Sea ice thickness
Encyclopedia
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 concentration with thickness and integrating over the ocean surface. Sea ice thickness determines a number of important fluxes such as heat flux between the air and ocean surface—see below—as well as salt and fresh water fluxes between the ocean since saline water ejects much of its salt content when frozen—see sea ice growth processes
. It is also important for navigators on icebreaker
s since there is an upper limit to the thickness of ice any ship can sail through.
is related to the ice thickness and surface temperature as follows:
where h is the ice thickness, Q* net heat flux, k is the thermal conductivity
of the ice, Ts is the ice surface temperature and Tw is the water temperature which is assumed to be freezing—note that this varies with the salinity
of the water, see freezing-point depression
. Thermal equilibrium
is assumed, true if the weather conditions are changing slowly or the ice is not too thick. If we do not assume thermal equilibrium, numerical solution
of the heat equation
based on past weather conditions is required.
The net heat flux can be decomposed into four components: latent heat
, sensible heat
, longwave and shortwave fluxes:
The latent heat flux is due to the latent heat
stored and released from the sublimation of water between the ice and air. It is normally calculated from a parameterization based on the wind speed and the difference in water vapor partial pressure
above the ice (2 or 10 m) and at the ice surface:
where kE is a constant,
is the air density, L is the latent heat of sublimation, v is windspeed, RH is relative humidity
, Ta is the air temperature at the 2 or 10 m level and e is a function for determining saturation water vapor pressure
--see also dewpoint. The sensible heat flux refers to actual physical heat transfer and its major component is due to surface convection
. It too is calculated from a paramerization, this time based on the difference in air and surface temperature:
where kH is a constant and Cp is the heat capacity
of air.
The longwave flux can be approximated from the Stefan-Boltzmann law. A typical formulation looks something like this:
where
is the emissivity
of the ice and
is the Stefan-Boltzmann constant
. Note the corrections for cloud-cover, cc, using a latitude-dependent cloud-cover coefficient, kcc.
Meanwhile, the shortwave flux is determined primarily from geometric consideration, with the cloud-cover and albedo
acting as multiplication coefficients:
where S is the solar constant
, a is the albedo
of the ice surface and
is the angle of the sun's rays relative to the Earth's surface as a function of latitude, 
, and time of day and year—see insolation
.
) by submarine sonar
or RADAR
systems can give good estimates of ice thickness provided there isn't too much snow (which is less dense than ice) on top. The E-M Bird ice thickness meter, designed by the Alfred Wegener Institute for Polar and Marine Research
, is carried aloft by helicopter and measures ice thickness with a combination of a pair of inductance coils
that measure the ice-water interface based inductance
variations—similar to a metal detector
--and a laser altimeter
which measures the ice surface.
It was used on a small scale in 2007 to supplement microwave radiometer measurements during the Pol-Ice campaign and on a much larger scale during the GreenICE (Greenland Arctic Shelf Ice and Climate Experiment) campaign conducted in 2004 and 2005.
s capable of measuring ice thickness from space. ICESat
, for instance, measured ice surface (of primarily glacial ice pack) using laser altimetry. Unfortunately, variations in surface elevation caused by differing ice thickness are so small that only averages over a relatively long time scale (one month, for instance) are significant.
The microwave
emissivity
of sea ice is found to vary quite significantly with thickness. This is caused mainly by changes in the salinity, particularly in the surface salinity which is a result of growth processes.
Martin et al.
use the following, empirical, equation to determine the thickness of new ice in the Chukchi Sea from satellite microwave radiometer measurements:
where
is the brightness temperature at polarization, p (horizontal or vertical) and frequency, 
, and 
and 
are constants. The relationship, being highly dependent on growth conditions, was not found to hold everywhere in the polar oceans.
Currently, the most accurate method for determining sea ice thickness from satellite data is based on infrared radiometry using satellites such as the Advanced Very High Resolution Radiometer (AVHRR). Since the emissivity of sea ice (indeed of most classes of objects) is fairly constant at infrared frequencies, measurements are used to estimate the physical surface temperature of the ice.
This, in turn, is used along with the prevailing weather conditions, which can be derived from circulation models or bouy
s to calculate the heat flux from which follows the ice thickness—see first section.
A promising new satellite instrument for detecting ice thickness is the Soil Moisture and Ocean Salinity (SMOS
) instrument.
SMOS is a polarimetric radiometer operating at 1.4 GHz (or L band
).
Generally, the lower the frequency of radiation, the more weakly it interacts with matter
(the photons don't have enough energy to induce many energy transitions)
thus L band radiation penetrates quite deeply into sea ice.
This implies that the instrument will supply at least some information on ice
thickness.
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...
-related variable whose determination from satellite measurements is still an unsolved problem. While ice concentration
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....
is often used as a marker for climate change, the more important variable is sea ice volume which can be determined by multiplying concentration with thickness and integrating over the ocean surface. Sea ice thickness determines a number of important fluxes such as heat flux between the air and ocean surface—see below—as well as salt and fresh water fluxes between the ocean since saline water ejects much of its salt content when frozen—see sea ice growth processes
Sea ice growth processes
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...
. It is also important for navigators on icebreaker
Icebreaker
An icebreaker is a special-purpose ship or boat designed to move and navigate through ice-covered waters. Although the term usually refers to ice-breaking ships, it may also refer to smaller vessels .For a ship to be considered an icebreaker, it requires three traits most...
s since there is an upper limit to the thickness of ice any ship can sail through.
Determining surface heat flux
The rate of heat transfer between ocean and air through an ice sheet can be determined from the ice thickness and the prevailing weather conditions. The net heat fluxHeat flux
Heat flux or thermal flux is the rate of heat energy transfer through a given surface. The SI derived unit of heat rate is joule per second, or watt. Heat flux is the heat rate per unit area. In SI units, heat flux is measured in W/m2]. Heat rate is a scalar quantity, while heat flux is a vectorial...
is related to the ice thickness and surface temperature as follows:
where h is the ice thickness, Q* net heat flux, k is 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....
of the ice, Ts is the ice surface temperature and Tw is the water temperature which is assumed to be freezing—note that this varies with the salinity
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...
of the water, see freezing-point depression
Freezing-point depression
Freezing-point depression describes the phenomenon in which the freezing point of a liquid is depressed when another compound is added, meaning that a solution has a lower freezing point than a pure solvent. This happens whenever a non-volatile solute is added to a pure solvent, such as water...
. 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...
is assumed, true if the weather conditions are changing slowly or the ice is not too thick. If we do not assume thermal equilibrium, numerical solution
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
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...
based on past weather conditions is required.
The net heat flux can be decomposed into four components: 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...
, sensible heat
Sensible heat
Sensible heat is the energy exchanged by a thermodynamic system that has as its sole effect a change of temperature.The term is used in contrast to a latent heat, which is the amount of energy exchanged that is hidden, meaning it cannot be observed as a change of temperature...
, longwave and shortwave fluxes:
The latent heat flux is due to 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...
stored and released from the sublimation of water between the ice and air. It is normally calculated from a parameterization based on the wind speed and the difference in water vapor partial pressure
Partial pressure
In a mixture of ideal gases, each gas has a partial pressure which is the pressure which the gas would have if it alone occupied the volume. The total pressure of a gas mixture is the sum of the partial pressures of each individual gas in the mixture....
above the ice (2 or 10 m) and at the ice surface:
where kE is a constant,
is the air density, L is the latent heat of sublimation, v is windspeed, RH is relative humidityRelative humidity
Relative humidity is a term used to describe the amount of water vapor in a mixture of air and water vapor. It is defined as the partial pressure of water vapor in the air-water mixture, given as a percentage of the saturated vapor pressure under those conditions...
, Ta is the air temperature at the 2 or 10 m level and e is a function for determining saturation water vapor pressure
Vapor pressure
Vapor pressure or equilibrium vapor pressure is the pressure of a vapor in thermodynamic equilibrium with its condensed phases in a closed system. All liquids have a tendency to evaporate, and some solids can sublimate into a gaseous form...
--see also dewpoint. The sensible heat flux refers to actual physical heat transfer and its major component is due to surface convection
Convection
Convection is the movement of molecules within fluids and rheids. It cannot take place in solids, since neither bulk current flows nor significant diffusion can take place in solids....
. It too is calculated from a paramerization, this time based on the difference in air and surface temperature:
where kH is a constant and Cp is the heat capacity
Heat capacity
Heat capacity , or thermal capacity, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount...
of air.
The longwave flux can be approximated from the Stefan-Boltzmann law. A typical formulation looks something like this:
where
is the emissivityEmissivity
The emissivity of a material is the relative ability of its surface to emit energy by radiation. It is the ratio of energy radiated by a particular material to energy radiated by a black body at the same temperature...
of the ice and
is the Stefan-Boltzmann constantStefan-Boltzmann constant
The Stefan–Boltzmann constant , a physical constant denoted by the Greek letter σ, is the constant of proportionality in the Stefan–Boltzmann law: the total energy radiated per unit surface area of a black body in unit time is proportional to the fourth power of the thermodynamic temperature.The...
. Note the corrections for cloud-cover, cc, using a latitude-dependent cloud-cover coefficient, kcc.
Meanwhile, the shortwave flux is determined primarily from geometric consideration, with the cloud-cover and albedo
Albedo
Albedo , or reflection coefficient, is the diffuse reflectivity or reflecting power of a surface. It is defined as the ratio of reflected radiation from the surface to incident radiation upon it...
acting as multiplication coefficients:
where S is the solar constant
Solar constant
The solar constant, a measure of flux density, is the amount of incoming solar electromagnetic radiation per unit area that would be incident on a plane perpendicular to the rays, at a distance of one astronomical unit...
, a is the albedo
Albedo
Albedo , or reflection coefficient, is the diffuse reflectivity or reflecting power of a surface. It is defined as the ratio of reflected radiation from the surface to incident radiation upon it...
of the ice surface and
is the angle of the sun's rays relative to the Earth's surface as a function of latitude, , and time of day and year—see insolationInsolation
Insolation is a measure of solar radiation energy received on a given surface area in a given time. It is commonly expressed as average irradiance in watts per square meter or kilowatt-hours per square meter per day...
.
Measurement
Ice thickness can be measured directly by taking an ice core and measuring it or drilling through the ice. Since this is laborious and time-consuming, more automated methods are normally sought. Measurements of ice depth below the waterline (or draftDraft (hull)
The draft of a ship's hull is the vertical distance between the waterline and the bottom of the hull , with the thickness of the hull included; in the case of not being included the draft outline would be obtained...
) by submarine sonar
Sonar
Sonar is a technique that uses sound propagation to navigate, communicate with or detect other vessels...
or RADAR
Radar
Radar is an object-detection system which uses radio waves to determine the range, altitude, direction, or speed of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. The radar dish or antenna transmits pulses of radio...
systems can give good estimates of ice thickness provided there isn't too much snow (which is less dense than ice) on top. The E-M Bird ice thickness meter, designed by the Alfred Wegener Institute for Polar and Marine Research
Alfred Wegener Institute for Polar and Marine Research
The Alfred Wegener Institute of Polar and Marine Research is a scientific organization located in Bremerhaven, Germany. The institute was founded in 1980 and is named after revolutionary meteorologist climatologist, and geologist Alfred Wegener...
, is carried aloft by helicopter and measures ice thickness with a combination of a pair of inductance coils
Inductor
An inductor is a passive two-terminal electrical component used to store energy in a magnetic field. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...
that measure the ice-water interface based inductance
Inductance
In electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit...
variations—similar to a metal detector
Metal detector
A metal detector is a device which responds to metal that may not be readily apparent.The simplest form of a metal detector consists of an oscillator producing an alternating current that passes through a coil producing an alternating magnetic field...
--and a laser altimeter
LIDAR
LIDAR is an optical remote sensing technology that can measure the distance to, or other properties of a target by illuminating the target with light, often using pulses from a laser...
which measures the ice surface.
It was used on a small scale in 2007 to supplement microwave radiometer measurements during the Pol-Ice campaign and on a much larger scale during the GreenICE (Greenland Arctic Shelf Ice and Climate Experiment) campaign conducted in 2004 and 2005.
Satellite instruments
There are a number of satellite-mounted altimeterAltimeter
An altimeter is an instrument used to measure the altitude of an object above a fixed level. The measurement of altitude is called altimetry, which is related to the term bathymetry, the measurement of depth underwater.-Pressure altimeter:...
s capable of measuring ice thickness from space. ICESat
ICESat
ICESat , part of NASA's Earth Observing System, was a satellite mission for measuring ice sheet mass balance, cloud and aerosol heights, as well as land topography and vegetation characteristics...
, for instance, measured ice surface (of primarily glacial ice pack) using laser altimetry. Unfortunately, variations in surface elevation caused by differing ice thickness are so small that only averages over a relatively long time scale (one month, for instance) are significant.
The microwave
Microwave
Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...
emissivity
Emissivity
The emissivity of a material is the relative ability of its surface to emit energy by radiation. It is the ratio of energy radiated by a particular material to energy radiated by a black body at the same temperature...
of sea ice is found to vary quite significantly with thickness. This is caused mainly by changes in the salinity, particularly in the surface salinity which is a result of growth processes.
Martin et al.
use the following, empirical, equation to determine the thickness of new ice in the Chukchi Sea from satellite microwave radiometer measurements:
where
is the brightness temperature at polarization, p (horizontal or vertical) and frequency, , and and are constants. The relationship, being highly dependent on growth conditions, was not found to hold everywhere in the polar oceans.Currently, the most accurate method for determining sea ice thickness from satellite data is based on infrared radiometry using satellites such as the Advanced Very High Resolution Radiometer (AVHRR). Since the emissivity of sea ice (indeed of most classes of objects) is fairly constant at infrared frequencies, measurements are used to estimate the physical surface temperature of the ice.
This, in turn, is used along with the prevailing weather conditions, which can be derived from circulation models or bouy
Bouy
Bouy is a commune of the Marne department in north-eastern France.Bouy is twinned with the english village of Everton in Nottinghamshire, UK.-See also:*Communes of the Marne department**...
s to calculate the heat flux from which follows the ice thickness—see first section.
A promising new satellite instrument for detecting ice thickness is the Soil Moisture and Ocean Salinity (SMOS
Soil Moisture and Ocean Salinity satellite
The Soil Moisture and Ocean Salinity Satellite is a part of ESA's Living Planet Programme intended to provide new insights into Earth's water cycle and climate...
) instrument.
SMOS is a polarimetric radiometer operating at 1.4 GHz (or L band
L band
L band refers to four different bands of the electromagnetic spectrum: 40 to 60 GHz , 1 to 2 GHz , 1565 nm to 1625 nm , and around 3.5 micrometres .-NATO L band:...
).
Generally, the lower the frequency of radiation, the more weakly it interacts with matter
(the photons don't have enough energy to induce many energy transitions)
thus L band radiation penetrates quite deeply into sea ice.
This implies that the instrument will supply at least some information on ice
thickness.
See also
- Measurement of sea iceMeasurement of sea iceMeasurement of sea ice is important for safety of navigation and for monitoring the environment, particularly the climate. Record keeping of direct observations began over a thousand years ago, but was sparse until the 1950s. Truly comprehensive records began with the satellite era in the late 1970s...
- 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,...
- Sea ice growth processesSea ice growth processesSea ice is a complex composite composed primarily of pure ice in various states of crystallization along with air bubbles and included pockets of brine...
- Polarstern research vessel