Steve,
First point: melting of the ice shelf (I think I understand that you are not questioning this point, but I would prefer to clarify)
Notations: T = Thinning rate, D = Dynamic thinning, S = Surface mass balance, M = Ice melt, Suffix g = grounded (upstream of the grounding line) and Suffix u = ungrounded (downstream of the grounding line)
Important point: what follows concerns the surroundings of the grounding line and is therefore not directly concerned by the melting away of the grounded line
Equations: Tg = Dg + Sg + Mg & Tu = Du + Su + Mu (The authors actually use elevation instead of thickness, which gives a slightly different formula in the case of the ice shelf: ungraunded)
Hypothesis: Dg ≈ Du, Sg ≈ Su and Mu ≈ 0, which results in Mu = Tu – Tg
Note from Sidd: in the case that Mg is not equivalent to zero then Mu = Tu - Tg + Mg and so the melt is even greater (the problem is that at the moment there is little knowledge of the term and its application in these cases)
Second point: the ice mass balance
Mass ice balance = Ice discharge (measured on the grounding line) + Surface mass balance + Water discharge (correspond, in our case, to the bed melting)
Note: The catastrophic ice mass balance is determined by the significant change in ice discharge, which is calculated by satellite measurements (elevation, velocity and position of the grounding line) and is not derived by calculation of the other elements!
Note: as the other elements are estimated any significant melting in the mass balance of the ice would have been detected, which was not the case
Third point: But a smaller and therefore non-detectable melt could have produced enough water to lubricate the bed.
The formation of sub-glacial lakes would have been detected (this is an area over which radar aircraft flights are more numerous) which was not the case
Fourth point: the explanation for the accelerated withdrawal of the grounding line
On the one hand, we have a theory that dates back to the 1970s, which was subsequently confirmed by models and verified and proven on many occasions in Antarctica as well as in Greenland.
It is a theory accepted and validated by the community of glaciologists.
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West Antarctica is full of volcanoes and for example there has historically been a sub-glacial eruption in the PIG (and of course it has been detected) and, still under the PIG there is geothermal heat (it is monitored from the presence of certain isotopes released in the melt water), so volcanism is important, but in the sense that "It never rains but it pours" or
"that's done it" "
we needed, another disgrace".
I advise you to start with Marine Ice Sheet Instability “For Dummies”, David Docquier June 22, 2016 (EGU Blogs)
https://blogs.egu.eu/divisions/cr/2016/06/22/marine-ice-sheet-instability-for-dummies-2/PS: perhaps others have other more useful references at hand and could kindly provide them to you