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| '''Sea ice thickness''' is an important [[climate]]-related variable whose determination from satellite measurements is still an unsolved problem. While [[sea ice concentration|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.
| | The stylish wardrobe of Maggie Gyllenhaal�s role in BBC Two�s hard-hitting political thriller, The Honourable Woman, has caught the attention of the eagle-eyed viewers.<br><br> |
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| ==Determining surface heat flux== | | The eight-part series, set against the backdrop of the Israeli-Palestinian conflict, centres around Nessa Stein, played by Gyllenhaal. Stein is an Anglo-Israeli businesswoman recently ennobled in the House of Lords who devotes herself to philanthropic purposes across the Middle East, but hides a secret past from her time spent in Gaza eight years earlier.<br><br>Through the unravelling of her public and private life played out on an international, political stage, Stein parades in an increasingly impressive selection of outfits.<br>�Because the character of Nessa is so complicated and multi layered, we looked at all sorts of different people as reference. I suppose we started off by looking at other powerful and stylish women through history, Jackie Kennedy, Eva Peron, Margaret Thatcher, Cleopatra� Edward K [http://www.encyclopedia.com/searchresults.aspx?q=Gibbon+costume Gibbon costume] designer for the series told The Independent<br><br> |
| | Maggie Gyllenhaal The [http://Www.Alexa.com/search?q=Honourable&r=topsites_index&p=bigtop Honourable] Woma<br> |
| | �And then we kind of threw all the reference away and started afresh. The way Maggie looked as Nessa was constantly evolving throughout the six month shoot.� |
| | The series opens with Nessa clad in a Roland Mouret power dress. Her day to day look is a sartorial dream with tailored suits by the likes of Stella McCartney, Acne, Escada, Pringle and vintage Chane<br> |
| | �Silk blouses and wide legged pants based on 1970s Yves Saint Laurent originals were created by Hilary Marschner� explains Gibb<br><br> |
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| 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 flux]] is related to the ice thickness and surface temperature as follows:
| | Outerwear includes coats by Mulberry, vintage finds from Jil Sander and a 1980s Gieves and Hawkes men�s co<br>. |
| | Even curled up in her panic room at night she sports silk slips by haute couture Parisian lingerie designer Carine Gilson and London based lingerie label Bod<br>. |
| | In pictures: Nessa Stein's wardrobe in The Honourable Woma<br> |
| | Shoes are by Acne, Christian Louboutin and [http://www.pcs-systems.co.uk/Images/celinebag.aspx Celine Bag Sale]. With bags from Mulberry and John Lewis. �Nessa's wardrobe runs the full gamut from designer, through High Street, Charity shops and bespoke pieces� says Gib<br><br> |
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| :<math>
| | �The clothing is always the way in [to the character]� Gyllenhaal told WWD. �I never played a character that didn�t care about what they were wearing.� |
| h Q^* = k (T_s - T_w)
| | The Honourable Woman continues tonight, BBC2 at 9pm. |
| </math>
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| | |
| where ''h'' is the ice thickness, ''Q''<sup>*</sup> net heat flux, ''k'' is the [[thermal conductivity]] of the ice, ''T<sub>s</sub>'' is the ice surface temperature and ''T<sub>w</sub>'' 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 analysis|numerical solution]] of the [[heat equation]] based on past weather conditions is required.
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| The net heat flux can be decomposed into four components: [[latent heat]], [[sensible heat]], longwave and shortwave fluxes:
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| :<math>
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| Q^* = Q_E + Q_H + Q_{LW} + Q_{SW}
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| </math>
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| 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:
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| :<math>
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| Q_E = k_E L \rho v \left [ RH e(T_a) - e(T_s) \right ]
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| </math>
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| where ''k<sub>E</sub>'' is a constant, <math>\rho</math> is the air density, ''L'' is the latent heat of sublimation, ''v'' is windspeed, ''RH'' is [[relative humidity]], ''T<sub>a</sub>'' 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:
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| :<math>
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| Q_H = k_H C_p \rho v (T_a - T_s)
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| </math>
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| where ''k<sub>H</sub>'' is a constant and ''C<sub>p</sub>'' is the [[heat capacity]] of air.
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| The longwave flux can be approximated from the [[Stefan-Boltzmann law]]. A typical formulation looks something like this:
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| :<math>
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| Q_{LW} = \epsilon_i \sigma \left [ 0.39 (1 - k_{cc}(\phi) cc^2) T_s^4 + T_s^3 (T_s - T_a) \right ]
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| </math>
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| where <math>\epsilon_i</math> is the [[emissivity]] of the ice and <math>\sigma</math> is the [[Stefan-Boltzmann constant]]. Note the corrections for cloud-cover, ''cc'', using a latitude-dependent cloud-cover coefficient, ''k<sub>cc</sub>.
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| Meanwhile, the shortwave flux is determined primarily from geometric consideration, with the cloud-cover and [[albedo]] acting as multiplication coefficients:
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| :<math>
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| Q_{SW} = S (1 - 0.62 cc)(1 - a) \cos \theta(\phi, t)
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| </math>
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| where ''S'' is the [[solar constant]], ''a'' is the [[albedo]] of the ice surface and <math>\theta</math> is the angle of the sun's rays relative to the Earth's surface as a function of latitude, <math>\phi</math>, and time of day and year—see [[insolation]].
| |
| <ref name="Yu_Lindsay2003">
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| {{cite journal
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| | author=Y. Yu and R. W Lindsay
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| | year=2003
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| | journal= [[Journal of Geophysical Research]]
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| | title=Comparison of thin ice thickness derived from RADARSAT Geophysical Processor System and AVHRR data sets
| |
| | volume=108
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| | issue=C12
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| | pages=3387
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| | doi=10.1029/2002JC001319
| |
| |bibcode = 2003JGRC..108.3387Y }}</ref>
| |
| <ref name="Cox_Weeks1988">
| |
| {{cite journal
| |
| | author=G. Cox and W. Weeks
| |
| | year=1988
| |
| | journal=Journal of Geophysical Research
| |
| | title=Numerical simulations of the profile properties of undeformed first-year sea ice during the growth season
| |
| | volume=93
| |
| | issue=C10
| |
| | pages=12499-12460
| |
| |bibcode = 1988JGR....9312499H |doi = 10.1029/JC093iC10p12499 }}</ref>
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| ==Measurement==
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| 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 [[draft (hull)|draft]]) 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 [[inductor|inductance coils]] that measure the ice-water interface based [[inductance]] variations—similar to a [[metal detector]]--and a [[LIDAR|laser altimeter]] which measures the ice surface.
| |
| <ref name="smos_final">
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| {{cite techreport
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| | author = G. Heygster, S. Hendricks, L. Kaleschke, N. Maass, P. Mills, D. Stammer, R. T. Tonboe and C. Haas
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| | title=L-Band Radiometry for Sea-Ice Applications
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| | institution=Institute of Environmental Physics, University of Bremen
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| | year=2009
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| | number=ESA/ESTEC Contract N. 21130/08/NL/EL
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| }}</ref>
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| 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.
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| ===Satellite instruments===
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| There are a number of satellite-mounted [[altimeter]]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.
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| 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. | |
| <ref name="Naoki_etal2008">
| |
| {{cite journal
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| | author=K. Naoki, J. Ukita, F. Nishio, M. Nakayama, J. C. Comiso and A. Gasiewski
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| | year=2008
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| | journal=Journal of Geophysical Research
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| | title=Thin sea ice thickness as inferred from passive microwave and in situ observations
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| | volume=113
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| | issue=C02S16
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| | doi=10.1029/2007JC004270
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| | bibcode=2008JGRC..11302S16N}}
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| </ref>
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| Martin et al.
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| <ref name="Martin_etal2004">
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| {{cite journal
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| | author=S. Martin, R. Drucker, R. Kwok and B. Holt
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| | year=2004
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| | journal=Journal of Geophysical Research
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| | title=Estimation of the thin ice thickness and heat flux for the Chukchi Sea Alaskan coast polynya from Special Sensor Microwave Imager data, 1990-2001
| |
| | volume=109
| |
| | issue=C10012
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| | doi=10.1029/2004GL022013
| |
| | bibcode=2005GeoRL..3205505M
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| }}</ref>
| |
| use the following, empirical, equation to determine the thickness of new ice in the Chukchi Sea from satellite microwave radiometer measurements:
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| :<math>
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| h=\exp \left [ \frac{T_h(37GHz)}{\alpha T_v(37GHz)} \right ] - \gamma
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| </math>
| |
| | |
| where <math>T_p(\nu)</math> is the brightness temperature at polarization, ''p'' (''h''orizontal or ''v''ertical) and frequency, <math>\nu</math>, and <math>\alpha</math> and <math>\gamma</math> are constants. The relationship, being highly dependent on growth conditions, was not found to hold everywhere in the polar oceans.
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| 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.
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| This, in turn, is used along with the prevailing weather conditions, which can be derived from [[general circulation model|circulation models]] or [[buoy]]s to calculate the heat flux from which follows the ice thickness—see first section.
| |
| <ref name="Yu_Lindsay2003"/>
| |
| <ref name="Drucker_etal2003">
| |
| {{cite journal
| |
| | author=R. Drucker, S. Martin and R. Moritz
| |
| | year=2003
| |
| | journal=Journal of Geophysical Research
| |
| | title=Observations of ice thickness and frazil ice in the St. Lawrence Island polynya from satellite imagery, upward-looking sonar and salinity/temperature moorings
| |
| | volume=108
| |
| | issue=C5
| |
| |doi=10.1029/2001JC001213
| |
| | bibcode=2003JGRC..108.3149D
| |
| }}</ref>
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| The main problem with this method is that it can only be used during cloud-free
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| conditions.
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| A promising new satellite instrument for detecting ice thickness is the Soil Moisture and Ocean Salinity ([[Soil Moisture and Ocean Salinity satellite|SMOS]]) instrument.
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| SMOS is a polarimetric radiometer operating at 1.4 GHz (or [[L band]]).
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| Generally, the lower the frequency of radiation, the more weakly it interacts with matter
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| (the photons don't have enough energy to induce many energy transitions)
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| thus L band radiation penetrates quite deeply into sea ice.
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| This implies that the instrument will supply at least some information on ice
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| thickness.
| |
| <ref name="smos_final"/>
| |
| <ref name="Kaleschke_etal2009">
| |
| {{cite journal
| |
| | author=L. Kaleschke, N. Maaß, C. Haas, S. Hendricks, G. Heygster, and R. T. Tonboe, R. T.
| |
| | title=A sea ice thickness retrieval model for 1.4 GHz radiometry and application to airborne measurements over low salinity sea ice
| |
| | journal=The Cryosphere Discussion
| |
| | volume=3
| |
| | pages=995–1022
| |
| | doi=10.5194/tc-4-583-2010
| |
| | bibcode=2010TCry....4..583K
| |
| | year=2009
| |
| }}</ref>
| |
| <ref name="Mills_Heygster2010">
| |
| {{cite journal
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| | author=Peter Mills and Georg Heygster
| |
| | journal=IEEE Transactions on Geoscience and Remote Sensing
| |
| | year=2011
| |
| | title=Sea ice emissivity modelling at L-band and application to Pol-Ice campaign field data
| |
| | number=2
| |
| | volume=49
| |
| | pages=612–627
| |
| | doi=10.1109/TGRS.2010.2060729
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| | url=http://peteysoft.users.sourceforge.net/smos_ieee.pdf
| |
| }}</ref>
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| | |
| ==See also==
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| * [[Measurement of sea ice]]
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| * [[Sea ice concentration]]
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| * [[Sea ice emissivity modelling]]
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| * [[Sea ice growth processes]]
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| * ''[[Polarstern]]'' research vessel
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| | |
| ==References==
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| {{Reflist|2}}
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| ==External links==
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| * [http://www.greenice.org/index.html Greenice]
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| * [http://www.awi.de/en Alfred Wegener Institute]
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| * [http://www.nasa.gov/topics/earth/features/seaice_skinny.html NASA: The Skinny on Sea Ice Thickness]
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| [[Category:Sea ice]]
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| [[Category:Climate]]
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| [[Category:Remote sensing]]
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| [[Category:Radiometry]]
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| [[Category:Climate change science]]
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The stylish wardrobe of Maggie Gyllenhaal�s role in BBC Two�s hard-hitting political thriller, The Honourable Woman, has caught the attention of the eagle-eyed viewers.
The eight-part series, set against the backdrop of the Israeli-Palestinian conflict, centres around Nessa Stein, played by Gyllenhaal. Stein is an Anglo-Israeli businesswoman recently ennobled in the House of Lords who devotes herself to philanthropic purposes across the Middle East, but hides a secret past from her time spent in Gaza eight years earlier.
Through the unravelling of her public and private life played out on an international, political stage, Stein parades in an increasingly impressive selection of outfits.
�Because the character of Nessa is so complicated and multi layered, we looked at all sorts of different people as reference. I suppose we started off by looking at other powerful and stylish women through history, Jackie Kennedy, Eva Peron, Margaret Thatcher, Cleopatra� Edward K Gibbon costume designer for the series told The Independent
Maggie Gyllenhaal The Honourable Woma
�And then we kind of threw all the reference away and started afresh. The way Maggie looked as Nessa was constantly evolving throughout the six month shoot.�
The series opens with Nessa clad in a Roland Mouret power dress. Her day to day look is a sartorial dream with tailored suits by the likes of Stella McCartney, Acne, Escada, Pringle and vintage Chane
�Silk blouses and wide legged pants based on 1970s Yves Saint Laurent originals were created by Hilary Marschner� explains Gibb
Outerwear includes coats by Mulberry, vintage finds from Jil Sander and a 1980s Gieves and Hawkes men�s co
.
Even curled up in her panic room at night she sports silk slips by haute couture Parisian lingerie designer Carine Gilson and London based lingerie label Bod
.
In pictures: Nessa Stein's wardrobe in The Honourable Woma
Shoes are by Acne, Christian Louboutin and Celine Bag Sale. With bags from Mulberry and John Lewis. �Nessa's wardrobe runs the full gamut from designer, through High Street, Charity shops and bespoke pieces� says Gib
�The clothing is always the way in [to the character]� Gyllenhaal told WWD. �I never played a character that didn�t care about what they were wearing.�
The Honourable Woman continues tonight, BBC2 at 9pm.