Inferring the degree of ice field deformation in the Baltic Sea using ENVISAT ASAR images
Markku Similä(1) and Juha Karvonen(1)
Finnish Institute of Marine Research,
PO Box 2,
If the the snow layer is thin and the weather is cold, the C-band
backscattering in the Baltic Sea is modulated by the ice surface
roughness. The presence or absence of large scale ice surface
roughness indicates the occurrence of mechanical ice deformation.
Hence it is reasonable to expect that in drift ice areas the
magnitude of the backscattering coefficient $sigma^0$ is strongly
correlated with the ice thickness. Relying on this hypothesis we
at Finnish Insitute of Marine Research (FIMR) have tested an
approach to estimate the degree of deformation of underlying ice
cover from a SAR image.
Our field data set consists of helicopter-borne electromagnetic
induction sensor (EM) based ice thickness measurements. These
measurements were made and processed by Alfred Wegener Insititute.
The data set analyzed here consists of EM measurement transects
(totally 480 km) combined with three nearly simultaneous ENVISAT
ASAR IMP images acquired in March 2005 as a part of the Finnish
ENVISAT ASAR CAL/VAL project ESSI ("ENVISAT and the Ice Conditions
in the Baltic Sea"). These two data sets were co-registered with
respect to each other.
Due to continuous ice field movement and location inaccuracies in
both data sets the registration is imprecise. This fact combined
with the ambiguities between the SAR signal magnitude and the ice
thickness value lead us to study a procedure where we consider ice
fields associated with certain backscattering coefficient, i.e we
assign a whole ice thickness distribution to each $sigma^0$
rounded to the nearest integer. E.g., in the regression approach
this dependence is unambiguous, i.e., a certain predictor value
($sigma^0$) corresponds a certain response (ice thickness value).
The critical step in the proposed approach is to estimate the
ice thickness distributions associated with different $sigma^0$
values in a coherent manner. To this end two geophysically
motivated consistency requirements were applied. First, the range
of admissable ice thickness values had its maximum range at the
largest $sigma^0$ and it was required to decrease with the
decreasing $sigma^0$ values. Secondly, the probability of an
occurrence of an ice ridge was required to increase with the
increasing $sigma^0$ value. We modelled the thickness
distributions as a mixture distribution with two components. One
component described the thickness distribution in the level and
rafted ice areas (in our data set an appropriate limit to this was
100 cm), the other component described thickness distributions for
the rest of values (in our data set the upper limit was 800 cm).
The densities of both components were estimated with kernel
density estimator with a Gaussian kernel. The smoothing parameter
$h$ was selected to be much larger for ridged ice than for level
ice. The proportions between level/rafted ice, on one hand, and
ridged ice, on the other hand, were controlled by the mixture
parameter $p$, which describes the relative proportion of deformed
ice. We remark that several analytic expressions were fitted to
the densities but no satisfying formula was found. There were two
contradicting requirements: a sharp peak for level/rafted ice and
a long, heavy tail for ridged ice.
First, the ice thickness densities were estimated for each
discretized $sigma^0$ in the range (-21 dB, -7 dB). Then the
estimated density for a given segment was obtained as a mixture of
all occurred densities along the segment. Each occurrence event is
indicated by the corresponding $sigma^0$. To test our approach
we determined the degree of ice deformation in a given segment as
a percentage of ice cover with ice thickness exceeding 2 m. The
deformation degrees increases in five percent intervals, starting
from zero (area of thick ice less than 5 % of the total area) to
four (area of thick ice more than 20 % of the total area). The
respective intervals were determined for estimated ice thickness.
If the segment length was chosen to be 15 km (16 segments in our
training set, 16 in the test set), the measured and estimated
deformation degrees agreed for three segments, deviated just one
category in ten cases and more in three cases. In the last three
cases the mean magnitude of backscattering strength was over -13.5
dB but according to the EM measurements the ice cover was thin,
i.e., of category zero.