The surface of ice exhibits the swath of phase-transition phenomena common to all materials and as such it acts as an ideal test bed of both theory and experiment. It is readily available, transparent, optically birefringent, and probing it in the laboratory does not require cryogenics or ultrahigh vacuum apparatus. Systematic study reveals the range of critical phenomena, equilibrium and nonequilibrium phase-transitions, and, most relevant to this review, premelting, that are traditionally studied in more simply bound solids. While this makes investigation of ice as a material appealing from the perspective of the physicist, its ubiquity and importance in the natural environment also make ice compelling to a broad range of disciplines in the Earth and planetary sciences. In this review we describe the physics of the premelting of ice and its relationship with the behavior of other materials more familiar to the condensed-matter community. A number of the many tendrils of the basic phenomena as they play out on land, in the oceans, and throughout the atmosphere and biosphere are developed.

Frost heave is the process by which the freezing of water-saturated soil causes the deformation and upward thrust of the ground surface. We describe the fundamental interactions between phase change and fluid flow in partially frozen, saturated porous media (soils) that are responsible for frost heave. Water remains only partially frozen in a porous medium at temperatures below 0 • C owing both to the depression of the freezing temperature at curved phase boundaries and to interfacial premelting caused by long-range intermolecular forces. We show that while the former contributes to the geometry of fluid pathways, it is solely the latter effect that generates the forces necessary for frost heave. We develop a simple model describing the formation and evolution of the ice lenses (layers of ice devoid of soil particles) that drive heave, based on integral force balances. We determine conditions under which either (i) a single ice lens propagates with no leading frozen fringe, or (ii) a single, propagating ice lens is separated from unfrozen soil by a partially frozen fringe, or (iii) multiple ice lenses form.

[1] Slow slip and tectonic tremor in subduction zones take place at depths where there is abundant evidence for distributed shear over broad zones ($10-10 3 m) composed of rocks with marked differences in mechanical properties. Here we model quasi-dynamic rupture along faults composed of material mixtures characterized by different rateand-state-dependent frictional properties to determine the parameter regime capable of producing slow slip in an idealized subduction zone setting. Keeping other parameters fixed, the relative proportions of velocity-weakening (VW) and velocity-strengthening (VS) materials control the sliding character (stable, slow, or dynamic) along the fault. The stability boundary between slow and dynamic is accurately described by linear analysis of a double spring-slider system with VW and VS blocks. Our results place bounds on the volume fractions of VW material present in heterogeneous geological assemblages that host slow slip and tremor in subduction zones.

[1] We examine how frictional heating drives the evolution of temperature, strength, and fracture energy during earthquake slip. For small slip distances, heat and pore fluid are unable to escape the shearing fault core, and the behavior is well approximated by simple analytical models that neglect any transport. Following large slip distances, the finite width of the shear zone is small compared to the thicknesses of the thermal and hydrological boundary layers, and the fault behavior approaches that predicted for the idealized case of slip on a plane. To evaluate the range in which the predictions of these two sets of approximations are valid, we develop a model that describes how frictional dissipation within a finite shear zone drives heat and mass transport through the surrounding static gouge. With realistic parameter values and slips greater than a few centimeters, the subsequent evolution of strength and fracture energy are approximated well by the planar slip model. However, the temperature evolution is much more sensitive to the finite shear zone thickness, and the ultimate temperature rise tends to be intermediate between that predicted for the two simplified cases. We explore the range of conditions necessary for melting to begin and focus in particular on the potential role of fault zone damage in facilitating fluid transport and promoting larger temperature increases. We discuss how the apparent scarcity of exhumed pseudotachylytes places constraints on some of the more uncertain fault zone parameters.

[1] The ice-till interface beneath soft-bedded glaciers can be marked by an abrupt transition from an ice layer above to unfrozen sediments below. Alternatively, the transition can be more gradual, with ice infiltrating the underlying sediments to form a fringe layer that contains a mixture of ice, liquid water, and sediment particles. The fringe thickness h is predicted to commonly be several decimeters to meters in scale, implying that significant sediment transport can occur when sliding occurs beneath. I adapt theories for the thermodynamic and mechanical balances that control freezing and melting in porous media to determine h as a function of effective stress N, the rate of basal heat flow, and key sediment properties. A fringe is expected only when N > p f % 1.1 (T m À T f ) MPa/°C, where T m À T f is the temperature drop below the pressure-melting point that is needed for ice to infiltrate the pore space; p f increases with decreased grain size. For sediment properties that are within the typical range expected of the tills beneath glaciers, p f = O (10 4 ) Pa. The rate that water can be transported through the fringe and frozen onto or melted from the glacier base can achieve a steady state that is in balance with the rate that latent heat is transported to or from the basal interface. At constant N, when a gradual increase in heat flow from the glacier base causes the rate of melting to decrease, h increases and continues to do so when the heat flow is great enough to produce freezing. As freezing becomes more rapid and h increases further, the rate of fluid supply to the glacier base reaches a maximum when the effective permeability is sufficiently reduced by the partial ice saturation in the fringe. Larger h can be achieved with slower freezing at the glacier base, but steady states with larger h are unstable. The maximum rate of fluid supply to the glacier base is greater at lower N, higher temperature gradients, and for sediments with higher permeabilities. Unsteady behavior can lead to large changes in h when there is a mismatch between the rate that latent heat can be extracted and the rate that fluid is supplied to the glacier base. Transient behavior driven by abrupt changes in N is characterized by rapid variations in freezing rate, followed by slower adjustments to h that are limited by the timescale for the conduction of latent heat. The resulting patterns of sediment deformation are expected to commonly be distributed over finite depth ranges even when shear is perfectly localized at any single instant in time.

We derive analytical expressions for the velocity of an insoluble particle near an advancing solidi"cation front when the intermolecular interactions are described by a power-law dependence between the "lm thickness and the undercooling. We predict that the maximum particle velocity, which corresponds to the lowest solidi"cation velocity at which particle trapping occurs, depends inversely on the particle radius. The critical velocity is less sensitive to the temperature gradient and the precise dependence changes with di!erent interaction types. When the critical velocity is exceeded, the particle becomes trapped within the solid region after being pushed slightly ahead of its initial position. The predicted particle displacement is typically only a fraction of the particle radius. Particle buoyancy can enhance or reduce the tendency for the particle to be captured, though it does not a!ect the parametric dependence of the critical velocity on the particle radius and the temperature gradient.

The best high-resolution records of climate over the past few hundred millennia are derived from ice cores retrieved from Greenland and Antarctica. The interpretation of these records relies on the assumption that the trace constituents used as proxies for past climate have undergone only modest post-depositional migration. Many of the constituents are soluble impurities found principally in unfrozen liquid that separates the grain boundaries in ice sheets. This phase behaviour, termed premelting, is characteristic of polycrystalline material. Here we show that premelting influences compositional diffusion in a manner that causes the advection of impurity anomalies towards warmer regions while maintaining their spatial integrity. Notwithstanding chemical reactions that might fix certain species against this prevailing transport, we find that-under conditions that resemble those encountered in the Eemian interglacial ice of central Greenland (from about 125,000 to 115,000 years ago)-impurity fluctuations may be separated from ice of the same age by as much as 50 cm. This distance is comparable to the ice thickness of the contested sudden cooling events in Eemian ice from the GRIP core.

Abstract.Vast quantities of clathrate hydrate are found in the Arctic and in marine sediments along continental margins. The clathrate structure traps enormous volumes of methane gas, which is both a possible source of global climate change and a potential energy resource. The growth rate and spatial distribution of gas hydrate in the shallow sediments are influenced by a variety of interacting physical processes. In order to quantify these processes, we develop mathematical models for hydrate formation in porous media. An analytical model is derived for the idealized problem of hydrate growth in a porous half-space which is cooled on its boundary. Our calculations predict the growth rate of a hydrate layer for a given rate of cooling and show that the volume of hydrate is strongly dependent on the two-phase equilibrium between hydrate and seawater. For a representative phase diagram we find that the volume of hydrate in the layer is less than 1% of the pore volume. Larger volumes of hydrate observed in some locations demand a sustained supply of gas and a long accumulation time. Numerical calculations are used to investigate situations that are more representative of conditions in marine sediments. A simple theoretical expression is derived for the rate of hydrate accumulation due to advection of methane gas from depth. Using typical estimates of fluid velocities in accretionary environments, we obtain an accumulation rate of 1% of the pore volume in 105 years. The predicted vertical distribution of hydrate is consistent with geophysical inferences from observed hydrate occurrences along the Cascadia margin. Similar distributions can arise from the combined effects of in situ methane production and warming due to ongoing sedimentation. Predicted differences between these two formation models may be detectable in geophysical and geochemical measurements.