Sea ice growth processes
Encyclopedia
Sea ice
is a complex composite composed primarily of pure ice in various states of crystallization
along with air bubbles and included pockets of brine
. Understanding its growth processes is important both for climate
scientists for use in simulation
s as well remote sensing
specialists since the composition and microstructural properties of the ice ultimately affect how it interacts with electromagnetic radiation
.
Sea ice growth models for predicting the ice distribution
and extent are also valuable for shipping concerns. An ice growth model can be combined with remote sensing
measurements in an assimilation
model as a means of generating more accurate ice charts
.
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 turbulant conditions, the frazil will consolidate
by mechanical action to form pancake ice
, which has a more random structure
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.
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.
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
, Q*, at the ice-water interface. If we assume that the ice is in thermal equilibrium
both with itself and its surroundings and that the weather conditions are known, then we can determine Q* by solving the following equation:
for Ts, the surface temperature. The water temperature, Tw, is assumed to be at or near freezing
, while the ice thickness, h, is assumed to be known and we can approximate the thermal conductivity
, k, as an average over the layers (which have different salinities) or simply use the value for pure ice. The net heat flux is a total over four components:
which are latent, sensible, longwave and shortwave 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.
While Cox and Weeks
assume thermal equilibrium, Tanboe
uses a more sophisticated thermodynamic model based on numerical solution of the heat equation
. 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:
where L is the latent heat
of fusion for water and
is the density of ice. The growth rate 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 and Nakawo and Sinha
and take the form:
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.:
where g is in cm/s.
contain empirical formulas relating sea ice temperature to brine salinity.
The relative brine volume, Vb, 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:
where S is sea ice salinity, Sb is brine salinity,
is the density of the ice and 
is brine density. Compare with this empirical formula from Ulaby et al.:
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:
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,
, overlaid, where h is ice thickness and a and b are constants.
.
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
.
Sea ice
Sea ice is largely formed from seawater that freezes. Because the oceans consist of saltwater, this occurs below the freezing point of pure water, at about -1.8 °C ....
is a complex composite composed primarily of pure ice in various states of crystallization
Crystallization
Crystallization is the process of formation of solid crystals precipitating from a solution, melt or more rarely deposited directly from a gas. Crystallization is also a chemical solid–liquid separation technique, in which mass transfer of a solute from the liquid solution to a pure solid...
along with air bubbles and included pockets of brine
Brine
Brine is water, saturated or nearly saturated with salt .Brine is used to preserve vegetables, fruit, fish, and meat, in a process known as brining . Brine is also commonly used to age Halloumi and Feta cheeses, or for pickling foodstuffs, as a means of preserving them...
. Understanding its growth processes is important both for climate
Climate
Climate encompasses the statistics of temperature, humidity, atmospheric pressure, wind, rainfall, atmospheric particle count and other meteorological elemental measurements in a given region over long periods...
scientists for use in simulation
Simulation
Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....
s as well remote sensing
Remote sensing
Remote sensing is the acquisition of information about an object or phenomenon, without making physical contact with the object. In modern usage, the term generally refers to the use of aerial sensor technologies to detect and classify objects on Earth by means of propagated signals Remote sensing...
specialists since the composition and microstructural properties of the ice ultimately affect how it interacts with electromagnetic radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
.
Sea ice growth models for predicting the ice distribution
Sea ice concentration
Sea ice concentration is a useful variable for climatescientists and nautical navigators. It is defined as the area ofsea ice relative to the total at a given point in the ocean....
and extent are also valuable for shipping concerns. An ice growth model can be combined with remote sensing
Remote sensing
Remote sensing is the acquisition of information about an object or phenomenon, without making physical contact with the object. In modern usage, the term generally refers to the use of aerial sensor technologies to detect and classify objects on Earth by means of propagated signals Remote sensing...
measurements in an assimilation
Data assimilation
Applications of data assimilation arise in many fields of geosciences, perhaps most importantly in weather forecasting and hydrology. Data assimilation proceeds by analysis cycles...
model as a means of generating more accurate ice charts
Sea ice concentration
Sea ice concentration is a useful variable for climatescientists and nautical navigators. It is defined as the area ofsea ice relative to the total at a given point in the ocean....
.
Overview
Several formation mechanisms of sea ice have been identified. At its earliest stages, sea iceconsists of elongated, randomly oriented crystals. This is called frazil
Frazil ice
Frazil ice is a collection of loose, randomly oriented needle-shaped ice crystals in water. It resembles slush and has the appearance of being slightly oily when seen on the surface of water...
and mixed with water in
the unconsolidated state is known as grease ice
Grease ice
Grease ice is a very thin, soupy layer of frazil crystals clumped together, which makes the ocean surface resemble an oil slick. Grease ice is the second stage in the formation of solid sea ice after ice floes and then frazil 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 turbulant conditions, the frazil will consolidate
by mechanical action to form pancake ice
Pancake ice
Pancake ice is a form of ice that consists of round pieces of ice with diameters ranging from a few inches to many feet, depending on the local conditions that affect ice formation. It may have a thickness of several inches....
, which has a more random structure
Another common formation mechanism,
especially in the Antarctic
Antarctic
The Antarctic is the region around the Earth's South Pole, opposite the Arctic region around the North Pole. The Antarctic comprises the continent of Antarctica and the ice shelves, waters and island territories in the Southern Ocean situated south of the Antarctic Convergence...
where precipitation
Precipitation (meteorology)
In meteorology, precipitation In meteorology, precipitation In meteorology, precipitation (also known as one of the classes of hydrometeors, which are atmospheric water phenomena is any product of the condensation of atmospheric water vapor that falls under gravity. The main forms of 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.
One of the more interesting processes to occur within consolidated ice packs is changes in
the saline
Salinity
Salinity is the saltiness or dissolved salt content of a body of water. It is a general term used to describe the levels of different salts such as sodium chloride, magnesium and calcium sulfates, and bicarbonates...
content. As the ice freezes, most of the salt
Salt
In chemistry, salts are ionic compounds that result from the neutralization reaction of an acid and a base. They are composed of cations and anions so that the product is electrically neutral...
content gets rejected and forms highly
saline brine
Brine
Brine is water, saturated or nearly saturated with salt .Brine is used to preserve vegetables, fruit, fish, and meat, in a process known as brining . Brine is also commonly used to age Halloumi and Feta cheeses, or for pickling foodstuffs, as a means of preserving them...
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
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
than
water, increasing pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
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.
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
Vertical growth
The downward growth of consolidated ice in calm conditions is determined by the rate of heat transferHeat transfer
Heat transfer is a discipline of thermal engineering that concerns the exchange of thermal energy from one physical system to another. Heat transfer is classified into various mechanisms, such as heat conduction, convection, thermal radiation, and phase-change transfer...
, Q*, at the ice-water interface. If we assume that the ice is in thermal equilibrium
Thermal equilibrium
Thermal equilibrium is a theoretical physical concept, used especially in theoretical texts, that means that all temperatures of interest are unchanging in time and uniform in space...
both with itself and its surroundings and that the weather conditions are known, then we can determine Q* by solving the following equation:
for Ts, the surface temperature. The water temperature, Tw, is assumed to be at or near freezing
Freezing
Freezing or solidification is a phase change in which a liquid turns into a solid when its temperature is lowered below its freezing point. The reverse process is melting....
, while the ice thickness, h, is assumed to be known and we can approximate the thermal conductivity
Thermal conductivity
In physics, thermal conductivity, k, is the property of a material's ability to conduct heat. It appears primarily in Fourier's Law for heat conduction....
, k, as an average over the layers (which have different salinities) or simply use the value for pure ice. The net heat flux is a total over four components:
which are latent, sensible, longwave and shortwave fluxes, respectively. For a description of the approximate parameterizations, see determining surface flux under sea ice thickness
Sea ice thickness
Sea ice thickness is an important climate-related variable whose determination from satellite measurements is still an unsolved problem. While ice concentration is often used as a marker for climate change, the more important variable is sea ice volume which can be determined by multiplying...
. The equation can be solved using a numerical root-finding algorithm
Root-finding algorithm
A root-finding algorithm is a numerical method, or algorithm, for finding a value x such that f = 0, for a given function f. Such an x is called a root of the function f....
such as bisection
Bisection method
The bisection method in mathematics is a root-finding method which repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing. It is a very simple and robust method, but it is also relatively slow...
: the functional dependencies on surface temperature are given, with e being the equilibrium vapor pressure.
While Cox and Weeks
assume thermal equilibrium, Tanboe
uses a more sophisticated thermodynamic model based on numerical solution of the heat equation
Heat equation
The heat equation is an important partial differential equation which describes the distribution of heat in a given region over time...
. 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:
where L is the latent heat
Latent heat
Latent heat is the heat released or absorbed by a chemical substance or a thermodynamic system during a process that occurs without a change in temperature. A typical example is a change of state of matter, meaning a phase transition such as the melting of ice or the boiling of water. The term was...
of fusion for water and
is the density of ice. The growth rate 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 and Nakawo and Sinhaand take the form:
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.:
where g is in cm/s.
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 more or less exactly based strictly on temperature—see freezing point depression. References andcontain empirical formulas relating sea ice temperature to brine salinity.
The relative brine volume, Vb, 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:
where S is sea ice salinity, Sb is brine salinity,
is the density of the ice and is brine density. Compare with this empirical formula from Ulaby et al.:where T is ice temperature in degrees Celsius
Celsius
Celsius is a scale and unit of measurement for temperature. It is named after the Swedish astronomer Anders Celsius , who developed a similar temperature scale two years before his death...
and S is ice salinity in parts-per-thousand
Parts-per notation
In science and engineering, the parts-per notation is a set of pseudo units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, they are pure numbers with no associated units of measurement...
.
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:
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
Weddell Sea
The Weddell Sea is part of the Southern Ocean and contains the Weddell Gyre. Its land boundaries are defined by the bay formed from the coasts of Coats Land and the Antarctic Peninsula. The easternmost point is Cape Norvegia at Princess Martha Coast, Queen Maud Land. To the east of Cape Norvegia is...
, Antarctica, with an exponential fit of the form,
, 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 fluidNon-Newtonian fluid
A non-Newtonian fluid is a fluid whose flow properties differ in any way from those of Newtonian fluids. Most commonly the viscosity of non-Newtonian fluids is not independent of shear rate or shear rate history...
.
Sea ice will deform primarily at fracture
Fracture
A fracture is the separation of an object or material into two, or more, pieces under the action of stress.The word fracture is often applied to bones of living creatures , or to crystals or crystalline materials, such as gemstones or metal...
points which in turn will form at the points of greatest stress and lowest strength
Strength of materials
In materials science, the strength of a material is its ability to withstand an applied stress without failure. The applied stress may be tensile, compressive, or shear. Strength of materials is a subject which deals with loads, deformations and the forces acting on a material. A load applied to a...
, or where the ratio between the two is a maximum. Ice thickness, salinity and porosity
Porosity
Porosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0–1, or as a percentage between 0–100%...
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
Coriolis
Coriolis may refer to:* Gaspard-Gustave Coriolis , French mathematician, mechanical engineer and scientist* Coriolis effect, the apparent deflection of moving objects from a straight path when viewed from a rotating frame of reference...
effects—see, for instance, Ekman spiral
Ekman spiral
The Ekman spiral refers to a structure of currents or winds near a horizontal boundary in which the flow direction rotates as one moves away from the boundary. It derives its name from the Swedish oceanographer Vagn Walfrid Ekman...
.
See also
- Sea iceSea iceSea ice is largely formed from seawater that freezes. Because the oceans consist of saltwater, this occurs below the freezing point of pure water, at about -1.8 °C ....
- Sea ice thicknessSea ice thicknessSea ice thickness is an important climate-related variable whose determination from satellite measurements is still an unsolved problem. While ice concentration is often used as a marker for climate change, the more important variable is sea ice volume which can be determined by multiplying...
- Sea ice concentrationSea ice concentrationSea ice concentration is a useful variable for climatescientists and nautical navigators. It is defined as the area ofsea ice relative to the total at a given point in the ocean....
- Sea ice emissivity modellingSea ice emissivity modellingWith 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,...