P. Wadhams et al.
24_________ _ __________________________ _________ _ ___________________________
(14) and the itération is prosecuted until convergence is reached, i.e. a minimum
of the / function is reached.
....
.
r . .
In order to avoid the occurrence of discontinuités m the région of the inverted
wave spectrum separating the neighbourhood of the azimuth cut-off length and
to allow the inverted spectrum to départ, if necessary, from the First guess spectrum, at the end of the itération step previously described, the first guess spectrum
is successively modified yielding second-guess, third-guess, etc. input spectra. This
is achieved using two techniques: (1) a partitioning scheme which décomposés the
wave spectra into their wave Systems components; and (2) an algorithm of cross
assignment of the wave Systems [17]. Our implémentation of the algorithm was
written in IDL language (Interactive Data Language) and implemented for cartesian SAR spectra like those obtained from SAR-PRI (Précision Image) images of
ERS-1 (earth resources satellite). It also includes an interpolation module which
works as a smoothing fïlter on SAR spectra sampling variability and noise. The
effects of the fïlter are spectral incréments being added to the wave spectrum at
each itération step. The updated guess spectrum, computed on a coarser resolution of the wave number domain, allows the inversion procedure to capture the
features of the measured SAR spectrum in order to increase the performances of
the inversion algorithm in terms of both a lower number of itération steps and a
better agreement between the simulated and measured SAR spectra.
3 Détection of Changes in Wave Dispersion
On the assumption that we hâve determined the shape of the correct wave number spectrum in the open sea and in ice, if necessary by the use of the inversion
technique described in Section 2, the next stage is to extract the relevant data on
the change in wave dispersion. Most spectra show a single strong peak. The wave
number and direction of the principal wave component are extracted from the
central point of this contoured peak. Equation (8) can be rearranged to yield
h = (kj - k) / c r kj k,
(23)
where k is the wave number in the open sea and r = (p; / pw). The main uncertainty in the estimation of h in Eq. (23) is thus the uncertainty in the estimation
of kj and k from imagery in which the wave number resolution is determined by
the pixel size. It is clear also from Eq. (8) that the change in wave number induced
by ice of a given thickness is greatest for the largest wave numbers (up to the cutoff), i.e. the shortest period waves. The technique therefore becomes less reliable
if the dominant wave period is very long, as is frequently the case in the Southern
Océan. However, in a case where local wind is low, so that the spectrum has a
strong swell peak at low wave number and a secondary wind-wave peak at high
wave number, the secondary peak can also be used for the analysis.
A further characteristic of the wave dispersion which can be used is the refraction at the ice edge. Following Snell's Law, Eq. (8) shows that a wave should be
refracted towards the normal as it crosses the ice edge. The directions of the wave
peaks found in the SAR spectra will, in principle, allow the refraction to be used
24_________ _ __________________________ _________ _ ___________________________
(14) and the itération is prosecuted until convergence is reached, i.e. a minimum
of the / function is reached.
....
.
r . .
In order to avoid the occurrence of discontinuités m the région of the inverted
wave spectrum separating the neighbourhood of the azimuth cut-off length and
to allow the inverted spectrum to départ, if necessary, from the First guess spectrum, at the end of the itération step previously described, the first guess spectrum
is successively modified yielding second-guess, third-guess, etc. input spectra. This
is achieved using two techniques: (1) a partitioning scheme which décomposés the
wave spectra into their wave Systems components; and (2) an algorithm of cross
assignment of the wave Systems [17]. Our implémentation of the algorithm was
written in IDL language (Interactive Data Language) and implemented for cartesian SAR spectra like those obtained from SAR-PRI (Précision Image) images of
ERS-1 (earth resources satellite). It also includes an interpolation module which
works as a smoothing fïlter on SAR spectra sampling variability and noise. The
effects of the fïlter are spectral incréments being added to the wave spectrum at
each itération step. The updated guess spectrum, computed on a coarser resolution of the wave number domain, allows the inversion procedure to capture the
features of the measured SAR spectrum in order to increase the performances of
the inversion algorithm in terms of both a lower number of itération steps and a
better agreement between the simulated and measured SAR spectra.
3 Détection of Changes in Wave Dispersion
On the assumption that we hâve determined the shape of the correct wave number spectrum in the open sea and in ice, if necessary by the use of the inversion
technique described in Section 2, the next stage is to extract the relevant data on
the change in wave dispersion. Most spectra show a single strong peak. The wave
number and direction of the principal wave component are extracted from the
central point of this contoured peak. Equation (8) can be rearranged to yield
h = (kj - k) / c r kj k,
(23)
where k is the wave number in the open sea and r = (p; / pw). The main uncertainty in the estimation of h in Eq. (23) is thus the uncertainty in the estimation
of kj and k from imagery in which the wave number resolution is determined by
the pixel size. It is clear also from Eq. (8) that the change in wave number induced
by ice of a given thickness is greatest for the largest wave numbers (up to the cutoff), i.e. the shortest period waves. The technique therefore becomes less reliable
if the dominant wave period is very long, as is frequently the case in the Southern
Océan. However, in a case where local wind is low, so that the spectrum has a
strong swell peak at low wave number and a secondary wind-wave peak at high
wave number, the secondary peak can also be used for the analysis.
A further characteristic of the wave dispersion which can be used is the refraction at the ice edge. Following Snell's Law, Eq. (8) shows that a wave should be
refracted towards the normal as it crosses the ice edge. The directions of the wave
peaks found in the SAR spectra will, in principle, allow the refraction to be used