (Loek) Van der Leek