Sea ice growth processes

Last updated October 23, 2024

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.

Overview

Several formation mechanisms of sea ice have been identified. At its earliest stages, sea ice consists of elongated, randomly oriented crystals. This is called frazil, and mixed with water in the unconsolidated state is known as grease ice. If wave and wind conditions are calm these crystals will consolidate at the surface, and by selective pressure begin to grow preferentially in the downward direction, forming nilas. In more turbulent conditions, the frazil will consolidate by mechanical action to form pancake ice, which has a more random structure.^[1]^[2] Another common formation mechanism, especially in the Antarctic where precipitation over sea ice is high, is from snow deposition: on thin ice the snow will weigh down the ice enough to cause flooding. Subsequent freezing will form ice with a much more granular structure.^[3]^[4]^[5]

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 brine inclusions between the crystals. 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 multi-year ice will tend to have both lower salinity and lower density than first-year ice.^[2]^[7] Sea-ice density is relatively stable during winter with values close to 910 kg/m³,^[8] but may decrease up to 720 kg/m³ during warming mainly due to increase in air volume. Air volume of sea ice in can be as high as 15% in summer^[9] and 4% in late autumn.^[10]

The main physical processes of sea-ice desalination are gravity drainage and flushing of surface meltwater and melt ponds.^[11] During winter, desalination is governed mostly by gravity drainage, while flushing becomes important during summer. Gravity drainage can be triggered both by atmospheric heat and bottom melt from oceanic heat.^[12] A typical salinity of first-year ice by the end of winter season is 4–6, while typical salinities of multiyear ice is 2–3. Snowmelt, surface flooding, and the presence of under-ice meltwater may affect sea-ice salinity. During the melt season, the only process of ice growth is related to the formation of false bottoms.^[13]

Vertical growth

The downward growth of consolidated ice under the 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 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 inertia, we can determine latent heat flux Q^* by solving the following equation:

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 freezing (Stefan problem). We can approximate the ice and snow thermal conductivities 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:

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 parameterizations, see determining surface flux under sea ice thickness. The equation can be solved using a numerical root-finding algorithm such as bisection: the functional dependencies on surface temperature are given, with e being the equilibrium vapor pressure. Shortwave radiation may increase ocean surface temperatures and corresponding ocean heat fluxes, affecting heat balance at the ice-ocean interface. This process is a part of Ice–albedo feedback.

While Cox and Weeks assume thermal equilibrium,^[14] Tonboe uses a more complex thermodynamic model based on numerical solution of the heat equation.^[15] 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:

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

where L is the latent heat of fusion for water and $\rho$ is the density of ice (for pure ice). For sea ice, L is the effective latent heat of sea ice and $\rho$ is the density of sea ice. These two parameters depend on sea-ice salinity, temperature, and volumetric gas fraction, as well as sea-ice thermal conductivity. 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^[14] and Nakawo and Sinha^[16] and take the form:

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.:

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

where g is in cm/s.^[16]

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 freezing point depression. There are empirical formulas relating sea ice temperature to brine salinity.^[17]^[15]^[2]

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:

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, $\rho _{i}$ is the density of the ice and $\rho _{b}$ is brine density. Compare with this empirical formula from Frankenstein and Garner:^[17]

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

where T is ice temperature in degrees Celsius and S is ice salinity in parts per thousand.

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:^[14]

{\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 porous, 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, $S=\exp(ah+b)$ , 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 fracture points which in turn will form at the points of greatest stress and lowest strength, or where the ratio between the two is a maximum. Ice thickness, salinity and porosity will all affect the strength of the ice. The motion of the ice is driven primarily by ocean currents, though to a lesser extent by wind. Note that stresses will not be in the direction of the winds or currents, but rather will be shifted by Coriolis effects—see, for instance, Ekman spiral.

Related Research Articles

In fluid mechanics, the Rayleigh number ( $Ra$ , after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a certain lower range denotes laminar flow; a value in a higher range, turbulent flow. Below a certain critical value, there is no fluid motion and heat transfer is by conduction rather than convection. For most engineering purposes, the Rayleigh number is large, somewhere around 10⁶ to 10⁸.

Seafloor spreading, or seafloor spread, is a process that occurs at mid-ocean ridges, where new oceanic crust is formed through volcanic activity and then gradually moves away from the ridge.

Isostasy or isostatic equilibrium is the state of gravitational equilibrium between Earth's crust and mantle such that the crust "floats" at an elevation that depends on its thickness and density. This concept is invoked to explain how different topographic heights can exist at Earth's surface. Although originally defined in terms of continental crust and mantle, it has subsequently been interpreted in terms of lithosphere and asthenosphere, particularly with respect to oceanic island volcanoes, such as the Hawaiian Islands.

Post-glacial rebound is the rise of land masses after the removal of the huge weight of ice sheets during the last glacial period, which had caused isostatic depression. Post-glacial rebound and isostatic depression are phases of glacial isostasy, the deformation of the Earth's crust in response to changes in ice mass distribution. The direct raising effects of post-glacial rebound are readily apparent in parts of Northern Eurasia, Northern America, Patagonia, and Antarctica. However, through the processes of ocean siphoning and continental levering, the effects of post-glacial rebound on sea level are felt globally far from the locations of current and former ice sheets.

Ocean stratification is the natural separation of an ocean's water into horizontal layers by density. This is generally stable stratification, because warm water floats on top of cold water, and heating is mostly from the sun, which reinforces that arrangement. Stratification is reduced by wind-forced mechanical mixing, but reinforced by convection. Stratification occurs in all ocean basins and also in other water bodies. Stratified layers are a barrier to the mixing of water, which impacts the exchange of heat, carbon, oxygen and other nutrients. The surface mixed layer is the uppermost layer in the ocean and is well mixed by mechanical (wind) and thermal (convection) effects. Climate change is causing the upper ocean stratification to increase.

Spice, spiciness, or spicity, symbol τ, is a term in oceanography referring to variations in the temperature and salinity of seawater over space or time, whose combined effects leave the water's density unchanged. For a given spice, any change in temperature is offset by a change in salinity to maintain unchanged density. An increase in temperature decreases density, but an increase in salinity increases density. Such density-compensated thermohaline variability is ubiquitous in the upper ocean. Warmer, saltier water is more spicy while cooler, less salty water is more minty. For a density ratio of 1, all the thermohaline variability is spice, and there are no density fluctuations.

The maximum potential intensity of a tropical cyclone is the theoretical limit of the strength of a tropical cyclone.

Double diffusive convection is a fluid dynamics phenomenon that describes a form of convection driven by two different density gradients, which have different rates of diffusion.

<span class="mw-page-title-main">Frost flower (sea ice)</span> Ice crystal found growing on young sea ice

Frost flowers are ice crystals commonly found growing on young sea ice and thin lake ice in cold, calm conditions. The ice crystals are similar to hoar frost, and are commonly seen to grow in patches around 3–4 cm in diameter. Frost flowers growing on sea ice have extremely high salinities and concentrations of other sea water chemicals and, because of their high surface area, are efficient releasers of these chemicals into the atmosphere.

With increased interest in sea ice and its effects on the global climate, efficient methods are required to monitor both its extent and exchange processes. Satellite-mounted, microwave radiometers, such SSMI, AMSR and AMSU, are an ideal tool for the task because they can see through cloud cover, and they have frequent, global coverage. A passive microwave instrument detects objects through emitted radiation since different substance have different emission spectra. To detect sea ice more efficiently, there is a need to model these emission processes. The interaction of sea ice with electromagnetic radiation in the microwave range is still not well understood. In general is collected information limited because of the large-scale variability due to the emissivity of sea ice.

The thermal history of Earth involves the study of the cooling history of Earth's interior. It is a sub-field of geophysics. The study of the thermal evolution of Earth's interior is uncertain and controversial in all aspects, from the interpretation of petrologic observations used to infer the temperature of the interior, to the fluid dynamics responsible for heat loss, to material properties that determine the efficiency of heat transport.

Conservative temperature $is a thermodynamic property of seawater. It is derived from the potential enthalpy and is recommended under the TEOS-10 standard as a replacement for potential temperature as it more accurately represents the heat content in the ocean.$

The density ratio of a column of seawater is a measure of the relative contributions of temperature and salinity in determining the density gradient. At a density ratio of 1, temperature and salinity are said to be compensated: their density signatures cancel, leaving a density gradient of zero. The formula for the density ratio, $, is:$

CICE is a computer model that simulates the growth, melt and movement of sea ice. It has been integrated into many coupled climate system models as well as global ocean and weather forecasting models and is often used as a tool in Arctic and Southern Ocean research. CICE development began in the mid-1990s by the United States Department of Energy (DOE), and it is currently maintained and developed by a group of institutions in North America and Europe known as the CICE Consortium. Its widespread use in Earth system science in part owes to the importance of sea ice in determining Earth's planetary albedo, the strength of the global thermohaline circulation in the world's oceans, and in providing surface boundary conditions for atmospheric circulation models, since sea ice occupies a significant proportion (4-6%) of Earth's surface. CICE is a type of cryospheric model.

Thermohaline staircases are patterns that form in oceans and other bodies of salt water, characterised by step-like structures observed in vertical temperature and salinity profiles; the patterns are formed and maintained by double diffusion of heat and salt. The ocean phenomenon consists of well-mixed layers of ocean water stacked on top of each other. The well-mixed layers are separated by high-gradient interfaces, which can be several meters thick. The total thickness of staircases ranges typically from tens to hundreds of meters.

Cold and dense water from the Nordic Seas is transported southwards as Faroe-Bank Channel overflow. This water flows from the Arctic Ocean into the North Atlantic through the Faroe-Bank Channel between the Faroe Islands and Scotland. The overflow transport is estimated to contribute to one-third of the total overflow over the Greenland-Scotland Ridge. The remaining two-third of overflow water passes through Denmark Strait, the Wyville Thomson Ridge (0.3 Sv), and the Iceland-Faroe Ridge (1.1 Sv).

The sea surface skin temperature (SST_skin), or ocean skin temperature, is the temperature of the sea surface as determined through its infrared spectrum (3.7–12 μm) and represents the temperature of the sublayer of water at a depth of 10–20 μm. High-resolution data of skin temperature gained by satellites in passive infrared measurements is a crucial constituent in determining the sea surface temperature (SST).

The recharge oscillator model for El Niño–Southern Oscillation (ENSO) is a theory described for the first time in 1997 by Jin., which explains the periodical variation of the sea surface temperature (SST) and thermocline depth that occurs in the central equatorial Pacific Ocean. The physical mechanisms at the basis of this oscillation are periodical recharges and discharges of the zonal mean equatorial heat content, due to ocean-atmosphere interaction. Other theories have been proposed to model ENSO, such as the delayed oscillator, the western Pacific oscillator and the advective reflective oscillator. A unified and consistent model has been proposed by Wang in 2001, in which the recharge oscillator model is included as a particular case.

Oceanic freshwater fluxes are defined as the transport of non saline water between the oceans and the other components of the Earth's system. These fluxes have an impact on the local ocean properties, as well as on the large scale circulation patterns.

False bottom is a form of sea ice that forms at the interface between meltwater and seawater via the process of double-diffusive convection of heat and salt.

References

↑ G. Maykut; T. Grenfell & W. Weeks (1992). "On estimating spatial and temporal variations in the properties of ice in the polar oceans". Journal of Marine Systems. 3 (1–2): 41–72. Bibcode:1992JMS.....3...41M. doi:10.1016/0924-7963(92)90030-C.
1 2 3 W. B. Tucker; D. K. Prerovich; A. J. Gow; W. F. Weeks; M. R. Drinkwater (eds.). Microwave Remote Sensing of Sea Ice. American Geophysical Union.
↑ Ehn, Jens K.; Hwang, Byong Jun; Galley, Ryan; Barber, David G. (2007-05-01). "Investigations of newly formed sea ice in the Cape Bathurst polynya: 1. Structural, physical, and optical properties". Journal of Geophysical Research. 112 (C5): C05002. Bibcode:2007JGRC..112.5002E. doi:10.1029/2006JC003702. ISSN 0148-0227.
↑ T. Maksym & T. Markus (2008). "Antarctic sea ice thickness and snow-to-ice conversion from atmospheric reanalysis and passive microwave snow depth". Journal of Geophysical Research. 113 (C02S12). Bibcode:2008JGRC..113.2S12M. doi: 10.1029/2006JC004085 .
↑ S. Tang; D. Qin; J. Ren; J. Kang & Z. Li (2007). "Structure, salinity and isotopic composition of multi-year landfast sea ice in Nella Fjord, Antarctica". Cold Regions Science and Technology. 49 (2): 170–177. Bibcode:2007CRST...49..170T. doi:10.1016/j.coldregions.2007.03.005.
1 2 Hajo Eicken (1992). "Salinity Profiles of Antarctic Sea ice: Field Data and Model Results". Journal of Geophysical Research. 97 (C10): 15545–15557. Bibcode:1992JGR....9715545E. doi:10.1029/92JC01588.
↑ M. Vancoppenolle; C. M. Bitz; T. Fichefet (2007). "Summer landfast sea ice desalination at Point Barrow, Alaska: Modeling and observations". Journal of Geophysical Research. 112 (C04022): C04022. Bibcode:2007JGRC..112.4022V. doi:10.1029/2006JC003493.
↑ Timco, G.W.; Weeks, W.F. (2010). "A review of the engineering properties of sea ice". Cold Regions Science and Technology. 60 (2): 107–129. Bibcode:2010CRST...60..107T. doi:10.1016/j.coldregions.2009.10.003.
↑ Wang, Q.; Lu, P.; Leppäranta, M.; Cheng, B.; Zhang, G.; Li, Z. (2020). "Physical Properties of Summer Sea Ice in the Pacific Sector of the Arctic During 2008–2018". Journal of Geophysical Research: Oceans. 125 (9). Bibcode:2020JGRC..12516371W. doi:10.1029/2020JC016371. ISSN 2169-9275.
↑ Salganik, Evgenii; Lange, Benjamin A.; Katlein, Christian; Matero, Ilkka; Anhaus, Philipp; Muilwijk, Morven; Høyland, Knut V.; Granskog, Mats A. (2023-11-20). "Observations of preferential summer melt of Arctic sea-ice ridge keels from repeated multibeam sonar surveys". The Cryosphere. 17 (11): 4873–4887. Bibcode:2023TCry...17.4873S. doi: 10.5194/tc-17-4873-2023 . ISSN 1994-0424.
↑ Notz, D., Worster, M. G. (2008), "In situ measurements of the evolution of young sea ice", Journal of Geophysical Research: Oceans, 113 (C3), Bibcode:2008JGRC..113.3001N, doi:10.1029/2007JC004333, hdl: 11858/00-001M-0000-0011-FA10-E
↑ Griewank, P. J., Notz, D. (2013), "Insights into brine dynamics and sea ice desalination from a 1-D model study of gravity drainage", Journal of Geophysical Research: Oceans, 118 (7): 3370–3386, Bibcode:2013JGRC..118.3370G, doi:10.1002/jgrc.20247, hdl: 11858/00-001M-0000-0014-69FD-7
↑ Salganik, E.; Katlein, C.; Lange, B.A.; Matero, I.; Lei, R.; Fong, A.A.; Fons, S.W.; Divine, D.; Oggier, M.; Castellani, G.; Bozzato, D.; Chamberlain, E.J.; Hoppe, C.J.M.; Muller, O.; Gardner, J.; Rinke, A.; Pereira, P.S.; Ulfsbo, A.; Marsay, C.; Webster, M.A.; Maus, S.; Høyland, K.V.; Granskog, M.A. (2023). "Temporal evolution of under-ice meltwater layers and false bottoms and their impact on summer Arctic sea ice mass balance". Elementa: Science of the Anthropocene. 11 (1): 00035. Bibcode:2023EleSA..11...35S. doi: 10.1525/elementa.2022.00035 . hdl: 10037/30456 .
1 2 3 G. Cox & W. Weeks (1988). "Numerical simulations of the profile properties of undeformed first-year sea ice during the growth season". Journal of Geophysical Research. 93 (C10): 12449–12460. Bibcode:1988JGR....9312449C. doi:10.1029/JC093iC10p12449.
1 2 G. Heygster, S. Hendricks, L. Kaleschke, N. Maass, P. Mills, D. Stammer, R. T. Tonboe and C. Haas (2009). L-Band Radiometry for Sea-Ice Applications (Technical report). Institute of Environmental Physics, University of Bremen. ESA/ESTEC Contract N. 21130/08/NL/EL.{{cite tech report}}: CS1 maint: multiple names: authors list (link)
1 2 M. Nakawo & N. K. Sinha (1981). "Growth rate and salinity profile of first-year sea ice in the high Arctic". Journal of Glaciology. 27 (96): 315–330. Bibcode:1981JGlac..27..315N. doi: 10.1017/S0022143000015409 .
1 2 Frankenstein, Guenther; Garner, Robert (1967). "Equations for Determining the Brine Volume of Sea Ice from −0.5° to −22.9°C". Journal of Glaciology. 6 (48): 943–944. doi: 10.1017/S0022143000020244 . eISSN 1727-5652. ISSN 0022-1430. S2CID 129064888.

This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.

[Maykut_etal1992-1] G. Maykut; T. Grenfell & W. Weeks (1992). "On estimating spatial and temporal variations in the properties of ice in the polar oceans". Journal of Marine Systems. 3 (1–2): 41–72. Bibcode:1992JMS.....3...41M. doi:10.1016/0924-7963(92)90030-C.

[Tucker_etal1992-2] 1 2 3 W. B. Tucker; D. K. Prerovich; A. J. Gow; W. F. Weeks; M. R. Drinkwater (eds.). Microwave Remote Sensing of Sea Ice. American Geophysical Union.

[3] Ehn, Jens K.; Hwang, Byong Jun; Galley, Ryan; Barber, David G. (2007-05-01). "Investigations of newly formed sea ice in the Cape Bathurst polynya: 1. Structural, physical, and optical properties". Journal of Geophysical Research. 112 (C5): C05002. Bibcode:2007JGRC..112.5002E. doi:10.1029/2006JC003702. ISSN 0148-0227.

[Maksym_Markus2008-4] T. Maksym & T. Markus (2008). "Antarctic sea ice thickness and snow-to-ice conversion from atmospheric reanalysis and passive microwave snow depth". Journal of Geophysical Research. 113 (C02S12). Bibcode:2008JGRC..113.2S12M. doi: 10.1029/2006JC004085 .

[Tang_etal2007-5] S. Tang; D. Qin; J. Ren; J. Kang & Z. Li (2007). "Structure, salinity and isotopic composition of multi-year landfast sea ice in Nella Fjord, Antarctica". Cold Regions Science and Technology. 49 (2): 170–177. Bibcode:2007CRST...49..170T. doi:10.1016/j.coldregions.2007.03.005.

[Eicken1992-6] 1 2 Hajo Eicken (1992). "Salinity Profiles of Antarctic Sea ice: Field Data and Model Results". Journal of Geophysical Research. 97 (C10): 15545–15557. Bibcode:1992JGR....9715545E. doi:10.1029/92JC01588.

[Vancoppenolle_etal2007-7] M. Vancoppenolle; C. M. Bitz; T. Fichefet (2007). "Summer landfast sea ice desalination at Point Barrow, Alaska: Modeling and observations". Journal of Geophysical Research. 112 (C04022): C04022. Bibcode:2007JGRC..112.4022V. doi:10.1029/2006JC003493.

[8] Timco, G.W.; Weeks, W.F. (2010). "A review of the engineering properties of sea ice". Cold Regions Science and Technology. 60 (2): 107–129. Bibcode:2010CRST...60..107T. doi:10.1016/j.coldregions.2009.10.003.

[9] Wang, Q.; Lu, P.; Leppäranta, M.; Cheng, B.; Zhang, G.; Li, Z. (2020). "Physical Properties of Summer Sea Ice in the Pacific Sector of the Arctic During 2008–2018". Journal of Geophysical Research: Oceans. 125 (9). Bibcode:2020JGRC..12516371W. doi:10.1029/2020JC016371. ISSN 2169-9275.

[10] Salganik, Evgenii; Lange, Benjamin A.; Katlein, Christian; Matero, Ilkka; Anhaus, Philipp; Muilwijk, Morven; Høyland, Knut V.; Granskog, Mats A. (2023-11-20). "Observations of preferential summer melt of Arctic sea-ice ridge keels from repeated multibeam sonar surveys". The Cryosphere. 17 (11): 4873–4887. Bibcode:2023TCry...17.4873S. doi: 10.5194/tc-17-4873-2023 . ISSN 1994-0424.

[11] Notz, D., Worster, M. G. (2008), "In situ measurements of the evolution of young sea ice", Journal of Geophysical Research: Oceans, 113 (C3), Bibcode:2008JGRC..113.3001N, doi:10.1029/2007JC004333, hdl: 11858/00-001M-0000-0011-FA10-E

[12] Griewank, P. J., Notz, D. (2013), "Insights into brine dynamics and sea ice desalination from a 1-D model study of gravity drainage", Journal of Geophysical Research: Oceans, 118 (7): 3370–3386, Bibcode:2013JGRC..118.3370G, doi:10.1002/jgrc.20247, hdl: 11858/00-001M-0000-0014-69FD-7

[13] Salganik, E.; Katlein, C.; Lange, B.A.; Matero, I.; Lei, R.; Fong, A.A.; Fons, S.W.; Divine, D.; Oggier, M.; Castellani, G.; Bozzato, D.; Chamberlain, E.J.; Hoppe, C.J.M.; Muller, O.; Gardner, J.; Rinke, A.; Pereira, P.S.; Ulfsbo, A.; Marsay, C.; Webster, M.A.; Maus, S.; Høyland, K.V.; Granskog, M.A. (2023). "Temporal evolution of under-ice meltwater layers and false bottoms and their impact on summer Arctic sea ice mass balance". Elementa: Science of the Anthropocene. 11 (1): 00035. Bibcode:2023EleSA..11...35S. doi: 10.1525/elementa.2022.00035 . hdl: 10037/30456 .

[Cox_Weeks1988-14] 1 2 3 G. Cox & W. Weeks (1988). "Numerical simulations of the profile properties of undeformed first-year sea ice during the growth season". Journal of Geophysical Research. 93 (C10): 12449–12460. Bibcode:1988JGR....9312449C. doi:10.1029/JC093iC10p12449.

[smos_final-15] 1 2 G. Heygster, S. Hendricks, L. Kaleschke, N. Maass, P. Mills, D. Stammer, R. T. Tonboe and C. Haas (2009). L-Band Radiometry for Sea-Ice Applications (Technical report). Institute of Environmental Physics, University of Bremen. ESA/ESTEC Contract N. 21130/08/NL/EL.{{cite tech report}}: CS1 maint: multiple names: authors list (link)

[Nakawo_Sinha1981-16] 1 2 M. Nakawo & N. K. Sinha (1981). "Growth rate and salinity profile of first-year sea ice in the high Arctic". Journal of Glaciology. 27 (96): 315–330. Bibcode:1981JGlac..27..315N. doi: 10.1017/S0022143000015409 .

[FrankensteinGarner1967-17] 1 2 Frankenstein, Guenther; Garner, Robert (1967). "Equations for Determining the Brine Volume of Sea Ice from −0.5° to −22.9°C". Journal of Glaciology. 6 (48): 943–944. doi: 10.1017/S0022143000020244 . eISSN 1727-5652. ISSN 0022-1430. S2CID 129064888.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

[16]

[17]