20th IAHR International Symposium on Ice
Lahti, Finland, June 14 to 18, 2010
A Case Study Testing the Impact of Scale
on Arctic Sea Ice Thickness Distribution
Cathleen Geiger1, Jackie Richter-Menge3, Tracy Deliberty1, Bruce Elder3,
Jennifer Hutchings4, Amanda Lawson1,
Joao Rodrigues2, Nicholas Toberg2, and Peter Wadhams2
1
Department of Geography
College of Earth, Ocean, and Environment
University of Delaware
216 Pearson Hall, Newark, DE 19716, USA
cgeiger@udel.edu, aklchem@udel.edu, tracyd@udel.edu
2
Polar Ocean Physics Group
Department of Applied Mathematics and Theoretical Physics
University of Cambridge
Wilberforce Road, Cambridge CB3 0WA, UK
p.wadhams@damtp.cam.ac.uk, nt283@cam.ac.uk, jmr64@cam.ac.uk
3
Cold Regions Research and Engineering Laboratory (CRREL)
72 Lyme Road, Hanover, NH 03755, USA
jacqueline.a.richter-menge@usace.army.mil
4
International Arctic Research Center (IARC)
University of Alaska Fairbanks
930 Koyukuk Drive, P.O. Box 757340
Fairbanks, Alaska 99775-7340, USA
jenny@iarc.uaf.edu
Abstract
We examine the variability of sea ice thickness distribution from the 20 km x 20 km nested
UK submarine survey taken on 18 March 2007 in the Beaufort Sea. The survey is centered
about a U.S. Navy ice camp. From 1-7 April 2007, two weeks later, a ground survey team
measured the snow and ice thickness within a 2 km circle of the ice camp during an NSFsponsored science program. Because sea ice drifts, the ice camp was additionally equipped
with a GPS buoy to provide a Lagrangian reference reporting position continuously from 15
March to 15 April. Results include a draft-to-thickness conversion ratio of 1.27 (including
snow load effects) using a statistical mode matching algorithm. We find a mean of 2.99m for
the ground survey and 3.07 ± 0.21m (average and range) for 2 km incremental scales of the
submarine survey relative to the camp. When truncating all submarine survey subsets to the
8m limit of the ground survey, we find even closer agreement (2.95 ± 0.20m). The range of
mean thicknesses over all scales is less than instrument uncertainties. This leads to the
conclusion that the mean thickness is nearly scale invariant in support of modeling
assumptions using a continuum approach with grid cell resolutions from 2 – 20 km. The
largest differences between scales are variations in relative amounts of deformed ice with
level-to-slightly deformed first-year ice dominating near the camp. Beyond the camp, we find
increased proportions of new ice, associated deformation, and deformation of thick first-year
and multi-year ice categories. The result is an increased skewing, broadening, and flattening
of the thickness distribution away from the strong narrow peak found close to the camp.
Hence while the mean thickness is does not change over these scales, the thickness
distribution does, and this difference may have a fundamental impact on modeling
calculations, especially heat fluxes, material behavior, momentum fluxes, and certainly local
biogeochemical interactions.
1. Introduction
In the Arctic, sporadic thickness observations from upward looking sonar profilers from
nuclear submarines are recorded as far back as 1958 (McLauren 1988) with analysis by
Rothrock et al (1999 and 2008), Wadhams and Davis (2000), and Tucker et al (2001). These
thickness records are extended into this century using global coverage ICESat altimetry
measurements from 2003 to 2008 (Kwok et al 2009). The combination of these records
(Kwok and Rothrock 2009) show that the rate of sea ice thickness loss is increasing from
maximum rates prior to 2000 of -0.08 m/yr to new winter and summer rates of -0.10 m/yr and
-0.20 m/yr, respectively. In these studies, the overall mean winter thickness of 3.64 m in 1980
is compared to a 1.89 m mean during the last ICESat winter record or a decrease of 1.75 m in
thickness. These long-term very-difficult-to-acquire thickness measurements are only
available near the center of the Arctic Ocean covering roughly 38% of the total hemispheric
ice cover (Kwok and Rothrock 2009). However, daily hemispheric passive microwave
records from NASA satellite platforms supported from 1978 to the present concur with these
loss rates in the form of statistically significant long-term decreases in ice extent (Parkinson
and Cavalieri 2008) with rates of -45,100 ± 4,600 km2/yr (-3.7% ± 0.4%/decade).
These increasing rates of change in ice extent and thickness have developed into
unprecedented summer minima extremes in 2005 (Kwok 2007) and most notably 2007
(Stroeve et al 2008). The major reduction in sea ice cover is caused by a combination of
complex factors including warming temperatures, thinner and weaker ice, and reduced ice
concentration (Rigor and Wallace 2002, Rigor et al 2004, Nghiem et al 2007). These events
significantly reduce the storage of multiyear ice in the Arctic, such that, even if the ice extent
recovers quickly, it may take many years for the multiyear thick sea ice to recover (Rigor et
al 2004). This is critical to the global heat balance since roughly 6% of the earth’s surface is
covered by sea ice. This ice surface area serves as a thermal regulator (working like an air
conditioner) to reflect solar radiation away from polar seas under 24-hour sun conditions
(Perovich et al 2007). Numerical prediction models including the 13 described in IPCC AR4
(Intergovernmental Panel on Climate Change Assessment Report 4) show that these changes,
and more importantly, the increases in these changes, are occurring faster than human
prediction systems can keep up with (Stroeve et al 2007). Hence, observation networks to
monitor these changes are becoming increasingly important with a need to devise an effective
Arctic Observing Network (AON) as described in the most recent SEARCH report (2008).
There is still a considerable amount to be learned about the relationship between sea ice
thickness and its resiliency to systematic warming of the environment. Most of sea ice lies
below the water’s surface. Hence, the most accurate way to measure sea ice thickness is
either directly by drilling (though limited in range) or over large areas using underwater
vehicles to measure the sea ice draft (ice below the water surface). Effective relationships
between ice draft and freeboard (ice above the water surface) are complicated by a variable
snow cover which makes it difficult to compute sea ice volume from an integration of
measurements collected above and below the water surface. The theoretical framework to
compute the isostatic balance is straightforward (Adolphs 1998) but the variability of snow
and ice types is of sufficient complexity that high uncertainties over varying scales introduces
many questions about the most effective means for systematically monitoring sea ice
thickness and its changes.
As noted in Kwok and Rothrock (2009), Submarine Arctic Science Cruise Exercise
(SCICEX) efforts have diminished since the turn of this century with few submarine cruises
available to collect the necessary ice draft data to assess changes in sea ice thickness. Here,
we report on one of those few events, specifically the submarine survey of the HMS
“Tireless” taken in the Beaufort Sea in 2007 March near the peak of seasonal maximum
extent and thickness. The case study presented is quite small (20 km box), but unprecedented
as it is followed by a ground survey of snow and sea ice thickness measurements taken two
weeks afterward at the center of the submarine’s survey area. An ice camp, supporting both
surveys, was equipped with a GPS buoy from which Lagrangian motion of the coherently
drifting sea ice could be tracked for co-registration across the two week time gap. The unique
coincidence of these two data sets provides the opportunity to test relationships of isostacy
and thickness distribution as a function of scale. In Section 2, we report on the processing
methods used to cast both observations into the common variable of total thickness including
snow loading effects. In Section 3, we discuss the effectiveness of the isostacy methods and
the impact of scale. We summarize with a list of considerations when devising an effective
Arctic Observing Network (AON) for monitoring sea ice thickness.
2. Data Collection, Processing, and Initial Results
This study comprises primarily from two data sets: 1) submarine single-beam sonar draft ice
measurements and 2) ground survey electromagnetic induction measurements validated
against drill-hole data. The submarine data were collected on 18 March 2007 within a 20 km
x 20 km box centered about the Applied Physics Laboratory Ice Station (APLIS) established
in the Beaufort Sea. Two weeks later a ground team under the NSF-sponsored project called
Sea-ice Experiment: Dynamic Nature of the Arctic (SEDNA) surveyed the ice thickness from
1-7 April at 5 m spacing along 6 1-km-long spokes originating from a central hub located
near the ice camp (Hutchings et al 2008). Continuous transmitting Global Position System
(GPS) position of the camp was used to co-register the two surveys relative to the drifting sea
ice. Both surveys were conducted near the time of maximum sea ice growth prior to melting.
An overview of respective surveys is shown in Figure 1.
As seen in Figure 1a, the submarine survey took 18 hours to complete through a series of
square and cross-track search patterns. From the GPS buoy located on the camp, we compute
the distance between submarine position and camp as a function of time and use that distance
to separate sonar-derived results into 2 km interval scales (1 km search radii) to compare with
the ground survey.
Figure 1. Two thickness surveys during 2007 APLIS. Panel (a) shows total thickness from
UK submarine sonar and corresponding RADARSAT-1 image. The ice camp is located in the
center of the survey area near 73°06’N. Color bar depicts time shift between imagery and sub
track with color bar height referencing thickness. Panel (b) shows transects on photograph
(Bruce Elder-CRREL) at start of ground survey from 1-7 April. Each leg in panel (b) is 1000
m except leg 3 which is 730m. True north is represented by N and black arrow.
2.1 Submarine Sonar
Around 200 km of sea ice draft data were gathered under the APLIS camp by the Royal Navy
submarine HMS “Tireless”. Processing of the raw records as well as statistical analysis were
done by the Polar Ocean Physics Group (POP), DAMTP, University of Cambridge.
The hull-mounted echo sounder Admiralty Type 780 upward-looking single beam sonar
produces a signal pulse of 0.3 ms through a 48 kHz transducer. The emitted signal has a
beam width of 3° fore-and-aft. Raw data from the upward looking sonar is a printout of the
time interval between transmission of a sound signal and reception of its echo, which is
displayed in the form of signal strength along the submarine's direction of motion. Data are
recorded in horizontal straight line format on electronically-sensitive paper rolls 254 mm
wide and 50 m long. Each roll is digitized and divided into segments containing 3600x1500
pixels.
Mean ice draft values and ice draft distributions from the entire transect of “Tireless”, from
Fram Strait to the gridded survey performed in the Beaufort Sea (and return), are recorded in
50 km lengths. This length was chosen early in the history of data analysis from submarine
records (Wadhams 1980) and is also used by US researchers because it offers a compromise
between having adequate data to provide a PDF without large errors, while not representing
too much track that the ice regime changes within a single section. Biases result primarily
from the sonar's variable footprint due to the 3° beam width spreading. These are typically
quoted with an overestimate of 36 cm for the mean value of ice draft over a 50 km length
(Wadhams et al 2010). More accurate values are being developed using intervals of bias as a
function of submarine depth and under-ice topography in a follow-on paper comparing the
single beam with an EM 3002 multibeam sonar, with a much smaller fore-and-aft beam width
(Rodrigues 2010). Signal degradation for the multibeam sonar occurred during the SEDNA
survey due to a wiring failure, but high quality ice topography data exist for other regions of
the transect, most notably north of Ellesmere Island.
Submarine ice draft measurements that are compared with the SEDNA ground survey are
taken from the same continuous measurements as the 50 km lengths reported elsewhere, but
on the scale of 2 km lengths. A large part of the 36 cm overestimated bias is the result of
mistaking thin ice for open water in the draft calculations. For intervals of 2 km, depending
on the amount of open water around the survey site, the bias may be significantly less than
for a 50 km section.
2.2 Ground Survey
Studies by Haas and Eicken (2001), Eicken et al (2001) and Haas et al (2008) show that sea
ice has a relatively small conductivity (<100 mS/m) compared to sea water (typically >2000
mS/m). This basic property provides the means to estimate sea ice thickness by measuring the
depth of the sea water-sea ice interface through electromagnetic induction (EMI) methods.
Applying these principles, we used an EMI device, specifically the hand-carried EM31
(Geonics EM31-MK2) explained in detailed in Eicken et al (2001) to infer sea ice thickness
along the 6 km ground survey under the SEDNA project (Hutchings et al 2008).
Thickness is estimated using an exponential fit (Eq. 1) and its inverse relationship (Eq. 2)
σ = A + B exp ( −C z )
z = zref − ln (σ − A) / C; zref = ln( B) / C
[1]
[2]
between the apparent conductivity, σ, and the depth, z, existing between the instrument and a
highly conductive surface (in this case the sea water-sea ice interface). Here A, B, and C are
empirically determined coefficients based on the operational parameters of the instrument
(Eqs. 1 and 2 and Table 1), local sea water salinity, seasonal brine volume, and conductivity
estimates in the sea ice (Eicken et al 2001). By definition, the argument within the logarithm
in Eq. 2 cannot be negative and hence as the apparent conductivity approaches A the
maximum possible depth, z, is reached. In the case of the EM31 device used here, the
maximum depth is ~8m.
Table 1. EMI Specs and Calibration
Frequency (f)
9.8 kHz
Coil Separation (r) 3.66 m
Offset Height (zo) 0.99 m
Relative Error*
10%
A
54.7
B
1178.4
C
0.872
* Level ice
Once the distance between instrument and bottom surface are determined, ice thickness, zi, is
computed directly by
zi = z − z0 − zs .
[4]
Here zo is the distance between the instrument and the top surface (which can be snow
covered or bare ice) and zs is the snow thickness. Snow thickness is measured directly at 5 m
intervals at every point an EMI reading is taken along the ground transect lines using a
MagnaProbe developed by Matthew Sturm (Sturm et al 2003).
The 10% relative error in Table 1 is based on the comprehensive study by Eicken et al (2001)
for the Beaufort Sea. Drill-hole measurements taken during our field campaign on both level
and ridged ice (not exceeding 4m) agree well with thicknesses derived from the coefficients
in Table 1 with no calibration offset based on a point-to-point analysis with drill holes.
2.3 Total Thickness, Distribution, and Integrated Thickness
A comparison between submarine draft and EMI thickness requires conversion of both data
sets to a compatible variable. For this study, we define the term “total thickness” as the sum
of the ice draft, ice freeboard, and snow depth. For the ground survey, these three properties
are summed directly from measurements as described in Section 2.2 with results shown in the
probability distribution (PDF) plot in Figure 2a. For submarine draft, it is necessary to infer a
freeboard including the effects of snow load to derive a total thickness. Two methods are
used here to estimate a sonar-draft-derived total ice thickness: 1) an isostacy method based on
the slope between samples of ground surveyed ice draft and their associated total thickness
(including snow load) and 2) a statistical approach which matches the modes of ground and
submarine thickness distributions (hereafter called mode matching).
The isostacy method uses the drill-hole measurements collected during the ground survey
whenever all three properties of snow thickness, ice thickness, and freeboard (water depth in
the drill hole) were collected. The results are plotted in Figure 2b with linear regression
providing the needed conversion factor from draft to total thickness from the resulting slope
(1.38±0.54 m-1). The mode matching method statistically computes the probability
distribution of the ground-surveyed total thickness (Figure 2a) and compares its dominant
mode to that of the sonar-draft distribution. The ratio of these two thickness modes provides
the draft-to-thickness conversion factor based on the dominant ice type of the area. The result
is an alignment of the total thickness modes for the two data sets. As shall become clearer in
the discussion, this method is primarily dependent on the thickness of the dominant ice type
rather than the entire spectrum of ice thickness.
Modal peaks can be matched by eye to align the two thickness distributions. This is
recommended for quick field-work applications or as an intuitive first check. This visual
approach suggests a ground-survey modal peak near 1.65m with a sonar draft peak centered
near 1.35m given the same 10 cm binning for each distribution (uncertainty of ±0.05 m due to
bin size). This gives a draft-to-thickness ratio of 1.22. A more rigorous mathematical
approach uses maximum likelihood for finding the mode as described in Press et al (1992)
which summarizes as follows. First, the data are sorted from thinnest to thickest. Beginning
with a small search window (not less than 3 in length), a mode probability is computed as a
function of window size, data size, and center gradient value across the window (half the
difference between first and last value within the sorted data window). The gradient and
associated probabilities are calculated sequentially as a running operation over the full range
of data with increasingly larger window sizes. A mathematical “likelihood” is computed for
each resulting gradient with the highest likelihood value (mode value) found in the center of
the steepest gradient relative to some optimal data length J. The inclusion of gradient
information takes into account any skew in the local distribution about the mode peak. This is
especially important for distributions which are not normally distributed, as is clearly the case
for sea ice.
To optimize compatibility when determining the mode for each data set for the draft-tothickness ratio, we limited the sample of sonar-draft data within 1 km (2 km scale) of the
camp GPS buoy. As seen from the results in Figure 2a, this includes only 226 sonar samples
which provide a discontinuous thickness distribution, but the sonar peak and its distribution is
significantly above white noise (Figure 2a) as discussed in more detail in the data fidelity
section following this.
Using the mode matching algorithm just described, we determine a ground-survey mode of
1.77 m for total ice thickness and 2-km-scale sonar draft of 1.39m. These values are both
higher (0.12m and 0.04m, respectively) than the visual estimate with skewness toward thicker
ice. The result is a draft-to-thickness conversion factor of 1.27 which is 0.05 larger than the
visual method. Recalling the submarine draft bias of 0.36 m and 10% relative uncertainty for
EMI (equivalent to 0.17 m near this mode), these mode estimates are within instrument
tolerances with a propagated uncertainty (quadrature sum of the independent errors) of 0.54
m when considering both instrument uncertainties combined.
Figure 2. Scale analysis. Panel (a) shows total thickness probability distribution (PDF) from the ground
survey (light blue) and 2-km-scale sonar-derived thickness (thick black line) using the draft ratio found
with the mode matching algorithm. The draft factor is subsequently applied to all sonar-derived total
thicknesses shown except the isostacy case in panel (b) and isostacy in inset of panel (e). White noise
denoted by the vertical uncertainty bars computed as a function of bin number. Panel (b) shows isostacy
relation between draft and total thickness at drill-hole sites. Panel (c) summarizes analysis of modal
thickness and PDF of mode as a function of scale. Panel (d) compares integrated thickness (mean) of
ground survey (diamonds) and sonar subsamples at scales relative to camp location. Panel (e) shows
total thickness for all sonar data (dark blue) with the bold-line distribution showing the 8m truncated
version for direct compatibility with the ground survey. Inset on panel (e) shows example integrated
thickness to illustrate differences in methodology as explained in the text. The grey uncertainty bar on
the 8m isostacy case is the range of integrated thickness when propagating the uncertainties in the slope
determination shown in panel (b). Colors are consistent throughout the figure.
Using mode matching results, we apply a draft ratio of 1.27 to the entire submarine data set
(value shown in Figure 2a). Then, we run the maximum likelihood mode algorithm over each
submarine subset within 2 to 30 km of the camp at 2 km intervals to determine the mode at
each scale. These results are reported in Figure 2c as both the mode thickness and probability
of the mode. The mean is additionally calculated as the integrated thickness of the cumulative
distribution with integral limits set successively from the thinnest ice to 4m, <8m, 8m
truncated, and all thicknesses. These results are subsequently used to examine thickness mean
(Figure 2d) and distribution (examples in Figures 2a and 2e) as a function of scale.
From this analysis, a mean of 2.99 m is found for the 2-km-scale 8m-limited ground survey.
Over the different scales of submarine-derived thickness, we find a mean and range of 3.07 ±
0.21m when integrating over all thicknesses (which do not exceed 20m in this case). When
truncating all submarine scales to the same 8m limit as the ground survey, we find the closest
compatibility to the ground survey with a mean thickness and range of 2.95 ± 0.20m. The
range of these results is within instrument accuracies and significantly smaller than bounds
determined using the isostacy method (see inset of Panel (e)). We note that these mean values
are smaller than the 3.6m basin-wide averages from the 1980s as reported in Kwok and
Rothrock (2009) but also considerably larger than the recent ICESat records reporting 1.89m
basin-wide means. Hence this location must be a sample of thicker-than-average ice from a
basin-wide perspective.
2.4 Data Fidelity
For our analysis, we wish to compare the dominant mean, mode, and shape of each thickness
distribution as a function of scale. To do this with confidence, we need to devise a metric to
quantify the fidelity of our data. Probability distribution functions (PDF) enumerate thickness
by category and hence exist in the frequency domain. From classic signal processing, white
noise, by definition, is a uniform signal strength across all frequencies (i.e., equal to inverse
bin number). Using white noise as a metric, we define a thickness distribution as continuous
when adjoining frequency bins vary less than white noise. We can further define a significant
mode as a cluster of continuously varying bins which significantly extend above other nearby
bins (i.e., the PDF of a significant mode must exceed nearby bin values plus white noise).
Applying this metric to our analysis, we see the clearest example of strong fidelity in the
ground survey, which contains 1156 samples with a significant peak at 1.65 m (Figure 2a)
and computed mode (through maximum likelihood method) of 1.77 m with all consecutive
bins changing continuously (gradients less than white noise). In contrast, the 2km sonar
subset, which matches the area of the ground survey, incorporates only 226 samples (Figure
2a). White noise levels indicate that this distribution is not continuous but there is one
significant mode with bins varying continuously near the modal peak. The lack of continuity
is remedied at the larger scales when sample sizes approach 1000 as discussed later.
Recognizing this important caveat, we quantitatively explore the thickness mean and mode as
a function of scale but restrict our study of thickness distribution shape to a qualitative
investigation.
3. Discussion
From the findings above, the following questions arise:
1) Why does the thickness distribution change systematically from a narrow modal peak at
the ice camp to a flatter and broader peak over the entire 20 km submarine survey box?
2) What practical considerations can be learned from the isostacy methods examined here to
optimize Arctic Observing Networks, especially those constrained by limited
observations?
Regarding question 1, we see from our analysis that the mode varies only slightly with scale
with a value and range of 1.47±0.03 m (Figure 2c). We also find an integrated thickness
value and range of 3.07 ± 0.21m over all scales for all submarine-derived thicknesses and
2.95 ± 0.20m over all scales for all thicknesses compatible with the 8m-limited ground survey
results. These ranges are within instrument uncertainty as cited in Section 2.1. The largest
deviations are within the first 6 km where discontinuity in the sonar thickness distribution is
likely responsible. From Figure 2d, we see that as sample number approaches 1000 near the
8-km scale, the mode and integrated thicknesses change little thereafter. Beyond this
continuity effect, we see a significant decrease of nearly half the PDF value of the mode peak
from ~0.06 to 0.04 (Figure 2c) from scales of 2 to 16 km. The modal peak flattens and
broadens with increasing scale as ice type diversity expands and skews the mode from
predominantly first-year level ice (Figure 2a) to increasing amounts of new ice and thicker
deformed ice types (Figures 2e). This is significant because it means that there is a clear
distinction in thickness distribution as a function of increasing ice deformation as one
proceeds in scale away from the camp.
Communication with logistics personnel reveals that it took several days using satellite maps
from the National Ice Center (NIC) and aircraft reconnaissance to find a suitable camp
location consisting of a thick multiyear floe (to support the ice camp village) next to an
undamaged first-year level ice floe for the runway. Hence, the strong modal peak of the
ground survey appears to be atypical for the region. While the location is atypical, we sought
to ensure consistency within the ground survey domain using aircraft reconnaissance to
determine appropriate transect lines. One of the survey lines (line 4 – Figure 1b) follows the
runway thereby constituting one sixths of the surveyed points over consistently level first
year ice. This was done deliberately to isolate individual lines by ice type with the remaining
lines covering 2 kilometers over multiyear floes (lines 5 and 6) and 3 kilometers (lines 1-3)
over newly deformed first year ice. These efforts give us confidence that the ground survey
is consistent and representative of the survey area.
These logistical issues are significant because
1) they demonstrate the power of visual reconnaissance for identifying deformation
processes (or lack thereof);
2) they emphasize the strategic importance of positioning surveys in the right locations;
3) most importantly, they fortuitously established ideal conditions to resolve smooth to
deformed thickness distributions (Figure 2a to 2e, respectively).
From Figure 2d, we see that the changes in thickness distribution away from the camp have
done little to impact the integrated thickness. In fact, as seen in the inset in Figure 2e, there is
far more variation in mean and mode between the two draft ratio methods, than the variations
in scale.
Recall, this survey is taken at the height of sea ice extent and thickness. Hence, we expect the
ice pack to be coming out of its winter growing season but not yet subjected to vast amounts
of solar heating. This means the dominant force at the end of winter (before the real melting
season begins) are the mechanical processes which redistribute thickness and precondition
the ice field before the increasing warming of the forthcoming melting season. Within this
study area, we see these thickness distributions clearly take place without an overall change
in the local integrated thickness. Granted, this is only a small case study so there is more
work to be done to determine the length scales at which the mean thickness changes as a
result of mechanical processes. However, we can at least show that thickness distribution
(and redistribution) can clearly change a great deal before there is a measured impact on the
overall mean. The repercussions are substantial in terms of differential heat fluxes, material
behavior, momentum fluxes, and certainly local biogeochemical interactions. In short, the
mean is not a very sensitive measure of change. If the mean thickness is changing, then many
other events have already taken place.
We can explore the second question by addressing the sensitivity of the isostacy method
relative to measurement practices. Despite the high quality in drill measurements shown in
Figure 2b, as noted by the high correlation coefficient, it is clear that a large range of ice
thicknesses are needed to adequately resolve the slope for draft factor determination. Given
the skewed tail of a sea ice thickness distribution, a draft factor derived using the slope
isostacy method requires the logistical complication of finding and measuring a number of
samples at the tail end of the thickness distribution. The ice types in the distribution tail are
comprised solely of damaged ice within ridges and rubble fields which are very difficult to
measure given the increased variability in snow load distribution near these features,
differential gravitational loading and bending, void volume within the structures, sea water
intrusion between ridge blocks, and many other factors all of which compound to less
accuracy in thickness determination. Hence, the mode matching method is clearly favored for
calibration of long-range instruments which can already distinguish ice thickness ranges
because it requires far less physical effort (optional drill holes for level ice only!) than the
isostacy method.
It is also striking to note that the ground survey (which logarithmically decays to 8m) and the
sonar-derived thickness data (when truncated to 8m) compare the best for all scales with only
a slightly larger amount of integrated ice beyond the 8m thick ice. From previous studies
(Melling et al 2005) we know that the Beaufort Sea contains only a small amount of thick ice
>8m and hence EMI surveys, despite their limited range, seem to provide reasonable
coverage for most of the ice present in this area and are shown here to be particularly
effective for calibrating long-range instruments which are trying to accumulate basin-wide
mean thickness statistics.
For process studies and research programs where more observations are allowed, we
additionally encourage the more comprehensive isostacy method to understand the impact of
thicker ice types on overall isostatic load especially as the overall structure of the ice pack is
currently in a state of flux due to recent basin-wide ice-loss episodes. Our results show
clearly that the mean is not providing the variability. It is only a first order measure of local
conditions. Numerical models need to reproduce the processes happening locally if they are
to effectively be used for forecasting purposes. Local to regional models with high quality
forecasting capabilities are needed whenever the application involves human activities. When
the activities involve polar operations, then knowledge of local thickness distributions will
become essential. In climate models, appropriate representation of thickness distribution has
proven to be essential to ensure the correct heat and momentum transfer across the polar airsea interface and in particular the correct material behavior (Maslowski and Lipscomb 2003).
Hence, approaches to optimizing an Arctic Observing System should include 1) a carefully
designed calibration program and 2) complementary process studies programs to address
issues of larger systems through small carefully crafted measurement campaigns of varying
degrees of scale and compatibility. Reiterating that stated in Section 1, ice draft represents the
larger portion of the ice volume and therefore has much smaller errors than freeboard for total
thickness determination. An investment in these types of measurements must remain a high
priority to ensure accuracy of the basin-scale mean thicknesses and their regional variations
as minimum requirements to provide the needed ground truth to check model performance
and prediction capabilities and most importantly to monitor changes that models have yet to
keep up with.
4. Summary and Concluding Remarks
We demonstrate a novel method to correct sonar ice draft measurements to ice thickness
estimates, using an independent thickness data set to correct for isostatic balance of the ice
pack. It appears this balance is independent of scale between the 2-30km length scales
examined in this small case study. Estimates of ice thickness are impacted by sampling rate
with 1000 data points needed to adequately characterize both the ice thickness mean and
distribution.
EMI and sonar sensors perform equally well when measuring the mean and distribution with
EMI being limited by spatial scale only when used in ground-survey mode (aircraft versions
also available). In this case, sonar is limited by sampling rate, but future efforts can easily
resolve this to allow for high data-volume calibration sites. Furthermore, we come to the
following conclusions to aid in the design of thickness monitoring systems:
1) Thickness PDF is well represented with 1000 independent measurements from small
scales (~1 km) and larger.
2) The choice of location is very important especially in terms of identifying regional ice
types proportional to their distribution. A 2 km square survey is not sufficient to
characterize regional thickness distribution but it may be sufficient to integrate with
mass balance autonomous deployment systems. Small scale surveys are also shown to
provide enormous value for calibration of long-range systems. Whenever possible,
short 1-2 week-long surveys combined with buoy deployments provide excellent
initial conditions for analysis, process studies, and modeling investigations (including
forecasting). A combination of long-distance underwater draft measurements over
regional scales and independent thickness measurements (which can be confined to
smaller scales) can be designed to fully represent the regional ice thickness mean and
variability.
3) A natural question arising from this study is “what is the length scale of ice thickness
mean given that so many ice thickness distributions can represent the same mean?”
The length scale of sea ice thickness has been discussed for years in many classic
texts (e.g., Rothrock 1975) but the inter-relationship between scales of contiguous
thickness distribution and scales of contiguous means is not understood at all. This
20km box study was only able to glimpse this issue. Future investigations are required
to determine the length scale over which the thickness PDF varies and when that
variation triggers a significant change in the mean. This scale is clearly greater than
30 km.
4) We suggest that variability in the measured ice thickness distribution between 2km
and 10km scales may be linked to cumulative history of sea ice deformation
distribution. Hutchings et al (2010) find that sea ice deformation during the SEDNA
experiment exhibits fractal scaling properties for length scales somewhere between
70km and 140km scale. The link between ice deformation and thickness, noted here,
and our knowledge of deformation scaling (Hutchings et al 2010) suggests that the ice
thickness distribution may become regionally representative at length scales of around
100km. Again, more observations are needed to really prove this.
5) The use of reconnaissance and satellite data to target particular survey areas that
represent regional ice thickness is not unreasonable, and could provide cost effective
methods to extend limited thickness survey resources to pan-Arctic representations of
ice thickness. Highly integrated and sustained monitoring programs are needed to
address this challenge.
Acknowledgments
This research was funded by the U.S. National Science Foundation (grants NSF ARC
0612527, 0612105, 0611991, and 0612402). The U.S. Navy’s Arctic Submarine Laboratory
provided access to the Applied Physics Laboratory (APL) Ice Station 2007 (APLIS07).
Thanks to Fred Karig and the APL team who ran APLIS07. The Alaska Satellite Facility
(ASF) of the Geophysical Institute of the University of Alaska Fairbanks and the National Ice
Center of the U.S. National Oceanic and Atmospheric Administration (NOAA) facilitated
near-real-time transfer of RADARSAT 1 ScanSAR-B imagery provided by the Canadian
Space Agency. We also thank Robert Harris from Hartford High School, Vermont, USA who
joined us through the ARCUS PolarTREC program for his help in setting up the ground
survey lines.
References
Adolphs, U., 1998. Ice thickness variability, isostatic balance and potential for snow ice
formation on ice floes in the South Polar Ocean, J. Geophys. Res., 103 (C11), 24,675–
24,691.
Eicken, H., W. B. Tucker III, D. K. Perovich, 2001. Indirect measurements of the mass
balance of summer Arctic sea ice with an electromagnetic induction technique.
Annals of Glaciology, 33: 194-200.
Haas, C. and H. Eicken, 2001. Interannual variability of summer sea ice thickness in the
Siberian and central Arctic under different atmospheric circulation regimes, JGR, 106
(C3) 4449-4462.
Haas, C., J. Lobach, S. Hendricks, L. Rabenstein, A. Pfaffling, 2008. Helicopter-borne
measurements of sea ice thickness using a small and lightweight digital EM system.
Journal of Applied Geophysics, Volume 67, Issue 3, March 2009, Pages 234-241.
Hutchings, J., A. Roberts, C. Geiger, J. Richter-Menge (2010), Spatial and temporal
characterisation of sea ice deformation, manuscript under review for Annals of
Glaciology, Proceedings from the International Glaciological Society International
Symposium on Sea Ice in the Physical and Biogeochemical System 31 May – 4 June
2010, Tromsø, Norway. Hutchings, J., C. Geiger, A. Roberts, J. Richter-Menge, M. Doble, R. Forsberg, K. Giles, C.
Haas, S. Hendriks, C. Khambhamettu, S. Laxon, T. Martin, M. Pruis, M. Thomas, P.
Wadhams, J. Zwally (2008) Role of ice dynamics in the sea ice mass balance, EOS,
Vol. 89, No. 50, 9 December.
Kwok, R., and Rothrock, D.A. (2009) Decline in Arctic sea ice thickness from submarine and
ICESat records: 1958-2008, GRL, 36, L15501, doi:10.1029/2009GL039035
Kwok, R. (2007), Near zero replenishment of the Arctic multiyear sea ice cover at the end of
2005 summer, Geophys. Res. Lett., 34, L05501, doi:10.1029/2006GL028737.
Kwok, R., G. F. Cunningham, M. Wensnahan, I. Rigor, H. J. Zwally, and D. Yi (2009),
Thinning and volume loss of the Arctic Ocean sea ice cover: 2003– 2008, J. Geophys.
Res., 114, C07005, doi:10.1029/2009JC005312.
Maslowski, W. and W. H. Lipscomb 2003, High resolution simulations of Arctic sea ice,
1979–1993, Polar Research 22(1), 67–74.
McLaren, A.S., 1988, Analysis of the under-ice topography in the Arctic Basin as recorded
by the USS Nautilus during August 1958, Arctic, 41, 11-1126.
Melling, H., D. A. Riedel, and Z. Gedalof (2005), Trends in the draft and extent of seasonal
ice pack, Canadian Beaufort Sea, Geophys. Res. Lett., 32(L24501),
doi:10.1029/2005GL024483.
Nghiem S. V., I. G. Rigor, D. K. Perovich, P. Clemente-Colón, J. W. Weatherly, G. Neumann
(2007), Rapid reduction of Arctic perennial sea ice, Geophys. Res. Lett., 34, L19504,
doi:10.1029/2007GL031138
Parkinson, C. L., and D. J. Cavalieri, 2008. Arctic sea ice variability and trends, 1979–2006,
J. Geophys. Res., 113, C07003, doi:10.1029/2007JC004558.
Perovich, D. K., B. Light, H. Eicken, K. F. Jones, K. Runciman, and S. V. Nghiem (2007),
Increasing solar heating of the Arctic Ocean and adjacent seas, 1979–2005:
Attribution and role in the ice-albedo feedback, Geophys. Res. Lett., 34, L19505,
doi:10.1029/2007GL031480.Reid, J., A. Pfaffling, and J. Vrbancich, 2006. Airborne
electromagnetic footprints in 1D earths. Geophysics, 71, G63-G72.
Press, W. H., S. A. Teukolsky, W. T. Vetterling, B.P. Flannery (1992). Chapter 13.3
Estimation of the Mode for Continuous Data, in Numerical Recipes in Fortran: The
Art of Scientific Computing. Cambridge Press. Second Edition, 462-464.
Reid, J. and J. Vrbancich, 2004. A comparison of the inductive-limit footprints of airborne
electromagnetic configurations Geophysics, 69, 1229-1239.
Rigor, I.G., and J.M. Wallace (2004), Variations in the age of Arctic sea-ice and summer sea
ice extent, Geophys. Res. Lett., 31, L09401, doi:10.1029/2004GL019492.
Rigor, I.G., J.M. Wallace, and R.L. Colony (2002), Response of Sea Ice to the Arctic
Oscillation, J. Climate, 15, 2648-63.
Rodrigues, J. (2010), Beamwidth effects on sea ice draft measurements from U.K.
submarines, submitted to CRST.
Rothrock, D. A., D. B. Percival, and M. Wensnahan, 2008.The decline in arctic sea-ice
thickness: Separating the spatial, annual, and interannual variability in a quarter
century
of
submarine
data,
J.
Geophys.
Res.,
113,
C05003,
doi:10.1029/2007JC004252
Rothrock, D. A., and M. Wensnahan (2007), The Accuracy of Sea Ice Drafts Measured from
U.S. Navy Submarines. Journal of Atmospheric and Oceanic Technology, vol. 24,
issue 11, p. 1936
Rothrock, D. A. (1975), The Energetics of the Plastic Deformation of Pack Ice by Ridging, J.
Geophys. Res., 80(33), 4514–4519.
SEARCH (2008). Arctic Observation Integration: Workshops Report. Fairbanks, Alaska:
SEARCH Project Office, Arctic Research Consortium of the United States (ARCUS) http://www.arcus.org/search/resources/reportsandscienceplans.php
Stroeve, J., M. Serreze, S. Drobot, S. Gearheard, M. Holland, J. Maslanik, W. Meier, and
T.Scambos, 2008. Arctic Sea Ice Extent Plummets in 2007, EOS, 89, 2, 13-20.
Sturm, M., Maslanik, J. A., Perovich, D. K., Stroeve, J. C., Richter-Menge, J., Markus, T.,
Holmgren, J., Heinrichs, J. F., and Tape, K., 2006. Snow depth and ice thickness
measurements from the Beaufort and Chukchi Seas collected during the AMSR-Ice03
Campaign, IEEE Transactions on Geoscience and Remote Sensing, v. 44, p. 30093020.
Tucker,W. B., J.W.Weatherly, D. T. Eppler, L. D. Farmer, and D. L. Bentley, 2001. Evidence
for rapid thinning of sea ice in the western Arctic Ocean at the end of the 1980s,
Geophys. Res. Lett., 28(14), 2851– 2854.
Wadhams, P., N. Hughes, J. Rodrigues and N. Toberg (2010), The thickness distribution of
Arctic sea ice in winter 2004 and 2007 from submarine upward sonar, submitted to
Nature Geoscience.
Wadhams. P., 2000: Chapter 5.2 The measurement of ice thickness, in Ice in the Ocean,
Gordon and Breach Science Publishers, Amsterdam, The Netherlands, 158-170.
Wadhams, P.; Horne, R. J. (1980). An analysis of ice profiles obtained by submarine sonar in
the Beaufort Sea. Journal of Glaciology, vol.25, Issue 93, pp.401-424
Wadhams, P and N. R. Davis (2000) Further evidence of ice thinning in the Arctic Ocean,
GRL, 27(24), 3973-3976.