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        Why calculated basal drags of ice streams can be fallacious
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        Why calculated basal drags of ice streams can be fallacious
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The Editor

Journal of Glacilogy

Sir,

Whillans and Van der Veen (1993) have performed valuable measurements of surface strains on Ice Streams B and C, Antarctica. Unfortunately, their paper does not present the raw numerical data which, as unquestionable fact, deserve to be put at the disposal of the entire scientific community. Following a bad habit, which appears to have become commonplace in glaciological literature, Whillans and Van der V een have published only the results inferred from these field data. In particular, they have published an inferred basal drag, which is found to be negative in some places on Ice Stream B. I believe this negative drag is a nonsensical result of questionable assumptions which underlie Whillans and Van der Veen’s analysis of the data. The speculative explanations of the negative drag offered by Whillans and Van der Veen may therefore be of doubtful validity.

In my opinion, the untenable result of Whillans and Van der Veen’s analysis, i.e. negative basal drag, comes from the assumption, introduced by Nye in the 1960s, that horizontal strain rates are uniform through the ice column. As Whillans and Van der Veen have recognized, the cold upper layer of the ice stream acts as a stress guide — as an almost rigid “lid” which caps the soft, warmer ice lasers below. Consequently, the strain rates in the upper layer should be much smaller than in the lower layers. Streamlines of ice-stream flow thus smooth readily from the bottom of the ice stream upwards. This behaviour is typical in polar ice sheets, as internal layering revealed by VHF sounding has shown (Robin and others, 1977).

Whillans and Van der Veen have indicated that the thickness of Ice Stream B along the entire grid varies between 1020 and 1070 m, and that the forward velocity is about 450 m a−1. When the thickness varies by 20 m only, a material point at the surface moves away from or closer to the bottom by 450 times; (20/1000) = 9 m a−1. The mean vertical strain rate is then 9 m a−1/1000 m = 9 10−3 a−1, and it is concentrated in the lower soft layer. Incompressibility requires that the horizontal strain rate in the direction of flow be of the same order (with opposite sign) as the vertical strain rate. The horizontal strain rate near the bed of the ice stream is hence likely to be one order of magnitude greater than the horizontal strain rate measured at the ice-stream surface, which is only of the order of 10−3a−1.

The soft basal layer should cope with most of the strains that fast sliding over a rough bed can generate. When the bed elevation increases, basal ice velocity should increase much more than the measured velocity in the nearly rigid “lid” at the surface of the ice stream. The assumption of depth-independent strain rates holds more or less in the cold upper layer but not at all in the warm lower layer. In the lower layer, there can be local extrusion flow over the bumps in the bed (as in Nve’s model of a glacier sliding over a bed with sinusoidal bumps). This local extrusion subjects the upper lid to a negative drag which may be reflected in Whillans and Van der Veen’s data.

In my opinion, what Whillans and Van der Veen have calculated is not the basal drag but more or less the shear Stress that the rapidly deforming lower layer exerts on the stiller upper layer in response to basal topography. In the lower layer, horizontal strain rates and the corresponding shear stresses are not depth-independent. Although the horizontal shear stress at the very bottom is always positive, in places it may have negative values at some distance above the bed. As recognized by Whillans and Van der Veen, their analysis of the surface strain-rate data misses any oscillation of the stress in the lower layer, where it is small, because their analysis averages the stresses and the resisting forces along a vertical.

Of course, precise numerical calculations that account for a depth-dependent viscosity would give more weight to my heuristic explanation, but I am retired and leave this task to younger people in possession of all the pertinent field data. (A word of advice: this more complex inverse problem cannot be solved without assuming some kind of sliding law-at the bed, even if this law has some parameters that need to be adjusted.)

It is fortunate that the method of Van der Veen and Whillans (1989) has led to an absurdity which Whillans and Van der Veen (1993) were courageous enough to publish. Without the clear example of how a questionable assumption can upset the interpretation of perfectly satisfactory data, other investigators would perhaps unwisely trust their method. Many other attractive, simplified methods of data analysis published in die 1960s and 1970s suffer from the same Hawed assumption but without generating the diagnostic consequences of an absurd result. These methods have therefore become embedded in standard glaciological knowledge. Their flawed assumptions are taken for granted by young scientists who wish to build a more general understanding of non-linear continuum mechanics atop the perhaps shaky platform that these earlier methods provide. We ought to be more demanding about the validity of die assumptions on which simplified solutions are grounded. To quote published papers, where they have already been used, should not alone be a justification.

References

Robin, G.de Q., Drcwry, D.J. and Meldrum, D.T. 1977. International studies of ice sheet and bedrock. Y7 Philos. Tram. R. Soc. London, Ser. B, 279 (963). 185196.
Van der Veen, C.J. and Whillans, I.M. 1989. Force budget: I. Theory and numerical methods. J. Glacial., 35 (119), 5360.
Whillans, I.M. and van der Veen, C.J. 1993. Patterns of calculated basal drag on Ice Streams B and C. Antarctica. J. Clacioi. 39 (133). 437446.