DETAILED THERMODYNAMICS OF SEA ICE
Daniel Feltham and Paul Taylor
Salt solutions freeze differently from pure water in various respects. The freezing temperature of a salt solution is a function of its salinity: Pure water has a freezing temperature of 0oC whereas seawater with a combined salt concentration of 35 ppt (35g of salt dissolved per kg of seawater) has a freezing temperature of -1.8oC. Sea ice seen in nature is dominated by two phases: pure ice and brine. Brine is a concentrated solution of salts that are rejected by the ice as it grows by reason of the extremely low solubility of the salts in ice.
A liquid solution is supercooled if its temperature lies below its equilibrium freezing temperature. When this is due to concentration changes, the solution is said to be constitutionally supercooled. Constitutional supercooling typically arises next to growing sea ice rejecting salts since the salts diffuse about 100 times slower than heat.
Constitutional supercooling is important since it (almost always) causes a morphological instability of the ice-liquid interface. This causes the ice-liquid interface to become highly convoluted, taking the form of a matrix of platelets. The convolutions of the surface increase its surface area, which enables more salt to diffuse away from the growing ice and encourages further growth. It is for this reason that dendritic growth is the dominant growth mechanism in sea ice whilst planar growth occurs without supercooling in fresh water.
(The underside of laboratory-grown sea ice showing ice platelets with c-axes that are predominantly horizontal, which restricts horizontal fluid motions relative to vertical ones. The scale on the left is in centimetres. The two circular holes are brine channels. Taken from Wettlaufer, Worster and Huppert, GRL, 24(10), pp1251, 1997.)
We model sea ice as a mushy layer. A mushy layer consists of a rigid, dendritic matrix of pure solid (ice) bathed in its interstitial melt (brine). Sea ice (a mushy layer) is porous so that when the porosity (the liquid fraction) is sufficiently high, significant brine flows can occur within the sea ice and brine channels can form. It can be shown that, in the absence of brine flow, the equations describing a mushy layer reduce to the thermodynamic model of sea ice introduced by Maykut and Untersteiner (1971), which was partially based on the phase change relationships measured for sea ice by Schwerdtfeger (1963).
We are using the mushy layer equations to model complex thermodynamic processes in sea ice which nonetheless have important consequences to climate modelling. In particular, we are studying some of the assumptions made in the routine application of sea ice thermodynamic models to climate simulation (such as ignoring diurnal variation) and applying our models to processes such as melt pond formation. Melt ponds form on sea ice during the summer due to melting of snow and/or the upper layer of sea ice. Because the albedo of melt ponds is lower than the surrounding ice, they preferentially absorb radiation that causes them to grow. We are modelling the seasonal evolution of melt ponds and aim to extract parameterisations of summer-time sea ice albedo for use in climate models.
(Heavily ponded sea ice in the Arctic summer, taken from the SHEBA archive - http://www.joss.ucar.edu/data/sheba/data/perovich/)
With others, we have shown that there exist instabilities of the sea ice-ocean interface when there is a shear flow in the ocean and the ice layer is reasonably porous. This instability can cause the sea ice-ocean interface to become corrugated, which affects oceanic surface drag and turbulent heat and mass transports in the ocean.
For more information about sea ice thermodynamics and mushy layers, contact Daniel Feltham.