Sea ice growth processes

Sea ice is a complex composite composed primarily of pure ice in various states of crystallization, but including air bubbles and pockets of brine. Understanding its growth processes is important for climate modellers and remote sensing specialists, since the composition and microstructural properties of the ice affect how it reflects or absorbs sunlight.

crystallographic plane

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Sea ice growth models for predicting the ice distribution and extent are also valuable for shipping. An ice growth model can be combined with remote sensing measurements in an assimilation model as a means of generating more accurate ice charts.

Overview

Several formation mechanisms of sea ice have been identified. At its earliest stages, sea ice consists of elongated, randomly oriented

One of the more interesting processes to occur within consolidated ice packs is changes in the saline content. As the ice freezes, most of the salt content gets rejected and forms highly saline

. With decreasing temperatures in the ice sheet, the size of the brine pockets decreases while the salt content goes up. Since ice is less dense than water, increasing pressure causes some of the brine to be ejected from both the top and bottom, producing the characteristic C-shaped salinity profile of first year ice. ^[6] Brine will also drain through vertical channels, particularly in the melt season. Thus will tend to have both lower salinity and lower density than first-year ice.^[2][7] This difference is primarily related to higher gas volume fraction of second- and multiyear ice.^[8]

The main physical processes of sea-ice desalination are gravity drainage and flushing of surface

Vertical growth

The downward growth of consolidated ice under assumption of zero heat flux from the ocean is determined by the rate of conductive heat flux, Q^*, at the ice-water interface. The ocean heat fluxes substantially vary both spatially and temporally, and strongly contribute to the summer sea ice melt and the absence of sea ice in some parts of the Arctic Ocean. If we also assume a linear temperature profile within ice and no effect from ice thermal intertia, we can determine latent heat flux Q^* by solving the following equation:

${\displaystyle Q^{*}=k_{i}{\frac {T_{si}-T_{w}}{h_{i}}}=k_{s}{\frac {T_{s}-T_{si}}{h_{s}}}}$

where T_si is the snow-ice interface temperature, T_s is the air-snow interface temperature, h_i and h_s are the ice and snow thicknesses. The water temperature, T_w, is assumed to be at or near

k_i and k_s, as an average over the layers. The surface heat budget defines the snow surface temperature T_s and includes four atmospheric heat fluxes:

${\displaystyle Q^{*}=Q_{E}\left[e(T_{s})\right]+Q_{H}(T_{s})+Q_{LW}(T_{s}^{4})+Q_{SW}}$

which are latent, sensible, longwave and shortwave radiation fluxes, respectively. For a description of the approximate

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While Cox and Weeks assume thermal equilibrium,

This would be appropriate when the ice is thick or the weather conditions are changing rapidly.

The rate of ice growth can be calculated from heat flux by the following equation:

${\displaystyle g={\frac {dh_{i}}{dt}}={\frac {Q^{*}}{L\rho }}}$

where L is the latent heat of fusion for water and ${\displaystyle \rho }$ is the density of ice (for pure ice). For sea ice, L is the effective latent heat of sea ice and ${\displaystyle \rho }$ is the density of sea ice. These two parameters depend on sea-ice salinity, temperature, and volumetric gas fraction. The growth rate of sea ice in turn determines the saline content of the newly frozen ice. Empirical equations for determining the initial brine entrapment in sea ice have been derived by Cox and Weeks^[12] and Nakawo and Sinha^[14] and take the form:

${\displaystyle S=S_{0}f(g)}$

where S is ice salinity, S₀ is the salinity of the parent water and f is an empirical function of ice growth rate, e.g.:

${\displaystyle f(g)={\frac {0.12}{0.12+0.88\exp(-4.2\times 10^{4}g)}}}$

where g is in cm/s.^[14]

Salt content

Brine entrapped in sea ice will always be at or near freezing, since any departure will either cause some of the water in the brine to freeze, or melt some of the surrounding ice. Thus, brine salinity is variable and can be determined based strictly on temperature—see

The relative brine volume, V_b, is defined as the fraction of brine relative to the total volume. It too is highly variable, however its value is more difficult to determine since changes in temperature may cause some of the brine to be ejected or move within the layers, particularly in new ice. Writing equations relating the salt content of the brine, the total salt content, the brine volume, the density of the brine and the density of the ice and solving for brine volume produces the following relation:

${\displaystyle V_{b}={\frac {S\rho _{i}}{S_{b}\rho _{b}-S\rho _{b}+S\rho _{i}}}}$

where S is sea ice salinity, S_b is brine salinity, ${\displaystyle \rho _{i}}$ is the density of the ice and ${\displaystyle \rho _{b}}$ is brine density. Compare with this empirical formula from Frankenstein and Garner:[15]

${\displaystyle V_{b}=10^{-3}S\left(-{\frac {49.185}{T}}+0.532\right)}$

where T is ice temperature in degrees

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In new ice, the amount of brine ejected as the ice cools can be determined by assuming that the total volume stays constant and subtracting the volume increase from the brine volume. Note that this is only applicable to newly formed ice: any warming will tend to generate air pockets as the brine volume will increase more slowly than the ice volume decreases, again due to the density difference. Cox and Weeks provide the following formula determining the ratio of total ice salinity between temperatures, T₁ and T₂ where T₂ < T₁:^[12]

${\displaystyle {\frac {S(T_{2})}{S(T_{1})}}={\frac {S_{b}(T_{2})\left(1-1/\rho _{i}\right)}{S_{b}(T_{1})}}{\frac {\rho _{b}(T_{2})}{\rho _{b}(T_{1})}}\exp \left\lbrace {\frac {c}{\rho _{i}\left[S_{b}(T_{1})-S_{b}(T_{2})\right]}}\right\rbrace }$

where c=0.8 kg m⁻³ is a constant. As the ice goes through constant warming and cooling cycles it becomes progressively more

, through ejection of the brine and drainage through the resulting channels.

The figure above shows a scatter plot of salinity versus ice thickness for ice cores taken from the Weddell Sea, Antarctica, with an exponential fit of the form, ${\displaystyle S=\exp(ah+b)}$, overlaid, where h is ice thickness and a and b are constants.

Horizontal motion

The horizontal motion of sea ice is quite difficult to model because ice is a non-Newtonian fluid. Sea ice will deform primarily at

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See also

• Sea ice
• Sea ice thickness
• Sea ice concentration
• Sea ice emissivity modelling

References