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Density of Glacier Ice

  • P. A. Shumskiy (a1)
Abstract

The density of glacier ice containing a given amount of air can be computed if it is assumed that both ice and air are subjected to a pressure due to the weight of overlying material. In this way it is possible to deduce the form that a curve of density versus depth should have for ice of a constant air content. Reasons for the divergence of observed depth-density profiles from those predicted by this theory are discussed, in particular the effect of the plastic-viscous behaviour of ice, which results in an air pressure differing from the hydrostatic pressure of the ice above. The empirical power-law relation between depth and density is discussed in the light of this theory, and is also used to derive relations for useful parameters characterizing the densification process such as rate of subsidence and rate of densification in terms of the depth, accumulation, and the constants entering the power law.

Résumé

On a calculé la densité de la glace des glaciers comprenant une proportion donnée d’air, en présumant que la glace et l’air sont soumis tous les deux à la pression des matières qui les recouvrent. De cette façon il est possible de déduire le trace de la courbe de la densité en fonction de la profondeur pour une glace dont le contenu d’air est constant. Les profils profondeur/densité observés ne correspondent pas à ceux prévus sur la base de cette théorie ; on discute les raisons de cette divergence: en particulier l’effet du caractère plastique de la glace, qui fait que la pression atmosphérique ne se trouve pas identique à la pression hydrostatique de la glace dans les couches supérieures. Les relations empiriques entre la profondeur, z, et la densité, ρ, s’expriment d’habitude par la formule z = n +c, k, c et n étant constants. La loi théorique, quoiqu’elle ne soit pas de cette forme, a pourtant avec la loi empirique un rapport approximatif quand il s’agit d’une variation de profondeurs s’échelonnant en-dessous d’une certaine limite; cette loi empirique, plus simple, est donc utilisée pour la série de profondeurs considérables, et sert à calculer des rapports de paramètres utiles caractéristiques du procédé de densification tels que la vitesse de l’affaissement et la vitesse de la densification; on peut ainsi exprimer ces vitesses comme fonctions de la profondeur, de l’alimentation et des constants k, c et n.

Zusammenfassung

Die Dichte von Gletschereis von bekanntem Luftgehalt lässt sich berechnen, wenn angenommen wird, dass sowohl Eis als auch Luft einem Druck des darüber lastenden Materials ausgesetzt werden. Auf dieser Weise ist es möglich, die Form abzuleiten, die eine Dichtenkurve in Abhängigkeit von Tiefe für Eis bei konstantem Luftgehalt haben sollte. Die Gründe für die Divergenz der beobachteten Tiefen-Dichtenprofile von den nach dieser Theorie vorhergesagten werden besprochen, insbesonders die Auswirkung des plastisch-viskosen Verhaltens des Eises, was einen Druck ergibt, der sich von dem hydrostatischen Druck des darüber liegenden Eises unterscheidet. Die empirische Beziehung z = kp n + c, zwischen Tiefe z und Dichte ρ, wobei k, n und c Konstanten sind, wird im Hinblick auf diese Theorie besprochen und wird ferner benutzt, um verwendbare Parameter abzuleiten, die den Verdichtungsvorgang charakterisieren, wie z.B. die Senkungs- und Verdichtungsgeschwindigkeit ausgedrückt als Funktion von Tiefe, Akkumulation und den Konstanten k, n und c.

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Copyright
References
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1. Richards, T. W. Speyers, C. L. The compressibility of ice. Journal of the American Chemical Society, Vol. 36, No. 3, 1914, p. 49194.
2. Dorsey, N. E. Properties of ordinary water-substance in all its phases. New York, Reinhold, 1940.
3. Butkovich, T. R. Density of single crystals of ice from a temperate glacier. Journal of Glaciology, Vol. 2, No. 18, 1955, p. 55359.
4. Bader, H. Sorge’s law of densification of snow on high polar glaciers. Journal of Glaciology, Vol. 2, No. 15, 1954, p. 31923.
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Journal of Glaciology
  • ISSN: 0022-1430
  • EISSN: 1727-5652
  • URL: /core/journals/journal-of-glaciology
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