Mapping the Thickness of Pancake Ice Using Océan Wave Dispersion...
21
Above this frequency propagation is not possible. A wave incident normally on
the ice at a frequency higher than <ûc will suffer total reflection at the ice edge.
Wadhams and Holt [12] pointed out an implication for frazil ice imaging on SAR.
Waves at the Bragg wavelength (30 cm for Seasat SAR considered in their paper)
hâve periods only just above Tc, so that they suffer extreme modification on passing into the ice, with a high reflection coefficient at the ice edge. There is therefore
little energy présent in a frazil ice slurry at these wavelengths and so frazil ice
appears dark on SAR imagery. The same argument applies to pancake ice, but in
this case the physical roughness of the upturned edges of the pancakes will make
this type of ice appear bright to SAR.
Reflection and transmission coefficients across the ice edge were derived by
Keller and Weitz [10] as
(1 - |R|2) = |T|2 k2/kj2,
(10)
giving an energy transmission coefficient t for normal transmission of
t = |T|2Ui/Uw = 4kki/(k + ki)2.
(11)
This model does not yield progressive wave decay inside the ice cover, although
it does imply wave refraction at the ice edge and the total exclusion of the shortest waves from the icefield. Clearly energy decay takes place in frazil slurries, and
Martin and Kauffman [3] observed an internai circulation within the slick in tank
experiments, which would lead to viscous energy losses. Recent laboratory experiments by Newyear and Martin [13] on very short waves in frazil ice also suggest
that the mass loading theory breaks down for wave periods of 1 s or less, when a
wavelength increase is observed relative to the open water relation. To résolve this
question, further laboratory experiments on the wave dispersion relation in frazil
ice were carried out during February 1997 in the European ice tank at Hamburg
Schiffbau-Versuchsanstalt by R. Hall, a student of P. Wadhams, with wave periods
of up to 2 s available, but with results which show no measurable change in wavelength.
2 Imaging of Waves by SAR
The potential of SAR to image océan surfaces has been recognised over the past
two décades [14] and the SAR imaging theory of a moving surface is now quite
well understood [15], The océan wave spectral information is not entirely mapped
in the SAR image plane. Since SAR images provide a snapshot of the sea surface,
the directional properties of the wave spectrum are lost in the SAR image plane.
Moreover, SAR imaging is frequently a strongly non-linear process induced by
motion effects of the océan surface. The velocity bunching mechanism associated with the orbital motion of the long waves is the most relevant source of nonlinearity which produces distortions of the SAR spectrum through an azimuthal
high wave number cut-off.
Considering the velocity bunching mechanism as fully non-linear and the other
21
Above this frequency propagation is not possible. A wave incident normally on
the ice at a frequency higher than <ûc will suffer total reflection at the ice edge.
Wadhams and Holt [12] pointed out an implication for frazil ice imaging on SAR.
Waves at the Bragg wavelength (30 cm for Seasat SAR considered in their paper)
hâve periods only just above Tc, so that they suffer extreme modification on passing into the ice, with a high reflection coefficient at the ice edge. There is therefore
little energy présent in a frazil ice slurry at these wavelengths and so frazil ice
appears dark on SAR imagery. The same argument applies to pancake ice, but in
this case the physical roughness of the upturned edges of the pancakes will make
this type of ice appear bright to SAR.
Reflection and transmission coefficients across the ice edge were derived by
Keller and Weitz [10] as
(1 - |R|2) = |T|2 k2/kj2,
(10)
giving an energy transmission coefficient t for normal transmission of
t = |T|2Ui/Uw = 4kki/(k + ki)2.
(11)
This model does not yield progressive wave decay inside the ice cover, although
it does imply wave refraction at the ice edge and the total exclusion of the shortest waves from the icefield. Clearly energy decay takes place in frazil slurries, and
Martin and Kauffman [3] observed an internai circulation within the slick in tank
experiments, which would lead to viscous energy losses. Recent laboratory experiments by Newyear and Martin [13] on very short waves in frazil ice also suggest
that the mass loading theory breaks down for wave periods of 1 s or less, when a
wavelength increase is observed relative to the open water relation. To résolve this
question, further laboratory experiments on the wave dispersion relation in frazil
ice were carried out during February 1997 in the European ice tank at Hamburg
Schiffbau-Versuchsanstalt by R. Hall, a student of P. Wadhams, with wave periods
of up to 2 s available, but with results which show no measurable change in wavelength.
2 Imaging of Waves by SAR
The potential of SAR to image océan surfaces has been recognised over the past
two décades [14] and the SAR imaging theory of a moving surface is now quite
well understood [15], The océan wave spectral information is not entirely mapped
in the SAR image plane. Since SAR images provide a snapshot of the sea surface,
the directional properties of the wave spectrum are lost in the SAR image plane.
Moreover, SAR imaging is frequently a strongly non-linear process induced by
motion effects of the océan surface. The velocity bunching mechanism associated with the orbital motion of the long waves is the most relevant source of nonlinearity which produces distortions of the SAR spectrum through an azimuthal
high wave number cut-off.
Considering the velocity bunching mechanism as fully non-linear and the other