The Strange Physics of Glaciers: Solid Ice That Flows Like Liquid

A glacier is a body of ice that moves. The motion is slow — typically meters per year, sometimes kilometers per year for surge glaciers, occasionally tens of meters per day during a calving event — but it is unambiguous, measurable, and continuous. Stake out a transect across a glacier in summer; come back in autumn; the stakes have moved downstream. The ice is solid. The ice is at temperatures well below freezing. And the ice is, by any operational definition, flowing like a viscous liquid. The explanation for this behavior is the most interesting bit of materials physics most people never learn.

The naive intuition is that solid ice cannot flow because solids do not flow. The intuition is wrong about all solids, not just ice — every solid, given enough time and pressure, undergoes creep, the slow plastic deformation that geologists call solid-state flow. Mountains slump. Salt domes rise through sedimentary basins like teardrops in oil. The continents themselves drift over the mantle in an analogous process at much larger scale. What makes glaciers special is that the timescale for ice creep is short enough to be observed within a single human lifetime, and the physics of why is well-characterized enough to make precise predictions.

The crystal structure of ice

Most natural ice on Earth is Ice Ih, the hexagonal crystal form that water freezes into at standard pressure. The crystal structure has water molecules arranged in a roughly tetrahedral pattern, with each molecule hydrogen-bonded to four neighbors. The hexagonal symmetry shows up in the snowflakes that grow from water vapor, the columnar structures in glacier ice, and the basal-plane preferred-orientation that gives glaciers their distinctive flow behavior.

The basal plane is the load-bearing concept. Within the hexagonal crystal, there is one specific crystallographic plane (the basal plane, perpendicular to the c-axis of the hexagonal lattice) along which ice crystals slip much more easily than along any other plane. The energy required to slide one layer of basal-plane atoms past the next is roughly two orders of magnitude lower than the energy required to slide along any other plane. The result is that ice crystals deform almost exclusively by basal-plane slip, and a body of ice with crystals oriented with their basal planes aligned will deform much faster than a body with random orientations.

Glaciers, after a few centuries of flow, develop preferred crystal orientations through dynamic recrystallization — crystals that happen to have their basal planes aligned with the local stress slip easily and survive; crystals oriented otherwise deform poorly, accumulate strain energy, and eventually recrystallize into orientations that fit the stress better. The process produces glacier ice with strong fabric — anisotropic mechanical properties that depend on the direction of stress relative to the crystal orientation. The flow law for glacier ice is consequently not the simple isotropic creep equation textbooks use; it is a tensor relationship that has occupied glaciologists for decades.

The Glen flow law

The empirical flow law for glacier ice was characterized by John Glen in the 1950s through laboratory experiments on ice samples under controlled stress. The result, now called Glen's flow law, is that the strain rate (rate of deformation) is proportional to the stress raised to a power, with the exponent typically around 3 for natural glacier ice at standard glacier stresses. The flow is non-Newtonian — doubling the stress more than doubles the flow rate — which is why glacier flow accelerates near steep cliffs and slows on flat terrain.

The exponent of 3 is not arbitrary; it falls out of the underlying dislocation-glide microphysics of crystalline materials at high homologous temperature (the ratio of operating temperature to melting temperature). All crystalline solids show similar power-law creep behavior near their melting points. Glaciers are doing the same thing rocks do at depth in the mantle, just at a much lower absolute temperature because ice has a much lower melting point. The mathematics is general; the specific parameters are material-dependent.

The power-law exponent has practical consequences for glacier modeling. A linear flow law would predict that doubling the surface slope doubles the flow rate; the cube law predicts that doubling the slope multiplies the flow rate by eight. Glaciers in steep alpine valleys flow much faster than glaciers in gentle plateau settings, and the cube law is the reason. Surging glaciers, which can accelerate by an order of magnitude over weeks, are doing so by changes in basal stress rather than changes in driving stress, because the cube law makes basal-stress reduction an extremely powerful accelerator.

Pressure-melting and basal sliding

The most interesting layer of glacier physics is what happens at the very bottom of the ice column, where the glacier contacts bedrock. The pressure at the bottom of a kilometer-thick glacier is around 9 megapascals (about 90 atmospheres). At that pressure, the melting point of water-ice is depressed by a few hundredths of a degree Celsius. If the glacier is exactly at the pressure-depressed melting point — which it often is at depth, due to the geothermal heat flux from the bedrock plus the heat released by deformation — then the bottom is a thin film of meltwater between solid ice and solid rock.

The meltwater layer changes everything. With a meltwater layer, the ice can slide over the bedrock with relatively little resistance, and the glacier's overall flow becomes a sum of internal deformation (plastic creep through the bulk of the ice) plus basal sliding (the entire ice column moving as a unit over the lubricated base). Cold-based glaciers, where the bottom is below the pressure-melting point, are frozen to the bedrock and flow only by internal deformation, typically meters per year. Warm-based glaciers, where the bottom is at the pressure-melting point, can flow by basal sliding, often hundreds of meters per year. The difference is determined by a few hundredths of a degree at the base.

The meltwater system at the base of warm-based glaciers is itself complex. The water collects in subglacial channels that grow and shrink with the seasons; subglacial lakes form behind ice dams and occasionally drain catastrophically; the basal water pressure modulates the basal friction in feedback loops that produce surge cycles in some glaciers. The 1972-1974 surge of Variegated Glacier in Alaska, observed in detail by glaciologists who had instrumented it before the surge, established the basal-water-pressure feedback as the canonical mechanism for surging behavior.

Strain heating and the thermal regime

Deformation of ice releases heat, just as deformation of any material does. For most everyday materials and stresses, the heat is negligible. For glaciers, the heat from deformation is comparable to the geothermal heat flux from the bedrock, and the two together govern the thermal regime of the lower ice column.

The strain heating is concentrated where the strain rate is highest, which under Glen's cube law is concentrated near the bedrock where the shear stress is highest. The result is that the basal layer of a glacier is significantly warmer than the upper layers — it can be at the pressure-melting point even when the surface is far below freezing. The thermal structure of an ice sheet is thus a sandwich: cold top, warm bottom, with the temperature profile determined by the balance of geothermal heat, strain heating, and the conduction of cold from the surface downward.

This sandwich structure has implications for ice-sheet stability that climate scientists have studied extensively. The Antarctic and Greenland ice sheets have warm-based regions where the ice slides on a meltwater layer, and cold-based regions frozen to the bedrock. The boundary between them is not stationary — small changes in surface temperature (over a century) or in geothermal heat flux (over millennia) can shift the boundary, with disproportionate effects on the ice sheet's discharge into the ocean. The Pine Island and Thwaites glaciers in West Antarctica, which together drain a significant fraction of the West Antarctic Ice Sheet, are warm-based and flowing rapidly into the Amundsen Sea, and the dynamics of their grounding lines (where the ice transitions from grounded on bedrock to floating on the ocean) are the dominant uncertainty in projections of sea level rise over the next century.

What glaciers reveal

The internal record of a glacier is a stratigraphic sequence of annual snow layers, each compressed by the weight of subsequent layers and gradually transformed from snow to firn to glacier ice. The transformation takes decades to centuries depending on temperature and accumulation rate. The annual layering is preserved as visible bands in the ice, as geochemical signals (oxygen-isotope ratios that record temperature, dust layers that record volcanic eruptions, atmospheric gas inclusions that record CO2 concentrations), and as pollen and other biological signals.

The deepest ice cores from Antarctica reach back nearly a million years (the EPICA Dome C core covers 800,000 years; ongoing efforts target 1.5 million years). The chronology is direct in the upper sections (counted annual layers) and modeled in the deeper sections (using strain estimates from glacier-flow models). The ice core record is the highest-resolution, longest, most chemically detailed climate record we have for the late Pleistocene and Holocene, and the entire field of paleoclimate depends on the glacier physics described above being well-enough understood to convert depth-in-core to age-in-years with confidence.

The future

The active research questions in glaciology are concentrated at the interfaces — grounding-line dynamics, subglacial hydrology, the ocean-ice interaction at marine ice cliffs, the response of cold-based ice to surface warming, the feedback between calving and upstream flow. The work is high-stakes because the glaciers' contributions to sea-level rise depend on these interface dynamics, and the interface dynamics involve physics (poromechanics of subglacial sediments, two-phase flow of ocean water under floating ice shelves, fracture mechanics of marine ice cliffs) that is at the edge of being modeled correctly.

The open questions are not abstract. The fate of West Antarctic ice over the next century is among the largest uncertainties in human-survivable climate scenarios, and the answer hinges on details of basal sliding, marine-ice-cliff stability, and ocean-driven melting under floating shelves. The community has made enormous progress in the last twenty years, and the remaining uncertainties are large enough to span the difference between manageable sea-level rise and civilization-disrupting sea-level rise. The physics of solid ice that flows is no longer just academic.

The summary

Glaciers are solid ice undergoing slow plastic flow, governed by crystal-scale dislocation glide along basal planes, accelerated near the melting point, and lubricated at the base by pressure-melted water films. The mathematics is the same as for any high-temperature creep in crystalline solids, but the specific parameters of ice put the timescale into a range observable within a human lifetime, which is what makes glacier flow such a good demonstration of solid-state flow physics. The internal structure preserves the longest-resolution climate record we have. The boundary dynamics control sea-level rise scenarios that govern the next century. The strange in-between behavior of solid ice near its melting point is one of the deepest connections we have between condensed-matter physics, climate science, and Earth-system history. Solids really do flow. The ice was just kind enough to do it fast enough that we could see it happening.