Subglacial floods (jökulhlaups) are well documented as occurring beneath present day glaciers and ice caps. In addition, it is known that massive floods have occurred from ice-dammed lakes proximal to the Laurentide ice sheet during the last ice age, and it has been suggested that at least one such flood below the waning ice sheet was responsible for a dramatic cooling event some 8000 years ago. We propose that drainage of lakes from beneath ice sheets will generally occur in a time-periodic fashion, and that such floods can be of severe magnitude. Such hydraulic eruptions are likely to have caused severe climatic disturbances in the past, and may well do so in the future.

ABSTRACT. In this paper we undertake a quantitative analysis of the dynamic process by which ice underneath a dry porous debris layer melts. We show that the incorporation of debris-layer airflow into a theoretical model of glacial melting can capture the empirically observed features of the so-called Østrem curve (a plot of the melt rate as a function of debris depth). Specifically, we show that the turning point in the Østrem curve can be caused by two distinct mechanisms: the increase in the proportion of ice that is debris-covered and/or a reduction in the evaporative heat flux as the debris layer thickens. This second effect causes an increased melt rate because the reduction in (latent) energy used for evaporation increases the amount of energy available for melting. Our model provides an explicit prediction for the melt rate and the temperature distribution within the debris layer, and provides insight into the relative importance of the two effects responsible for the maximum in the Østrem curve. We use the data of Nicholson and Benn (2006) to show that our model is consistent with existing empirical measurements.

When a mining company begins extraction from a finite resource, it does so in the presence of numerous uncertainties. One key uncertainty is the future price of the commodity being extracted, since a large enough drop in price can make a resource no longer cost-effective to extract, resulting in the mine being closed down. By specifying a stochastic price process, and implementing a financial-type model which leads to the use of partial differential equations, this paper creates the framework for efficiently capturing the probability of a mine remaining open throughout its planned extraction period, and derives the associated expected lifetime of extraction. An approximation to the abandonment price is described, which enables a closedform solution to be derived for the probability of operational success and expected lifetime. This approximation compares well with the full solution obtained using a semi-Lagrangian numerical technique.

Ice cauldrons are depressions which form at the surface of ice sheets when an underlying subglacial lake empties, in particular when subglacial volcanic eruptions occur. Notable examples of such cauldrons occur on the surface of the Vatnajökull ice cap in Iceland. More generally, cauldrons will form when a subglacial lake empties during a jökulhlaup. The rate of subsidence of the ice surface is related to the rate at which the subglacial water empties from the lake. We use a viscous version of classical beam theory applied to the ice sheet to determine the relation between the subsidence rate and flood discharge. We use the results to make inferences concerning ring fracture spacings in cauldrons, the consequent effect on flood discharge dynamics and the likely nature of subsidence events in the Antarctic Ice Sheet.

Antarctica contains some of the most productive regions on Earth for collecting meteorites. These small areas of glacial ice are known as meteorite stranding zones, where upward-flowing ice combines with high ablation rates to concentrate large numbers of englacially transported meteorites onto their surface. However, meteorite collection data shows that iron and stony-iron meteorites are significantly under-represented from these regions as compared with all other sites on Earth. Here we explain how this discrepancy may be due to englacial solar warming, whereby meteorites a few tens of centimetres below the ice surface can be warmed up enough to cause melting of their surrounding ice and sink downwards. We show that meteorites with a high-enough thermal conductivity (for example, iron meteorites) can sink at a rate sufficient to offset the total annual upward ice transport, which may therefore permanently trap them below the ice surface and explain their absence from collection data.

Contemporary calculations for the flux of extraterrestrial material falling to the Earth’s surface (each event referred to as a “fall”) rely upon either short-duration fireball monitoring networks or spatially limited ground-based meteorite searches. To date, making accurate fall flux estimates from the much-documented meteorite stranding zones of Antarctica has been prohibited due to complicating glacial ice dynamics and difficulties in pairing together distinct meteorite samples originating from the same fall. Through glaciological analysis and use of meteorite collection data, we demonstrate how to overcome these barriers to making flux estimates. Furthermore, by showing that a clear latitudinal variation in fall frequencies exists and then modeling its mathematical form, we are able to expand our Antarctic result to a global setting. In this way, we hereby provide the most accurate contemporary fall flux estimates for anywhere on Earth. Inverting the methodology provides a valuable tool for planning new meteorite collection missions to unvisited regions of Antarctica. Our modeling also enables a reassessment of the risk to Earth from larger meteoroid impacts—now 12% higher at the equator and 27% lower at the poles than if the flux were globally uniform.

The theoretical basis of subglacial channel dynamics can be traced back to the work of Röthlisberger (1972) and Nye (1953). Röthlisberger (1972) considered the channels’ behaviour to be governed by a mix between water friction melting back the channel walls and the viscous closure of the surrounding ice; Nye (1953) derived a viscous closure rate for the ice. While their modelling is evidently well constructed, two aspects of their work have gone undeveloped. The first is the consideration of a finite glacier depth within the viscous closure law, instead of the assumption of an infinite glacier depth. The second is the allowance of a region of open channel flow, so that a channel’s water may transition from a region of closed channel flow to one where the water is exposed to the atmosphere. This paper helps close these two gaps, showing how Nye’s equation for the rate of ice closure can be modified, and how the point of transition between closed and open channel flow may be determined.

National reporting organizations and regulatory bodies for the minerals and mining sector are requiring publicly reported OreReserve estimates to take account of uncertainties. Whilst methodologies that account for physical uncertainty appear relatively well developed, methodologies which can take account of economic uncertainty appear much less so. To counter this shortfall, we present an efficient and general methodology which can quantify the effect of price uncertainty within reserve estimates, providing both the expected reserve size and the associated distribution (box whisker plot). This statistical information can be used by interested parties to understand precisely where the reserve risks lie, which we highlight in a worked example.