This project aims to develop a sea ice modeling system that can accurately predict sea ice conditions in the marginal ice zones of the Chukchi and Beaufort Seas. The researchers analyzed 123 MODIS images from 2014 to study the floe size distribution, which will be used to parameterize and validate the model. Preliminary results show the floe size distribution can be described by a power law, and the exponent varies seasonally from less negative in winter to more negative in summer, indicating more large floes in winter and small floes breaking up in spring and melting in summer. Comparing MODIS and SAR images also yielded consistent floe size distributions over different scales.

1. The Floe Size Distribution
in the Marginal Ice Zone
of the Beaufort and Chukchi Seas
This work is funded by the Office of Naval Research
under the program Emerging Dynamics of the Marginal
Ice Zone, grant N00014-12-1-0112. We thank NASA
for the MODIS images.
American Geophysical Union
Fall Meeting, San Francisco
Monday, December 15, 2014
Marginal Ice Zone Processes
Poster C11A-0349
Harry Stern1, Axel Schweiger1, Margaret Stark1,
Jinlun Zhang1, Phil Hwang2, Thomas Kraemer3,
and Michael Steele1
1Polar Science Center, Applied Physics Laboratory
University of Washington, Seattle USA
2Scottish Marine Institute, Oban, Argyll, UK
3UiT The Arctic University of Norway, Tromsø, Norway
harry@apl.washington.edu
Introduction
Methods
Results – Part II
Acknowledgements
• The long-term goal of this project is to develop a robust, high-resolution
coupled sea ice–ocean modeling and assimilation system that is capable
of accurately predicting sea-ice conditions in the marginal ice zone of the
Chukchi and Beaufort seas on seasonal time scales, with realistic
simulations of the ice thickness and floe size distributions.
• Toward this end, we have analyzed the floe size distribution (FSD) in
123 NASA/MODIS satellite images from March to September, 2014.
This information will be used for parameterization, calibration, and
validation of the model FSD.
• MODIS images are downloaded automatically from the NASA Global
Imagery Browse Service via the Web Map Service interface. Cloud-free
regions in the images are delineated manually based on visible and near-
infrared bands 3-6-7.
• Cloud-free regions are segmented into ice and water. A morphological
erosion operation is used to separate floes that are touching. Individual
floes are then identified using a recursive algorithm that finds groups of
connected ice pixels. A dilation operation is applied to restore the floes to
their original sizes.
• As a measure of floe size, we use the mean caliper diameter: the distance
between parallel calipers that are tangent to the floe, averaged over all
orientations of the calipers.
Results – Part III
• In the literature on FSD, some researchers plot the reverse cumulative
number density instead of the non-cumulative number density. If the
non-cumulative FSD (as in Figure 2) is a power law, the cumulative
FSD is NOT a power law over a finite domain; rather, it is of the form:
(power law) − h where the constant h is the “missing area” under the
FSD that would be present if the FSD extended to infinite floe size.
Alaska
• Previous results by us [1] and others have established that the FSD is
adequately described by a power-law relationship of the form y = cx−p
where x is the mean caliper diameter and y is the number of floes per unit
area. The exponent p characterizes the shape of the distribution. The
valid range of x depends on the resolution of the sensor (at the small end)
and the extent of the image (at the large end). The question is: if FSDs
are derived from two satellite images with different ranges of x, will they
have the same exponent p, i.e. the same scaling relationship of floe sizes?
Results – Part I
References
1. Schweiger, A., H. Stern, M. Stark, J. Zhang, P. Hwang, and M. Steele
(2013). Quantifying the Floe Size Distribution in the Marginal Ice Zone
from Satellite Imagery for use in Model Development and Validation,
AGU Fall Meeting, Poster OS11B-1656.
2. Toyota, T., C. Haas, and T. Tamura (2011). Size distribution and shape
properties of relatively small sea-ice floes in the Antarctic marginal ice
zone in late winter, Deep-Sea Research II, 58, 1182-1193,
doi:10.1016/j.dsr2.2010.10.034.
3. Hwang, B., and J. Ren (2014). Monitoring Spring-to-Summer Sea Ice
Floe Breakup Using High Resolution SAR, AGU Fall Meeting, Poster
C11A-0339.
Figure 1. MODIS image of August 2, 2014, with ice floes (color) within
the cloud-free region (black outline). A TerraSAR-X image from the same
day is overlaid (gray rectangle). Center location is 74°N 149°W.
• Figure 1 shows coincident
MODIS and SAR images from
which we have derived FSDs,
shown in Figure 2. The pixel
size of MODIS is 250 meters;
that of SAR is about 8 meters.
• The closely matching slopes in
this log-log plot show that the
important but difficult-to-observe
small-scale FSD is consistent
with the large-scale FSD.
SAR image
MODIS image
60 km
Figure 2. FSD for the MODIS and
SAR images shown in Figure 1.
MODIS
SAR
• How does the FSD change over the course of the year? Figure 3 shows
the evolution of the exponent (or slope, in log-log space) of the FSD from
winter to summer. Each circle is centered at the location of a MODIS
image (cloud-free region) that we have analyzed. The area of the circle is
the same as the area of the cloud-free region. The color of the circle is
related to the slope of the FSD, as shown in the legend below.
Figure 3. Slope of the FSD for three
time periods: March-April, May-June,
and July-August, 2014.
Figure 4 (below). Evolution of the
exponent (or slope) of the FSD from
March to September, 2014. Each dot is
the average for the month; the vertical
segments are ± 1 standard deviation.
March-April
May-June
July-August
Slope shallower than −2.3
Slope between −2.3 and −2.6
Slope steeper than −2.6
• The slope is shallow in winter and
steep in summer, meaning that there
are more large floes in winter and
fewer large floes in summer, relative
to the number of small floes.
• The seasonal cycle (Figure 4) is
consistent with large floes breaking
apart in spring (slope becomes more
negative) and small floes melting
preferentially in summer (slope
becomes less negative in Sept).
Alaska
Results – Part IV
• Figure 5 (right) is taken from [2]
with annotation added by us. It
shows concave-down cumulative
FSDs (colored curves), which the
authors interpret as two physical
regimes with a break-point at about
40 meters. However, if we add a
constant correction h = 80 to the blue
curve, we arrive at the black line: we
interpret this FSD as a single power-
law, with the curvature arising from
the finite size of the domain.
• Two techniques look promising for extracting floes from SAR images.
Figure 6 (left). Floes identified by the watershed
algorithm (see [3]) in the TerraSAR-X image of
Figure 1. Image size 30 x 60 km, pixel size 8 m.
Figure 7 (right). Floes
identified by our algorithm
in a RADARSAT-2 image
from the Barents Sea.
Image size 40 x 40 km,
pixel size 50 m.