Sir, Calving from floating glaciers: reply to Professor F. Loewe’s comments

In his comments Professor Loewe claims the following things:

1. The manner of calving of Rink Gletscher and Jakobshavn Isbræ is not typical for the ice streams of western Greenland.

2. Rink Gletscher and Jakobshavn Isbræ are not floating glaciers and therefore cannot be used to prove the theory of calving proposed.

3. The front of a floating glacier is not always bent downwards as predicted by the theory.

4. The often observed backward tilting of the icebergs detached at the calvings should be in contradiction to the downward bending of the front predicted by the theory.

My attitude to these points is as follows:

1. I agree that the manner of calving of Rink Gletscher and Jakobshavn Isbræ is not typical for the ice streams of western Greenland, but I think that the reason is that these glaciers have floating fronts, in distinction to the main part of the ice streams terminating in Disko Bugt and the Umanak district in western Greenland.

2. My opinion is based on the following:

   • a. The slope of the surface of the two glaciers is very small.

   • b. The biggest icebergs from the two glaciers do not turn over at the calvings, but float away, the old glacier surface turning upwards (Reference Carbonnell and BauerCarbonnell and Bauer, 1968, p. 21; Reference SorgeSorge, 1933, p. 13).

   • c. According to figs. 12 and 13 in my article, the level of the southern part of the surface of Rink Gletscher is about 80 m above sea-level. According to Reference Carbonnell and BauerCarbonnell and Bauer (1968) p. 50, the height of the front is 70–75 m above sea-level.

     Putting the mean density of the ice as 0.9 Mg/m³ (Reference SorgeSorge, 1933, p. 13) and the mean density of sea-water to 1.02 Mg/m³ (Reference SteenstrupSteenstrup, 1893, p. 84), we get

     

     Under the assumption of a floating front, the ratio of total ice thickness to front height above sea-level is thus determined to be

     

     Due to the severe crevassing of the surface, the ratio is quite likely less. So, no reason exists for assuming the frontal thickness of Rink Gletscher to be more than 720 m, of which less than 650 m is below sea-level. According to Reference SorgeSorge (1933, p. 19), the depth of the fjord immediately in front of the glacier is 692 m. Consequently at least a part of the front must be floating, as is also stated by Reference SorgeSorge (1933, p. 16).

     Moreover, only the outermost part of the glacier needs to be afloat in order to make possible the deformation procedure described in my paper. As seen from fig. 6 in the article, significant downward movements take place only in a region extending from the front of the glacier to less than the thickness of the glacier behind the front.

3. It is true that the theory at the state at which it was put forward in the article, will always lead to a downward movement of the front. This is due to the simplification of neglecting temperature variations and the resulting variation of the cross-sectional rigidity in the vertical direction. When dealing with deformations, the moment of the forces acting at the front must be calculated with respect to the centre of the transformed cross-section. If the rigidity of the cross-section is constant in the vertical direction, the centre is situated at the midpoint of the cross-section and the front is bent downwards. If a temperature gradient exists, the centre is situated above the midpoint, more and more the greater the temperature gradient, and at a certain gradient the moment changes its sign resulting in an upward bending of the front. Also the depth of the crevasses influences the sign and magnitude of the bending moment. An improved theory taking into account the influence of temperature and depth of crevasses is under elaboration.

4. The fact that the icebergs often tilt backwards has nothing to do with what causes a depression of the glacier into the sea. The question of whether an iceberg will tilt forward or backward depends on:

   • a. Shape of front—and fracture cross-sections.

   • b. Magnitude of depression.

   • c. Slope and thickness of the frontal part.

   • d. Distance from the front to the fracture cross-section.

   • e. Relative density of the glacier ice.

     Assuming front and fracture cross-sections perpendicular to the glacier surface, a rough calculation with reasonable values of density, depression and slope of the frontal part leads us to expect that backward tilt will occur if the distance from the front to the fracture cross-section is more than about half the thickness of the glacier, while forward tilt will occur if it is less. This is in agreement with observations made by Ole Olesen of Grønlands Geologiske Undersøgelse and the author at Daugård Jensen Gletscher during the Grønlands Geologiske Undersøgelse expedition to East Greenland, July–August 1968, where both ways of tilting of icebergs detached at calvings were observed and photographed. Further details will appear in a paper under elaboration.

Finally I should like to remark, that the theory at the state at which it was put forward in the article was a first approximation only, as was also pointed out. On the other hand, it is my opinion, that the basic idea put forward in the article holds, viz. that the stresses induced by the moment at the front of the glacier play a major role in the calving procedure. At present a more correct theory is under elaboration.

19 December 1968