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The cryosphere (from the Greek kryos, "cold" or "frost") comprises all parts of the Earth system where water is present in solid form, including ice sheets, ice shelves, glaciers, sea ice, lake and river ice, seasonal snow cover, and perennially frozen ground (permafrost). Within Earth system science, glaciology, and physical oceanography, the cryosphere is an active subsystem that influences Earth's energy budget, contributes to the formation of the dense waters that fill the deep ocean, and is a major control on sea level.

Most of Earth's surface ice is hexagonal ice I_h, which exists at a high homologous temperature (_T_/_T__m ≈ 0.8 to 1.0, where T_m = 273.15 K is the melting temperature at 1 atm). Because cryospheric reservoirs lie close to the triple point of water (273.16 K, 611.657 Pa), small changes in radiative forcing or ocean heat transport can cause phase changes that absorb or release large amounts of latent heat, both of fusion (L_f ≈ 3.34 × 10⁵ J/kg) and of sublimation (L_s ≈ 2.83 × 10⁶ J/kg). This makes the cryosphere both a sensitive indicator and a non-linear amplifier of climate change.

Although the cryosphere holds less than 2% of all water in the hydrosphere, it contains about 69% of Earth's fresh water. The potential contribution of each component to sea level is expressed as its sea-level equivalent (SLE): 361.8 gigatonnes (Gt) of water, or about 395 km³ of grounded ice, raises global mean sea level by 1 mm when spread over the ocean area of 3.618 × 10⁸ km².

Approximate size of the main components of the cryosphere

The northern permafrost region also stores about 1,400 to 1,600 petagrams of organic carbon (see below).

Land ice forms from snow in places where annual accumulation exceeds summer melting. Fresh snow has a low density (about 50 to 150 kg/m³) and a porosity of about 85 to 95%. As each year's snow is buried, it compacts through sintering, vapour transport, grain rearrangement, and recrystallization, becoming firn (about 400 to 830 kg/m³). The rate of densification depends on temperature and accumulation rate and is commonly described by the Herron–Langway model. At a depth of typically 50 to 120 m, firn reaches the pore close-off density of about 830 kg/m³. The interconnected air channels then become sealed into isolated bubbles, and the firn becomes impermeable glacial ice (about 917 kg/m³ for pure ice at 0 °C).

The trapped bubbles preserve samples of past atmospheric air, including CO₂, CH₄, and N₂O. Because the air is sealed off only at the base of the firn, the gas is younger than the surrounding ice. Together with the stable isotope ratios (δ¹⁸O and δD) of the ice itself, these records allow polar ice cores to reconstruct climate over the past 800,000 years.

The evolution of a glacier or ice sheet is governed by its mass balance. At a point where the ice thickness is H, conservation of mass requires that the rate of thickness change equal the surface mass balance (SMB) plus the basal mass balance (BMB; negative for melting, positive for freeze-on) minus the divergence of the ice flux q = _H_ ū, where ū is the depth-averaged horizontal velocity:

Integrating over the area of a marine-terminating ice sheet gives its total mass balance (in Gt/yr):

where BMB_tot is usually small for grounded ice and:

• Surface mass balance is the difference between accumulation (snowfall, frost deposition, and wind-drifted snow, with refreezing of meltwater in the firn retaining mass that would otherwise run off) and ablation (meltwater runoff, sublimation, and wind erosion). The elevation at which annual accumulation equals annual ablation (SMB = 0) is the equilibrium line altitude (ELA), which separates the accumulation zone above from the ablation zone below.
• Ice discharge D is the flux of ice across the grounding line or calving front, D = ∮ ρ_i H (ū · n) d_s_. This ice is lost to the ocean through calving and through melting beneath ice shelves and at the fronts of tidewater glaciers.

Ice behaves as a brittle elastic solid at high strain rates, fracturing to form crevasses. Under sustained stress over periods longer than hours to days, however, polycrystalline ice deforms continuously as a non-linearly viscous (shear-thinning) material. Deformation occurs mainly by dislocation creep on the basal (0001) planes of individual ice crystals and is described by Glen's flow law, formulated by John Glen in 1955:

where ε̇_ij = ½(∂_u__i/∂_x__j + ∂_u__j/∂_x__i) is the strain-rate tensor, τ_ij is the deviatoric stress tensor, τ_e = (½ τ_klτ_kl)^1/2 is the effective stress, and n is the creep exponent. A value of n = 3 is standard, although values of about 1.8 to 4 have been reported for different stresses and deformation mechanisms. The rate factor A follows an Arrhenius relation:

where T^* = T + β_C p is the temperature corrected for the lowering of the melting point by pressure (β_C ≈ 7.4 × 10⁻⁸ K/Pa). The activation energy Q_c is about 60 kJ/mol below −10 °C and about 115 kJ/mol above it, an increase attributed to processes at grain boundaries near the melting point.

In the shallow ice approximation, the driving stress is balanced locally by vertical shear, τ_xz(z) = −_ρ__i g (s − z) ∂_s_/∂_x_, where s is the surface elevation. Integrating the flow law twice through the ice thickness gives the ice flux due to internal deformation:

• *_q_**_def = −(2_A_/(n + 2)) (ρ_i g)ⁿ |∇_s_|^_n_−1 ∇_s_ H^_n_+2

so that, for n = 3, the magnitude of the flux is proportional to |∇_s_|³ H⁵ and is extremely sensitive to ice thickness.

Where the base of a glacier is at the pressure-melting point (a temperate or polythermal bed), warmed by geothermal heat, frictional heating, and surface meltwater reaching the bed through moulins, the ice can also move by basal sliding and by deformation of water-saturated sediment (till). Johannes Weertman (1957) explained sliding over hard beds by a combination of regelation around small obstacles and enhanced creep around large ones, leading to sliding laws of the form:

where τ_b is the basal drag, u_b the sliding speed, C a friction coefficient, and m ≈ 1/3. Later work by Lliboutry, Iken, Schoof, and others incorporated the formation of water-filled cavities, making sliding depend on the effective pressure:

the difference between the ice overburden pressure and the subglacial water pressure p_w, and limiting basal drag to a Coulomb friction value, τ_b ≤ μ N_eff. When meltwater reaching a poorly connected (linked-cavity) drainage system raises p_w toward the overburden pressure (N_eff → 0), the ice is partly lifted off its bed, basal drag falls, and ice streams and outlet glaciers can flow at hundreds to thousands of metres per year.

Ice shelves fringe about 75% of the Antarctic coastline, including the large Ross and Filchner–Ronne ice shelves, and occur in northern Greenland. Grounded ice streams flowing toward the coast cross the grounding line, where the ice becomes thin enough to float. Flotation requires ρ_i H = ρ_sw d_w, where ρ_sw is the density of seawater and d_w the water depth. Beyond the grounding line the ice spreads over the ocean as a floating ice shelf, typically a few hundred metres to more than 1,000 m thick.

Because floating ice experiences no basal friction, flow within an ice shelf is dominated by longitudinal stretching and lateral shear and is described by the shallow shelf approximation. At the calving front, the outward pressure of the ice column exceeds the opposing hydrostatic pressure of the seawater, producing a depth-averaged longitudinal stress:

In a freely floating ice tongue, this stress stretches the ice seaward. When an ice shelf is confined within an embayment, or grounded locally on seabed highs (ice rises and pinning points), drag along its sides and at these contacts resists the flow. This transmits a compressive "buttressing" stress upstream across the grounding line, which restrains the outflow of grounded ice.

Ice shelves can lose this buttressing role in two main ways. Warm, modified Circumpolar Deep Water entering the cavity beneath an ice shelf can melt it from below, at rates that can exceed 10 to 50 m/yr near deep grounding lines. Alternatively, surface meltwater can fracture the shelf from above and cause rapid disintegration, as happened to the Larsen B Ice Shelf in 2002. In either case, the loss of buttressing causes the grounded glaciers that fed the shelf to accelerate, by several times in the case of Larsen B, and to thin.

Unlike land ice, which forms from compacted snow, sea ice forms by the freezing of seawater. At any given time it covers about 7% of the world ocean, reaching about 15 × 10⁶ km² in the Arctic in March and about 18 × 10⁶ km² around Antarctica in September.

Pure water has its maximum density at 3.98 °C and freezes at 0 °C. Dissolved salt in seawater (salinity S ≈ 34 to 35 g/kg) lowers the freezing point to T_f ≈ −0.054 S ≈ −1.9 °C, below the temperature of maximum density. Cooling surface seawater therefore becomes steadily denser until it freezes, causing convection that cools the whole surface layer above the polar halocline to the freezing point before ice can form.

Ice formation begins with millimetre-sized crystals called frazil ice, which collect into a soupy layer of grease ice. In calm water this freezes into a thin elastic sheet called nilas; in rough water the crystals instead form rounded pancake ice, which later freezes together. Once a continuous sheet has formed, further growth occurs at its base. The base remains at the freezing point T_f, while the top surface is exposed to cold air at temperature T_s, so the latent heat released at the base must be conducted upward through the ice (thermal conductivity k_i ≈ 2 W m⁻¹ K⁻¹) and through any snow cover, which conducts heat much less well (k_s ≈ 0.15 to 0.30 W m⁻¹ K⁻¹).

Neglecting snow and the heat stored in the ice, the growth rate is set by a balance between conduction and the oceanic heat flux F_w (Stefan's law, 1891):

With no ocean heat flux, integration shows that ice thickness increases with the square root of the accumulated freezing degree-days, θ_FDD = ∫(T_f − T_s) d_t_:

Because the growth rate is inversely proportional to thickness, thin new ice grows quickly (several centimetres per day in cold conditions) and loses heat rapidly to the atmosphere, whereas thick ice insulates the ocean. Multi-year ice therefore approaches an equilibrium thickness, typically 2 to 4 m in the Arctic, at which winter growth balances summer melt.

Pack ice moves in response to wind and ocean currents and is commonly modelled as a viscous–plastic material. Divergence opens linear cracks called leads and areas of open water called polynyas, where new ice forms rapidly. Convergence piles ice into pressure ridges, with keels extending 10 to 30 m below the surface.

The ice crystal lattice incorporates almost none of the dissolved ions in seawater. Some concentrated brine is initially trapped in pockets and channels between the crystals, giving new ice a bulk salinity of about 10 g/kg or more. This falls to about 4 to 6 g/kg in first-year ice through gravity drainage during growth, and to below about 1 to 3 g/kg in multi-year ice after summer meltwater flushes the brine out. Most of the salt is expelled into the ocean beneath the ice, a process called brine rejection. In coastal Antarctic polynyas, such as those of the Weddell and Ross seas, and on Arctic continental shelves, continued winter ice production adds cold, salty water to the shelf. This raises its density enough to form the dense water that becomes Antarctic bottom water and feeds the thermohaline circulation.

Sea ice is central to the ice–albedo feedback. Snow-covered sea ice reflects about 80 to 85% of incoming sunlight and bare ice about 50 to 65%, whereas open ocean, with an albedo of about 0.06, absorbs about 94%. When sea ice melts earlier in spring, the exposed dark ocean absorbs much more solar energy during the long polar summer days. This warms the upper ocean, delays freezing in autumn, and contributes to Arctic amplification.

Because floating ice is in hydrostatic equilibrium, Archimedes' principle states that it displaces a mass of seawater equal to its own mass:

If the ice were pure water melting into pure water, its meltwater would exactly fill the volume it displaced, and melting would not change sea level. However, ice shelves are fresh and sea ice is much less salty than seawater, so their meltwater (density ρ_fw ≈ 1,000 kg/m³) is less dense than the seawater (ρ_sw ≈ 1,026 kg/m³) they displaced:

Melting floating ice therefore raises sea level slightly, by about 2.6% of the submerged ice volume. At present this contributes about 0.05 mm/yr. If all floating ice on Earth melted, sea level would rise by about 4 cm, roughly 1,600 times less than the potential contribution of about 65 m from grounded ice.

Permafrost is defined on a thermal basis as ground (soil, sediment, peat, or rock, regardless of its ice or water content) that remains at or below 0 °C for at least two consecutive years. In the Northern Hemisphere, the permafrost region covers about 21 × 10⁶ km², roughly 24% of the exposed land surface, across Siberia, Alaska, northern Canada, and the Tibetan Plateau. Permafrost itself underlies about 14 × 10⁶ km² (about 15%). Permafrost also occurs beneath the shallow, flooded Arctic continental shelves (subsea permafrost). It is classified by the fraction of the landscape it underlies: continuous (more than 90%), discontinuous (50 to 90%), sporadic (10 to 50%), and isolated patches (less than 10%).

Ground temperature is governed by one-dimensional heat conduction with phase change:

where the apparent heat capacity C_eff = C_v + ρ_d L_f ∂_w__u/∂_T_ includes the latent heat associated with changes in the unfrozen water content w_u (ρ_d is the dry bulk density of the soil). A typical profile consists of:

1. The active layer, the surface layer above the permafrost table, typically 0.3 to 3 m thick, which thaws each summer and refreezes each winter. It supports plant roots and seasonal microbial activity.
2. The permafrost body, which extends from the permafrost table to the permafrost base and ranges from a few metres thick at its southern margin to about 1,500 m in parts of unglaciated Siberia. The seasonal temperature cycle fades with depth, becoming less than 0.1 °C at the depth of zero annual amplitude (about 10 to 20 m). Below this depth, temperature rises along the geothermal gradient (typically 15 to 30 K/km) until it reaches 0 °C at the base of the permafrost. Unfrozen zones within or beneath permafrost, often under deep lakes and rivers, are called taliks.

Many permafrost deposits, especially the late-Pleistocene, ice-rich silts known as yedoma in Siberia and Alaska, contain excess ground ice: ice that occupies more volume than the pore space of the thawed soil, in some cases 50 to 90% of the ground by volume. This ice takes the form of large polygonal ice wedges, segregated ice lenses, and ice-cored hills (pingos). When warming, or the loss of the insulating moss layer in a wildfire, deepens the active layer into ice-rich permafrost, the melting ice can no longer support the ground. The surface subsides, forming slumps, tilted "drunken" forests, and waterlogged thermokarst lakes. This abrupt thaw can expose carbon several metres deep within years, rather than the centuries required by gradual thaw from the surface.

Over tens of thousands of years, cold and waterlogged conditions slowed decomposition so that it lagged behind plant production. Freeze–thaw mixing of the soil (cryoturbation) and the deposition of wind-blown silt progressively buried plant and animal remains below the permafrost table. The northern permafrost region now holds an estimated 1,400 to 1,600 PgC. Of this, about 1,035 ± 150 PgC lies in the upper 3 m, and several hundred PgC lies in deeper yedoma and river-delta deposits. Further carbon is stored in subsea permafrost and methane clathrates.

The Arctic has warmed nearly four times faster than the global average since 1979. As the permafrost thaws, this old carbon re-enters the active carbon cycle by two microbial pathways, depending on local drainage and oxygen supply:

• Aerobic respiration in well-drained soils, where bacteria and fungi decompose the organic matter using oxygen and release carbon dioxide.
• Anaerobic decomposition in waterlogged thermokarst lakes, fens, and wetlands, where oxygen and alternative electron acceptors (NO₃⁻, Fe(III), SO₄²⁻) are quickly used up. Fermenting bacteria break organic matter down to acetate, H₂, and CO₂, which methanogenic archaea convert to methane:

CH₃COO⁻ + H⁺ → CH₄ + CO₂   (acetoclastic methanogenesis) CO₂ + 4H₂ → CH₄ + 2H₂O   (hydrogenotrophic methanogenesis)

Most of the carbon released is expected to be CO₂. Methane, much of which escapes as bubbles (ebullition) that bypass methane-oxidizing bacteria in the water, makes up only a small fraction of the carbon. Because methane has a 100-year global warming potential of about 27 to 30, however, it could account for a substantial share, perhaps a third, of the warming caused by permafrost carbon release. The IPCC Sixth Assessment Report assessed the resulting feedback as about 18 (range 3 to 41) PgC of CO₂ released per °C of global warming by 2100.

Thawing permafrost and retreating glaciers also release other stored substances:

• Mercury: northern permafrost soils store a large amount of mercury bound to organic matter. Estimates range from about 600 to about 1,650 gigagrams; the higher estimate would be nearly twice the amount in all other soils, the ocean, and the atmosphere combined. After thaw, sulfate- and iron-reducing bacteria in anoxic wetlands and sediments, carrying the hgcAB genes, can convert inorganic Hg²⁺ into neurotoxic methylmercury (CH₃Hg⁺), which accumulates in food webs.
• Acid drainage and pollutants: glacial retreat exposes freshly ground, sulfide-bearing rock such as pyrite (FeS₂) to air and water. Its oxidation produces sulfuric acid and releases iron, aluminium, arsenic, and other metals into streams. Melting glaciers also release persistent organic pollutants such as DDT and PCBs, and black carbon, deposited from the atmosphere during the 20th century.
• Microorganisms: viable microorganisms, including ancient viruses revived in the laboratory, have been recovered from Pleistocene permafrost. A 2016 anthrax outbreak on the Yamal Peninsula was linked to the thaw of infected animal carcasses.

Changes in global mean sea level (GMSL) result from changes in the density of ocean water (the steric component) and in the mass of water in the ocean (the barystatic component):

where z_b is the depth of the sea floor and A_ocean is the area of the ocean. These terms are monitored by three independent observing systems:

• Satellite altimetry (TOPEX/Poseidon, Jason-1, -2, and -3, and Sentinel-6 Michael Freilich) measures the total change.
• The Argo array of profiling floats measures the steric component.
• The GRACE and GRACE-FO gravity missions measure changes in ocean mass.

The rate of rise has increased from about 1.4 mm/yr over most of the 20th century to about 2.1 mm/yr in 1993–2002 and about 4.7 mm/yr in 2014–2023. The main contributions in recent decades are:

1. Thermal expansion (about 40%; roughly 1.4 to 1.8 mm/yr). The ocean has absorbed about 90% of Earth's energy imbalance, and warming water expands, increasing its volume without adding mass.
2. Glaciers (about 20%; about 270 Gt/yr, or 0.75 mm/yr, in 2000–2019). Although glaciers contain less than 1% of the world's land ice, they respond quickly to warming and many lie at relatively low elevations and latitudes, in regions such as Alaska, the Canadian Arctic, Patagonia, High Mountain Asia, the Andes, Svalbard, and the Alps.
3. The Greenland ice sheet (about 20%; roughly 250 to 280 Gt/yr, or about 0.7 to 0.8 mm/yr). Greenland is the largest single source of ice loss. Its losses come roughly equally from increased surface melt and runoff and from faster ice discharge. Melt is enhanced by darkening of the ablation zone through snow-grain growth, dust, and pigmented glacier algae such as Ancylonema nordenskiöldii. Discharge has increased through the acceleration and retreat of marine-terminating outlet glaciers, including Jakobshavn Isbræ, Helheim, and Kangerlussuaq, driven by warm Atlantic-origin water entering deep fjords. As the ice surface lowers into warmer air, melting increases further (the melt–elevation feedback).
4. The Antarctic ice sheet (about 10%; roughly 150 Gt/yr, or about 0.4 mm/yr, and increasing). The Antarctic interior is very cold (mean annual temperatures of about −30 to −60 °C), so surface runoff is negligible, and snowfall is expected to increase slightly with warming, as warmer air holds more moisture according to the Clausius–Clapeyron relation. Antarctic loss is driven almost entirely by ocean-forced increases in ice discharge. This is concentrated in the West Antarctic Ice Sheet, especially the Amundsen Sea sector, which includes Thwaites and Pine Island glaciers, and in the Antarctic Peninsula and parts of East Antarctica such as Totten Glacier.

Changes in the storage of water on land, for example in groundwater and reservoirs, make up the remainder of the budget.

Meltwater from a shrinking ice sheet does not raise sea level uniformly. Regional relative sea level departs from the global mean because of gravitational, rotational, and solid-Earth deformation (GRD) effects, described by the sea-level equation introduced by Farrell and Clark in 1976 and developed further by W. Richard Peltier, Jerry X. Mitrovica, and others:

• Glacial isostatic adjustment: over thousands of years the mantle behaves as a viscous fluid (viscosity about 10²¹ Pa·s). Removing an ice load causes immediate elastic uplift of the crust, followed by slow viscous uplift as mantle material flows back. Regions covered by ice during the last glacial period, such as Fennoscandia and Hudson Bay, are still rising, so relative sea level there is falling by up to about 10 mm/yr. The surrounding peripheral bulge, for example along the east coast of the United States, is subsiding, which adds to local sea-level rise.
• Gravitational attraction: a large ice sheet pulls nearby ocean water toward it. When the ice sheet loses mass, its attraction weakens and the crust beneath it rebounds. As a result, relative sea level falls within roughly 2,000 km of a shrinking ice sheet, while in the far field sea level rises by up to about 20 to 30% more than the global average. Melting in Greenland therefore raises sea level most in the Southern Hemisphere, and melting in West Antarctica raises it most in North America and Europe. Changes in Earth's rotation modify this pattern further.

The West Antarctic Ice Sheet (about 5.3 m SLE), which rests on bedrock up to about 2,500 m below sea level, and the marine basins of East Antarctica (including the Wilkes, Aurora, and Recovery basins, holding about 19 m SLE) are marine ice sheets. They are grounded below sea level, often on retrograde beds that deepen toward the interior.

Marine ice sheet instability (MISI) was proposed by Johannes Weertman in 1974 and John Mercer in 1978, and placed on a firm theoretical footing by Christian Schoof in 2007. For an ice sheet without buttressing, with Glen exponent n and sliding exponent m, Schoof showed that the ice flux across the grounding line depends on the ice thickness there, h_g:

For n = 3 and m = 1/3, the exponent is 4.75, so the flux increases roughly with the fifth power of grounding-line thickness. Because floating requires h_g = (ρ_sw/_ρ__i) d_w, it also increases roughly with the fifth power of water depth.

• On a prograde bed (deepening toward the ocean), a grounding line that retreats moves into shallower water. The outflow decreases and falls below the supply of ice from upstream, so the grounding line advances again. The position is stable.
• On a retrograde bed (deepening inland), a grounding line that retreats moves into deeper water, where the ice is thicker. The outflow increases and exceeds the supply from upstream, so the ice thins and the grounding line retreats further. Retreat can therefore become self-sustaining and difficult to reverse, until the grounding line reaches a seaward-rising section of bed or until buttressing from an ice shelf, for example in a narrow embayment, restrains the outflow.

Marine ice-cliff instability (MICI), proposed by Pollard, DeConto and Richard Alley in 2015, is a hypothesized brittle-failure mechanism that could add to MISI under strong atmospheric warming:

1. Hydrofracturing: liquid water is denser than ice, so a water-filled crevasse has a water pressure at its tip greater than the surrounding ice pressure. The crevasse can therefore propagate through the full thickness of an ice shelf within hours to days, breaking the shelf apart.
2. Ice-cliff failure: if the ice shelf is removed where the ice at the grounding line is more than about 800 to 1,000 m thick, a cliff about (1 − ρ_i/_ρ__sw) H ≈ 90 m or more high is left standing above the water. At such heights, stresses at the cliff face can exceed the strength of glacial ice (about 1 MPa), so the cliff collapses. On a retrograde bed this exposes progressively taller cliffs inland.

The importance of MICI remains debated. Some subsequent studies found that it is not required to explain past sea levels, and that cliff failure may be slower or limited by other processes.

• Ice sheet dynamics
• Polar ice cap
• Glacial lake outburst flood
• Permafrost carbon cycle
• Sea level rise