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| [[Image:sea ice emissivity model flow diagram.png|thumb|upright=2.5|alt=Sea ice emissivity data flow diagram|[[Data flow diagram]] describing the relevant steps in a radiative-transfer-based sea ice emissivity model<ref name="Mills_Heygster2011">
| | There was no error. Stephen L. Miles was back on Baltimore's air passages and the Law Workplace of Stephen L. Miles was back in business. Have no idea Miles? If you can remember back to the days when this town bled Colts white and blue on Sundays; when the O's were winners; when Jack Luskin was the most inexpensive guy in town, and when the Gino Giant outsold the [http://Www.nexopia.com/users/garyneinstein/blog/12-auto-injurylegal-process-2014 Huge Mac] - then Miles' image and voice will resonate with you.<br><br>If you are in a vehiclemishap, write down every little information personal injury advice you can believe of to offer to your lawyer. Take down the license plate number of other automobiles at the scene. Know the names of any insurance companies that could be included. Keep the tickets or reports written by authorities present at the time of the accident. The more you prepare for a case, the faster you can get it over with.<br><br>Personal injury lawyers deal with [http://Moneynetwork.stockoptionspicks.com/blogs/viewstory/608049 individuals] who have actually been hurt due to the negligence of another person. They work to get insurance provider companies and individuals at fault to pay what is due. The insurance provider business could not pay for discomfort and suffering as a result of the accident.<br><br>In addition, some states have actually enacted legislation that involves "strict liability". The owner is responsible for their canine's actions whether they knew the pet dog was dangerous or not. Should you have any kind of queries relating to in which as well as how you can use [http://testing6.nittanylink.com/ActivityFeed/MyProfile/tabid/60/userId/101884/Default.aspx Toronto personal injury attorney], you'll be able to e mail us in our web site. Anytime their pet dog bites someone they are held accountable no matter the circumstance or scenarios.<br><br>personal injury is a field that is tough to have a case in. That's why you need an injury attorney who has great deals of experience. Look for a lawyer who has a history of success in this certain field, guaranteeing your case is handled with the greatest proficiency.<br><br>After the personal injury law firm that is approached researches the case, it might occasionally choose not get involved. There might be various factors for this. Once the case is accepted, an arrangement about the fees and costs needs to be reached. For accident cases, contingent fees prevail practice. This means that the law firm earns money from the claim that is granted; it is generally revealed in terms of portion. The firm does not get paid for its services if the claim is refused. Some insist on the client paying in case of rejection of the claim, but others may waive such costs. Clarify prior to signing up.<br><br>Fourth, search for a lawyer who has actually been practicing law for a long period of time. Inspect his successful cases. This is a beneficial way to be sure of the capability of the attorney. |
| {{cite techreport
| |
| |author=Peter Mills and Georg Heygster
| |
| |title=Sea ice brightness temperature as a function of ice thickness: Computed curves for AMSR-E and SMOS (frequencies from 1.4 to 89 GHz)
| |
| |url=http://peteysoft.users.sourceforge.net/tstudy.pdf
| |
| |institute=Institute of Environmental Physics, University of Bremen
| |
| |number=DFG project HE-1746-15
| |
| |year=2011}}</ref>
| |
| ]]
| |
| 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 [[Advanced Microwave Sounding Unit|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 help us detect sea ice more efficiently, we need to model these emission processes. The interaction of sea ice with electromagnetic radiation in the microwave range is still not well understood.
| |
| | |
| ==Radiative transfer modelling==
| |
| | |
| [[Image:Rt diag.gif||thumb|right|upright=2|alt=Sea ice RT|Diagram illustrating radiative transfer in a discontinuous medium, such as sea ice.<ref name="smos_final"/>]]
| |
| | |
| When scattering is neglected, sea ice emissivity can be modelled through [[radiative transfer]]. The diagram to the right shows a ray passing through an ice sheet with several layers. These layers represent the air above the ice, the snow layer (if applicable), ice with different electro-magnetic properties and the water below the ice. Interfaces between the layers may be continuous (in the case of ice with varying salt content along the vertical axis, but formed in the same way and in the same time period), in which case the reflection coefficients, ''R<sub>i</sub>'' will be zero, or discontinuous (in the case of the ice-snow interface), in which case reflection coefficients must be calculated—see below. Each layer is characterized by its physical properties: temperature, ''T<sub>i</sub>'', complex permittivity, <math>\epsilon_i</math> and thickness, <math>\Delta z_i</math>, and will have an upwelling component of the radiation, <math>T_i \uparrow</math>, and a downwelling component, <math>T_i \downarrow</math>, passing through it. Since we assume plane-parallel geometry, all reflected rays will be at the same angle and we need only account for radiation along a single line-of-sight.
| |
| | |
| Summing the contributions from each layer generates the following [[sparse matrix|sparse]] [[system of linear equations]]:
| |
| | |
| :<math>
| |
| T_i \uparrow - \tau_i (1-R_i) T_{i+1} \uparrow - \tau_i R_i T_i \downarrow
| |
| = (1 - \tau_i) T_i
| |
| </math> | |
| :<math>
| |
| T_i \downarrow - \tau_i (1-R_{i-1}) T_{i-1} \downarrow - \tau_i R_{i-1} T_i \uparrow
| |
| = (1 - \tau_i) T_i
| |
| </math>
| |
| <ref name="Mills_Heygster2010">
| |
| {{cite journal
| |
| | title=Sea ice emissivity modelling at L-band and application to Pol-Ice campaign field data
| |
| | journal=IEEE Transactions on Geoscience and Remote Sensing
| |
| | year=2011
| |
| | author=Peter Mills and Georg Heygster
| |
| | number=2
| |
| | volume=49
| |
| | pages=612–627
| |
| | url=http://peteysoft.users.sourceforge.net/smos_ieee.pdf
| |
| | doi=10.1109/TGRS.2010.2060729
| |
| }}</ref>
| |
| | |
| where ''R<sub>i</sub>'' is the ''i''th [[reflection coefficient]], calculated via the
| |
| [[Fresnel equations]] and <math>\tau_i</math> is the ''i''th [[transmission coefficient]]:
| |
| | |
| : <math>
| |
| \tau_i = \exp \left (- \frac{\alpha_i \, \Delta z_i}{\cos \theta_i} \right )
| |
| </math>
| |
| | |
| where <math>\theta_i</math> is the transmission angle in the ''i''th layer, from [[Snell's law]], <math>\Delta z_i</math> is the layer thickness and <math>\alpha_i</math> is the [[attenuation coefficient]]:
| |
| | |
| : <math>
| |
| \alpha_i = \frac{4 \pi \nu}{c} \mathrm{Imag}\, n_i
| |
| </math>
| |
| | |
| where <math>\nu</math> is the frequency and ''c'' is the speed of light—see [[Beer's law]].
| |
| The most important quantity in this calculation, and also the most difficult to establish with any certainty, is the complex [[refractive index]],
| |
| ''n<sub>i</sub>''. Since sea ice is non-[[magnetic]], it can be calculated from relative [[permittivity]] alone:
| |
| | |
| <math>
| |
| n_i=\sqrt{\epsilon_i}
| |
| </math>
| |
| | |
| ==Effective permittivity==
| |
| | |
| As established in the previous section, the most important quantity in radiative transfer calculations of sea ice is the [[relative permittivity]]. Sea ice is a complex composite composed of pure ice and included pockets of air and highly saline [[brine]]. The electro-magnetic properties of such a mixture will be different from, and normally somewhere in between (though not always—see, for instance, [[metamaterial]]), those of its constituents. Since it is not just the relative composition that is important, but also the geometry, the calculation of [[effective permittivity|effective permittivities]] introduces a high level of uncertainty.
| |
| | |
| Vant et al.
| |
| <ref name="Vant_etal1978"> | |
| {{cite journal
| |
| | author=M. R. Vant, R. O. Ramseier and V. Makios
| |
| | journal=Journal of Applied Physics
| |
| | year=1978
| |
| | title=The complex-dielectric constant of sea ice at frequencies in the range 0.1-4.0 GHz
| |
| | volume=49
| |
| | number=3
| |
| | pages=1246–1280
| |
| | doi = 10.1063/1.325018
| |
| }}</ref>
| |
| have performed actual measurements of sea relative permittivities at frequencies between 0.1 and 4.0 GHz which they have encapsulated in the following formula: | |
| | |
| <math>
| |
| \epsilon^* = a V_b + b
| |
| </math>
| |
| | |
| where <math>\epsilon^*</math> is the real or imaginary effective relative permittivity, ''V<sub>b</sub>'' is the relative brine volume—see [[sea ice growth processes]]—and ''a'' and ''b'' are constants. This empirical model shows some agreement with [[dielectric mixture model]]s based on [[Maxwell's equations]] in the [[low frequency limit]], such as this formula from Sihvola and Kong
| |
| :<ref name="Sihvola_Kong1988"> | |
| {{cite journal
| |
| | author=A. H. Sihvola nd J. Kong
| |
| | journal=IEEE Transactions on Geoscience and Remote Sensing
| |
| | year=1988
| |
| | title=Effective Permittivity of Dielectric Mixtures
| |
| | volume=26
| |
| | number=4
| |
| | pages=
| |
| }}</ref>
| |
| | |
| <math>
| |
| \epsilon_{eff}=\epsilon_1+\frac{V_b \epsilon_1 (\epsilon_2-\epsilon_1)/
| |
| (\epsilon_1+ P(\epsilon_2-\epsilon1)}{1-P V_b(\epsilon_2-\epsilon_1)/
| |
| \left [\epsilon_1+P (\epsilon_2-\epsilon_1) \right ]}
| |
| </math>
| |
| | |
| where <math>\epsilon_1</math> is the relative permittivity of the background material (pure ice), <math>\epsilon_2</math> is the relative permittivity of the inclusion material (brine) and ''P'' is a depolarization factor based on the geometry of the brine inclusions. Brine inclusions are frequently modelled as vertically oriented needles for which the depolarization factor is ''P''=0.5 in the vertical direction and ''P''=0. in the horizontal.
| |
| The two formulas, while they correlate strongly, disagree in both relative and absolute magnitudes.
| |
| <ref name="Mills_Heygster2010"/> | |
| | |
| Pure ice is an almost perfect [[dielectric]] with a real permittivity of roughly 3.15 in the [[microwave]] range which is fairly independent of frequency while the imaginary component is negligible, especially in comparison with the brine which is extremely lossy.
| |
| <ref name="Tucker_etal1992">
| |
| {{cite book
| |
| | title=Microwave Remote Sensing of Sea Ice
| |
| | editors=W. B. Tucker, D. K. Prerovich, A. J. Gow, W. F. Weeks, M. R. Drinkwater
| |
| | publisher=American Geophysical Union}}
| |
| </ref>
| |
| Meanwhile, the permittivity of the [[brine]], which has both a large real part and a large imaginary part, is normally calculated with a complex formula based on [[Debye relaxation]] curves.<ref name="Tucker_etal1992"/>
| |
| | |
| ==Scattering==
| |
| | |
| Emissivity calculations based strictly on radiative transfer tend to underestimate the brightness temperatures of sea ice, especially in the higher frequencies, because both included brine and air pockets within the ice will tend to [[scattering|scatter]] the radiation.
| |
| <ref name="Ulaby_etal1986">
| |
| {{cite book
| |
| | title=Microwave Remote Sensing, Active and Passive
| |
| | year=1986
| |
| | editors=F. T. Ulaby, R. K. Moore and A. K. Fung
| |
| | publisher=Addison Wesley
| |
| | address=London, England}}
| |
| </ref>
| |
| Indeed, as ice becomes more opaque with higher frequency, radiative transfer becomes less important while scattering processes begin to dominate.
| |
| Scattering in sea ice is frequently modelled with a [[Born approximation]]
| |
| <ref name="Maetzler1998">
| |
| {{cite journal
| |
| | author=Christian Maetzler
| |
| | title=Improved born approximation for scattering in a granular medium
| |
| | year=1998
| |
| | journal=Journal of Applied Physics
| |
| | volume=83
| |
| | number=11
| |
| | pages=
| |
| | doi = 10.1063/1.367496
| |
| }}</ref>
| |
| such as in strong fluctuation theory.
| |
| <ref name="Stogryn1986">
| |
| {{cite journal
| |
| | author=A. Stogryn
| |
| | title=A study of microwave brightness temperatures of snow from the point of view of strong fluctuation theory
| |
| | year=1986
| |
| | journal=IEEE Transactions on Geoscience and Remote Sensing
| |
| | volume=24
| |
| | number=2
| |
| | pages=220–231
| |
| }}</ref>
| |
| <ref name="Johnsen1998">
| |
| {{cite thesis
| |
| | author=Klaus-Peter Johnsen
| |
| | title=Radiometrische Messungen im Arktischen Ozean-Vergleich von Theorie und Experiement
| |
| | year=1998
| |
| | institution=University of Bremen
| |
| }}</ref>
| |
| | |
| Scattering coefficients calculated at each layer must also be vertically integrated. The Microwave Emission Model of Layered Snowpack (MEMLS)
| |
| <ref name="Wiesmann_Maetzler1999"> | |
| {{cite journal
| |
| | author=A. Wiesmann and C. Maetzler
| |
| | year=1999
| |
| | journal=Remote Sensing of the Environment
| |
| | title=Microwave emission model for layered snowpacks
| |
| | volume=70
| |
| | pages=307–316
| |
| }}</ref>
| |
| uses a six-flux radiative transfer model to integrate both the scattering coefficients and the effective permittivities with scattering coefficients calculated either empirically or with a distorted Born approximation.
| |
| | |
| Scattering processes in sea ice are relatively poorly understood and scattering models poorly validated empirically.
| |
| | |
| ==Other factors==
| |
| | |
| There are many other factors not accounted for in the models described above. Mills and Heygster,<ref name="Mills_Heygster2010"/> for instance, show that sea ice ridging may have a significant effect on the signal. In such case, the ice can no longer be modelled using plane-parallel geometry. In addition to ridging, surface scattering from smaller-scale roughness must also be considered. | |
| | |
| Since the microstructural properties of sea ice tend to be [[anisotropic]], permittivity is ideally modelled as a [[tensor]]. This anisotropy will also affect the signal in the higher [[Stokes parameters|Stokes components]], relevant for polarimetric radiometers such as [[WINDSAT]].
| |
| Both a sloping ice surface, as in the case of ridging—see [[polarization mixing]],
| |
| <ref name="smos_final">
| |
| {{cite techreport
| |
| | author = G. Heygster, S. Hendricks, L. Kaleschke, N. Maass, P. Mills, D. Stammer, R. T. Tonboe and C. Haas
| |
| | title=L-Band Radiometry for Sea-Ice Applications
| |
| | institution=Institute of Environmental Physics, University of Bremen
| |
| | year=2009
| |
| | number=ESA/ESTEC Contract N. 21130/08/NL/EL
| |
| }}</ref>
| |
| as well as scattering, especially from non-symmetric scatterers,
| |
| <ref name="Emde2005"> | |
| {{cite thesis
| |
| | author=Claudia Emde
| |
| | title=[http://www.sat.ltu.se/members/claudia/publications/thesis.pdf A Polarized Discrete Ordinate Scattering Model for Radiative Transfer Simulations in Spherical Atmospheres]
| |
| | year=2005
| |
| }}</ref>
| |
| will cause a transfer of intensity between the different Stokes components—see [[vector radiative transfer]].
| |
| | |
| ==See also==
| |
| | |
| * [[Sea ice growth processes]]
| |
| * [[Metamaterial]]
| |
| * [[Sea ice concentration]]
| |
| * [[Sea ice thickness]]
| |
| | |
| ==References==
| |
| {{Reflist|2}}
| |
| | |
| [[Category:Sea ice]]
| |
| [[Category:Remote sensing]]
| |
| [[Category:Radiometry]]
| |
| [[Category:Electromagnetic radiation]]
| |
| [[Category:Climate change modelling]]
| |
There was no error. Stephen L. Miles was back on Baltimore's air passages and the Law Workplace of Stephen L. Miles was back in business. Have no idea Miles? If you can remember back to the days when this town bled Colts white and blue on Sundays; when the O's were winners; when Jack Luskin was the most inexpensive guy in town, and when the Gino Giant outsold the Huge Mac - then Miles' image and voice will resonate with you.
If you are in a vehiclemishap, write down every little information personal injury advice you can believe of to offer to your lawyer. Take down the license plate number of other automobiles at the scene. Know the names of any insurance companies that could be included. Keep the tickets or reports written by authorities present at the time of the accident. The more you prepare for a case, the faster you can get it over with.
Personal injury lawyers deal with individuals who have actually been hurt due to the negligence of another person. They work to get insurance provider companies and individuals at fault to pay what is due. The insurance provider business could not pay for discomfort and suffering as a result of the accident.
In addition, some states have actually enacted legislation that involves "strict liability". The owner is responsible for their canine's actions whether they knew the pet dog was dangerous or not. Should you have any kind of queries relating to in which as well as how you can use Toronto personal injury attorney, you'll be able to e mail us in our web site. Anytime their pet dog bites someone they are held accountable no matter the circumstance or scenarios.
personal injury is a field that is tough to have a case in. That's why you need an injury attorney who has great deals of experience. Look for a lawyer who has a history of success in this certain field, guaranteeing your case is handled with the greatest proficiency.
After the personal injury law firm that is approached researches the case, it might occasionally choose not get involved. There might be various factors for this. Once the case is accepted, an arrangement about the fees and costs needs to be reached. For accident cases, contingent fees prevail practice. This means that the law firm earns money from the claim that is granted; it is generally revealed in terms of portion. The firm does not get paid for its services if the claim is refused. Some insist on the client paying in case of rejection of the claim, but others may waive such costs. Clarify prior to signing up.
Fourth, search for a lawyer who has actually been practicing law for a long period of time. Inspect his successful cases. This is a beneficial way to be sure of the capability of the attorney.