ABSTRACT. The simple calving laws currently used in ice-sheet models do not adequately reflect the complexity and diversity of calving processes. To be effective, calving laws must be grounded in a sound understanding of how calving actually works. Here, we develop a new strategy for formulating calving laws, using (a) the Helsinki Discrete Element Model (HiDEM) to explicitly model fracture and calving processes, and (b) the continuum model Elmer/Ice to identify critical stress states associated with HiDEM calving events. A range of observed calving processes emerges spontaneously from HiDEM in response to variations in ice-front buoyancy and the size of subaqueous undercuts. Calving driven by buoyancy and melt under-cutting is under-predicted by existing calving laws, but we show that the location and magnitude of HiDEM calving events can be predicted in Elmer/Ice from characteristic stress patterns. Our results open the way to developing calving laws that properly reflect the diversity of calving processes, and provide a framework for a unified theory of the calving process continuum.

Crumpling a thin sheet of material into a small volume requires energy for creating a network of deformations such as vertices and ridges. Scaling properties of a single elastic vertex or ridge have been analysed theoretically, and crumpling of a sheet by numerical simulations. Real materials are however elasto-plastic and large local strains induce irreversible plastic deformations. Hence, a numerical model that can be purely elastic or elasto-plastic is introduced. In crumpled elastic sheets, the ridge patterns are found to be similar, independent of the width to thickness (L/h) ratio of the sheet, and the fractal dimension of crumpled sheets is given by scaling properties of the energy and average length of ridges. In crumpled elasto-plastic sheets, such a similarity does not appear as the L/h ratio affects the deformations, and the fractal dimension (Dpl) is thereby reduced. Evidence is also found of Dpl not being universal but dependent on the plastic yield point of the material.

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Precipitation of exceptionally 13C-depleted authigenic carbonate is a result of, and thus a tracer for, sulphate-dependent anaerobic methane oxidation, particularly in marine sediments. Although these carbonates typically are less depleted in 13C than in the source methane, because of incorporation of C also from other sources, they are far more depleted in 13C (δ13C as light as −69‰ V-PDB) than in carbonates formed where no methane is involved. Here we show that oxidation of biogenic methane in carbon-poor deep groundwater in fractured granitoid rocks has resulted in fracture-wall precipitation of the most extremely 13C-depleted carbonates ever reported, δ13C down to −125‰ V-PDB. A microbial consortium of sulphate reducers and methane oxidizers has been involved, as revealed by biomarker signatures in the carbonates and S-isotope compositions of co-genetic sulphide. Methane formed at shallow depths has been oxidized at several hundred metres depth at the transition to a deep-seated sulphate-rich saline water. This process is so far an unrecognized terrestrial sink of methane.

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