Sea ice

Sea ice is frozen ocean water. A local thermodynamic description uses thermal conduction, a surface energy balance and the Stefan condition; salinity, mechanical transport and fractional ice coverage add further physics.

The horizontal sea-ice drift momentum balance per unit area includes air and water drag forces, the Coriolis force, depth-integrated internal ice stress and the sea-surface pressure gradient. Here $m$ is ice-plus-snow mass per area and $\Sigma$ is a depth-integrated stress tensor.

// Target: geophysics.bigb

A sea-ice lead is a fracture or elongated opening in a sea-ice cover, containing open water or young thin ice. Divergence and shear create leads, while freezing and convergence close them.

// Target: geophysics.bigb

Sea-ice lead-width distributions depend on observational thresholds, resolution and whether leads are counted individually or weighted by area. Observations commonly exhibit a broad, approximately power law range, with many narrow leads and a relatively heavy tail.

// Target: geophysics.bigb

A sea-ice thickness distribution assigns fractional horizontal area to ice thickness intervals: $g(h)dh$ is the fraction between $h$ and $h+dh$. Include open water as a mass at $h=0$ when normalizing over the entire ocean area. The first moment is ice volume per ocean area. With growth rate $f$ and velocity $v$, its conservative evolution is ${\partial }_{t}g+\nabla \cdot (vg)+{\partial }_h(fg)=\psi$, with mechanical redistribution of sea ice represented by $\psi$.

// Target: geophysics.bigb

Mechanical redistribution of sea ice changes thickness-class area through ridging, rafting and lead formation. In the conservative thickness-distribution equation, local volume conservation gives $\int h\psi (h)dh=0$; area normalization including open water gives $\int \psi (h)dh=\nabla \cdot v$ when thermodynamic boundary fluxes are accounted for consistently.

// Target: geophysics.bigb

Snow ice forms when flooded snow or a seawater-snow mixture freezes. Snow loading of a thin floe can depress the ice surface below water level and initiate flooding; wave overwash is another route.

// Target: geophysics.bigb

Nilas is a thin, flexible, relatively continuous initial sea-ice sheet. Further freezing at its underside in quiet water produces congelation ice.

// Target: geophysics.bigb

The sea-ice crystal fabric describes grain shapes and crystallographic orientations. Calm-water congelation ice tends to develop vertical columns with predominantly horizontal crystal c-axes, whereas accumulated frazil ice produces a granular texture with much less systematic orientation.

// Target: geophysics.bigb

The Odden ice tongue is an intermittent extension of young sea ice into the Greenland Sea. Repeated formation and export of frazil ice and pancake ice can produce brine rejection without a steadily thickening local ice cover, increasing the salinity of the water left behind.

A melt pond is liquid water collected in a depression on melting ice. Its lower albedo than snow-covered ice can strengthen ice-albedo feedback. Pond drainage and connected pores can redistribute an oil spill under sea ice during warming.

Sea ice anchored to a coast, grounded feature or other fixed support is fast ice. It can be smooth or deformed, young or old. Currents can transport an oil spill under sea ice beneath it even though the ice itself remains stationary.

Multi-year sea ice has survived at least one summer melt season. Its age, thickness, salinity and deformation history affect how it responds to further melting and mechanical forcing. Ice age does not uniquely determine ridge shape.

First-year sea ice is ice that has formed since the preceding summer melt season and has not yet survived a summer. It is usually thinner than older ice, although deformation can create thick sea-ice pressure ridges in a young cover.

Congelation ice grows by freezing onto the underside of an existing sheet. Competitive growth selects grains whose fast basal-plane growth can advance downward, yielding columnar sea-ice crystal fabric with brine-bearing intergranular regions.

// Target: geophysics.bigb

Sea-ice draft is the depth of the ice underside below the local water surface. Total thickness also includes the part above the water. A sea-ice pressure ridge has a spatially variable draft, and its peak draft differs from its mean along a track.

A decline in Arctic sea ice can mean reduced extent, concentration, thickness, volume or survival of older ice. These measures differ: extent counts areas above a concentration threshold, whereas area weights actual coverage. Comparisons require consistent season, geographical domain and measurement method.

Loss of summer sea ice need not be irreversible at fixed external forcing. Open water can release excess heat in autumn, and thin ice grows faster than thick ice during winter because it offers less resistance to thermal conduction. Continued climate change can nevertheless shift the long-term ice cover downward. A one-summer perturbation and persistent forcing are different physical experiments.

A pressure ridge is a pile of fractured sea ice formed by horizontal convergence. Ice displaced upward forms a sail; ice displaced downward forms a keel. Newly formed ridges contain angular blocks and pores, and freezing, melting and further deformation alter their strength and shape.

A sonar ridge-identification rule can miss a shallow peak near a deeper peak because the intervening valley fails the required separation criterion. This apparent shadowing suppresses short observed spacings even without an acoustic blind zone. Finite beam width and genuine geometric occlusion can impose additional limitations. The resulting minimum resolvable spacing need not be a universal physical exclusion distance.

Here $n(H)dH$ is the expected number of ridge peaks per track length with sea-ice draft in $[H,H+dH]$. If total line density is $\mu$ and mean peak draft is $h_m>h_0$, integration gives $b=1/(h_m-h_0)$ and $B=\mu b{e}^{b{h}_0}$. The normalized peak draft has a shifted exponential distribution. This is a model over a specified draft range, not a universal description of every ridge.

For nonoverlapping triangular sea-ice pressure ridges with a common along-track side slope $\tan \delta$, a ridge whose peak exceeds $h$ contributes $2\cot \delta dh$ of track length in a draft interval $dh$. Summing over peaks proves the identity. Above the cutoff of an exponential ridge-draft model, $g(h)=A{e}^{-bh}$ with $A=2B/(b\tan \delta )$. This draft occupation is not the normalized peak probability density function; level ice and shallower parts supply the remaining probability.

Relative tangential motion across a fracture in sea ice can break and pile blocks along the fracture. Local convergence at rough contacts makes ridging possible even when the large-scale deformation is mainly shear.

Wave attenuation is a reduction of a chosen wave component as it travels through sea ice. An amplitude coefficient $\alpha$ corresponds to an energy coefficient $2\alpha$. Wave scattering at a planar interface can remove energy from the forward wave without dissipating total energy; viscous dissipation, collisions and internal ice losses irreversibly convert mechanical energy to heat.

Represent disconnected frazil ice and pancake ice as an upper layer with effective density, thickness and viscosity, rather than a continuous elastic plate. Linear Navier-Stokes equations in that layer are coupled to underlying water through velocity and stress conditions. A complex wavenumber describes both dispersion and wave attenuation in sea ice. A simpler conservative limit keeps ice mass loading but removes the elastic bending term; it does not predict viscous attenuation. The suspension model's effective viscosity is a fitted property, and a compact pancake cover need not behave like dilute frazil.

Interfaces between ice floes and open water reflect and redirect surface gravity waves. The effective attenuation depends on floe thickness, diameter, spatial arrangement and wave period. For very small diameter relative to wavelength, a floe responds nearly with the water and scatters weakly. Individual-floe interference and the number of interfaces per unit distance prevent a universal monotonic diameter law.

A polynya is a persistent or recurrent area of open water or relatively thin ice within surrounding sea ice. Wind can maintain it by transporting ice away; an oceanic heat flux can prevent freezing. Open-water width supplies an open-water fetch over which wind waves can grow.

In a uniformly wind-forced polynya with normalized heat loss $f$, let $H=L+c_{p}m{C}_{\infty }$, $K=f/H$, $J=3S/(4\rho )$ and $r=\rho -{\rho }_s$. The dilute equilibrium model gives $b{u}^2=Jx$, $\varphi bu=Kx$ and $rg\varphi b{b}^{\prime }=S/4$. Hence $u=(rgKx/\rho {)}^{1/3}$, $b=Jx/u^2$ and $\varphi =(K/J)u$. This similarity solution is valid only while the frazil ice volume fraction is small and no exported crystal flux has been neglected improperly.

The simplest Pease polynya model balances offshore ice export at speed $U$ against production of new ice at thickness rate $F$ within an open strip of width $L$. Newly formed ice is collected into an edge of prescribed thickness $H$, with negligible residence time. Per unit coastline length, conservation gives $H(U-\dot{L})=FL$. For constant positive parameters,Thus the equilibrium width is $HU/F$ and the relaxation time is $H/F$. If warming reduces $F$ while $U,H$ stay fixed, both increase. With $F\le 0$ the positive-freezing equilibrium ceases to apply. Finite frazil ice residence, variable atmospheric forcing and alongshore transport require extensions of the model.

The North Water Polynya, also called Pikialasorsuaq, lies between northern Greenland and the Canadian Arctic in the Smith Sound and northern Baffin Bay region. An upstream ice arch can restrict replenishment of drifting Arctic ice while winds and currents export newly formed ice. Ocean heat contributes in some parts of the polynya.

The Northeast Water Polynya is a recurrent open-water region off northeast Greenland. Ice barriers, local currents and winds organize ice divergence; summer opening and winter new-ice export need not have the same dominant forcing. Its regional northward coastal flow must not be confused with assuming that every current along east Greenland flows southward.

A sensible-heat polynya is maintained by ocean heat delivered through currents, mixing or upwelling, sufficient to inhibit local sea ice growth. Mechanical export and sensible heating may act together, so this classification identifies a dominant mechanism rather than an exclusive geographical class.

A latent-heat polynya remains relatively open because winds or currents remove newly formed sea ice. Sustained cooling can produce large amounts of ice even while local ice concentration remains low. Opening is maintained by export, not by latent heat warming the ocean enough to prevent freezing.

Pancake ice consists of approximately disk-shaped young ice floes, often with raised edges formed by collisions. Wave-driven collisions and motion in the surrounding frazil ice can dissipate energy.

Consolidated pancake ice forms when pancake ice packs, rafts and freezes together with interstitial frazil ice. Its heterogeneous granular structure can retain stacked layers and acquire later columnar basal growth.

// Target: geophysics.bigb

Frazil ice consists of small suspended ice crystals formed in supercooled turbulent water. A layer of crystals can damp surface gravity waves through viscous dissipation, even when individual crystals scatter very little wave energy.

Let $q$ be the depth-integrated volume flux, $E$ the entrainment rate, $R$ the upward export of pure ice, and $e=c_p(T-T_{\infty })-L\varphi$. Then $q^{\prime }=E-R$, $[\overline{C}q{]}^{\prime }=C_{\infty }E$ and $[eq{]}^{\prime }=-f-R[c_p(T-T_{\infty })-L]$. Export carries negative relative enthalpy, so it is not a heat-loss term with the same sign as atmospheric cooling. Total production is the increase in advected ice plus its exported amount. When both retained ice fraction and total processed fraction are small, equilibrium salinity and conservation of energy give production $f/(L+c_{p}m{C}_{\infty })$ even when retained and exported fractions differ.

The marginal ice zone is the transition between open ocean and compact sea ice, where interacting ice floes and surface gravity waves can dominate the mechanical evolution.

An ice-edge band is an elongated concentration of ice floes separated from neighbouring ice by open water. In one mechanism, an off-ice wind opens polynyas; short wind waves then exert wave radiation stress on their downwind floes. Wave forcing compacts floes into bands, opposed by incoming longer-period swell. Collisions and mergers can produce fewer, larger bands.

If forward-going surface-gravity-wave energy decays as $a^2(x)=a_0^2{e}^{-\kappa x}$ and local wave force is $F=C{\rho }_{w}g{R}^2{a}^2$, its spatial decrease is $-{\partial }_{x}F=C{\rho }_{w}g{R}^2\kappa a^2$. In a weak-reflection independent-layer approximation, $\kappa \simeq p{R}^2/d$. Standard deep-water wave radiation stress gives $C=1/2$, hence a compaction-force density ${\rho }_{w}gp{R}^4{a}^2/(2d)$. Different amplitude or force conventions change the coefficient; the force formula alone does not fix $\kappa$. This quantity is force per horizontal area, not automatically the three-dimensional stress in the ice skeleton.

An ice floe is a connected floating piece of sea ice. Its diameter relative to wavelength and its thickness affect the reflection, transmission and dissipation of surface gravity waves.

Sea-ice free drift neglects internal stress transmitted from neighboring ice. An isolated floe is governed by air and water drag forces, the Coriolis force and sea-surface tilt; steady drift also neglects acceleration.

// Target: geophysics.bigb

For stationary level water and wind stress approximated by $F={\rho }_a{C}_a{U}^2$ in the wind direction, equilibrium with quadratic water drag gives $F^2=({\rho }_w{C}_w{)}^2{q}^4+(mf{)}^2{q}^2$. The signed angle to the right of the wind is $\theta =\arctan [mf/({\rho }_w{C}_{w}q)]$. This neglects the floe velocity relative to the wind in the air drag; the exact relative-wind equation adds ${\rho }_a{C}_a|U-v|$ to the angle denominator.

A single-category model represents local ice by one thickness $h$ and one surface temperature $T_s$. With basal freezing temperature $T_m$, atmospheric temperature $T_A$, thermal conductivity $k$ and atmospheric heat transfer coefficient ${\lambda }_A$, quasistatic thermal conduction giveswhile $T_s<T_m$. If $F_O$ is upward ocean heat flux, the Stefan condition gives $\rho L\dot{h}={\lambda }_A(T_m-T_A)/(1+{\lambda }_{A}h/k)-F_O$. During surface melting, $T_s=T_m$ and $\rho L\dot{h}=-{\lambda }_A(T_A-T_m)-F_O$ when $T_A\ge T_m$. Thickness is constrained to be nonnegative, and the open-water energy balance applies after complete melt.

In a cycle starting at the atmospheric temperature maximum, positive thickness at the next maximum is a peak-temperature survival test. It is not sufficient for perennial ice: with sinusoidal forcing, surface melting continues for another quarter-cycle. If ocean heat was neglected during winter growth, the leading thickness at the next temperature maximum isLiteral year-round survival must be tested through the end of the subsequent melt season, rather than at the temperature maximum alone. For the specified forcing with annual mean atmospheric temperature $T_m$, the zero-ocean-heat upper bound on winter growth obeys $h_m^2/2+h_m/a=2H^2$, where $a={\lambda }_A/k$ and $H^2=\kappa \tau /\mathcal{S}$, with $\mathcal{S}$ the inverse Stefan number. Thus $h_m<2a{H}^2$, already less than the atmospheric melt over the full subsequent warm half-cycle. Positive ocean heat only strengthens the failure to produce literal perennial ice from an ice-free start.

For $T_A=T_m+\Delta T\cos (t/\tau )$ and $F_O={\lambda }_O(T_O-T_m)$, put $r=F_O/({\lambda }_A\Delta T)$. Open-water freezing requires $r<1$ and starts at $t_1=\tau \arccos (-r)$. Neglecting ocean heat during growth is a bulk approximation when $r(1+{\lambda }_A{h}_m/k)\ll 1$. It cannot hold pointwise at the onset or maximum, where the atmospheric removal and ocean input are comparable. The actual maximum satisfies $-\cos (t_2/\tau )=r[1+{\lambda }_{A}h(t_2)/k]$; neglecting $F_O$ gives $t_2=3\pi \tau /2$.