A rate and state friction law for saline ice

Sea ice friction models are necessary to predict the nature of interactions between sea ice floes. These interactions are of interest on a range of scales, for example, to predict loads on engineering structures in icy waters or to understand the basin-scale motion of sea ice. Many models use Amonton's friction law due to its simplicity. More advanced models allow for hydrodynamic lubrication and refreezing of asperities; however, modeling these processes leads to greatly increased complexity. In this paper we propose, by analogy with rock physics, that a rate- and state-dependent friction law allows us to incorporate memory (and thus the effects of lubrication and bonding) into ice friction models without a great increase in complexity. We support this proposal with experimental data on both the laboratory (∼0.1 m) and ice tank (∼1 m) scale. These experiments show that the effects of static contact under normal load can be incorporated into a friction model. We find the parameters for a first-order rate and state model to be A = 0.310, B = 0.382, and μ0 = 0.872. Such a model then allows us to make predictions about the nature of memory effects in moving ice-ice contacts.

Mesozoic climates: General circulation models and the rock record

General circulation models (GCMs) use the laws of physics and an understanding of past geography to simulate climatic responses. They are objective in character. However, they tend to require powerful computers to handle vast numbers of calculations. Nevertheless, it is now possible to compare results from different GCMs for a range of times and over a wide range of parameterisations for the past, present and future (e.g. in terms of predictions of surface air temperature, surface moisture, precipitation, etc.). GCMs are currently producing simulated climate predictions for the Mesozoic, which compare favourably with the distributions of climatically sensitive facies (e.g. coals, evaporites and palaeosols). They can be used effectively in the prediction of oceanic upwelling sites and the distribution of petroleum source rocks and phosphorites. Models also produce evaluations of other parameters that do not leave a geological record (e.g. cloud cover, snow cover) and equivocal phenomena such as storminess. Parameterisation of sub-grid scale processes is the main weakness in GCMs (e.g. land surfaces, convection, cloud behaviour) and model output for continental interiors is still too cold in winter by comparison with palaeontological data. The sedimentary and palaeontological record provides an important way that GCMs may themselves be evaluated and this is important because the same GCMs are being used currently to predict possible changes in future climate. The Mesozoic Earth was, by comparison with the present, an alien world, as we illustrate here by reference to late Triassic, late Jurassic and late Cretaceous simulations. Dense forests grew close to both poles but experienced months-long daylight in warm summers and months-long darkness in cold snowy winters. Ocean depths were warm (8 degrees C or more to the ocean floor) and reefs, with corals, grew 10 degrees of latitude further north and south than at the present time. The whole Earth was warmer than now by 6 degrees C or more, giving more atmospheric humidity and a greatly enhanced hydrological cycle. Much of the rainfall was predominantly convective in character, often focused over the oceans and leaving major desert expanses on the continental areas. Polar ice sheets are unlikely to have been present because of the high summer temperatures achieved. The model indicates extensive sea ice in the nearly enclosed Arctic seaway through a large portion of the year during the late Cretaceous, and the possibility of sea ice in adjacent parts of the Midwest Seaway over North America. The Triassic world was a predominantly warm world, the model output for evaporation and precipitation conforming well with the known distributions of evaporites, calcretes and other climatically sensitive facies for that time. The message from the geological record is clear. Through the Phanerozoic, Earth's climate has changed significantly, both on a variety of time scales and over a range of climatic states, usually baldly referred to as "greenhouse" and "icehouse", although these terms disguise more subtle states between these extremes. Any notion that the climate can remain constant for the convenience of one species of anthropoid is a delusion (although the recent rate of climatic change is exceptional). (c) 2006 Elsevier B.V. All rights reserved.