TCThe CryosphereTCThe Cryosphere1994-0424Copernicus GmbHGöttingen, Germany10.5194/tc-9-269-2015Arctic sea ice thickness loss determined using subsurface, aircraft, and satellite observationsLindsayR.lindsay@apl.uw.eduSchweigerA.Polar Science Center, Applied Physics Laboratory, University of Washington, 1013 NE 40th Street, Seattle, WA 98105, USAR. Lindsay (lindsay@apl.uw.edu)10February2015912692836August201428August201430December201411January2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://www.the-cryosphere.net/9/269/2015/tc-9-269-2015.htmlThe full text article is available as a PDF file from https://www.the-cryosphere.net/9/269/2015/tc-9-269-2015.pdf
Sea ice thickness is a fundamental climate state variable that provides an
integrated measure of changes in the high-latitude energy balance. However,
observations of mean ice thickness have been sparse in time and space, making
the construction of observation-based time series difficult. Moreover,
different groups use a variety of methods and processing procedures to
measure ice thickness, and each observational source likely has different and
poorly characterized measurement and sampling errors. Observational sources
used in this study include upward-looking sonars mounted on submarines or
moorings, electromagnetic sensors on helicopters or aircraft, and lidar or
radar altimeters on airplanes or satellites. Here we use a curve-fitting
approach to determine the large-scale spatial and temporal variability of
the ice thickness as well as the mean differences between the observation
systems, using over 3000 estimates of the ice thickness. The thickness
estimates are measured over spatial scales of approximately 50 km or time
scales of 1 month, and the primary time period analyzed is 2000–2012 when
the modern mix of observations is available. Good agreement is found between
five of the systems, within 0.15 m, while systematic differences of up to
0.5 m are found for three others compared to the five. The trend in annual
mean ice thickness over the Arctic Basin is -0.58 ± 0.07 m decade-1
over the period 2000–2012. Applying our method to the period
1975–2012 for the central Arctic Basin where we have sufficient data (the SCICEX
box), we find that the annual mean ice thickness has decreased from 3.59 m
in 1975 to 1.25 m in 2012, a 65 % reduction. This is nearly double the
36 % decline reported by an earlier study. These results provide
additional direct observational evidence of substantial sea ice losses found
in model analyses.
Introduction
In recent years great interest has developed in the changes seen in Arctic
sea ice as ice extent and volume have markedly decreased. While ice extent
is reasonably well observed by satellites, observations of ice thickness
have been, until recently, sparse. Sea ice model reanalyses (e.g., Schweiger
at al., 2011) provide useful estimates of thickness and volume loss but so
far do not directly incorporate observations of ice thickness. An
observational record that does not depend on a sea ice model therefore
remains of substantial interest. Historically, a great number of ice
thickness measurements have been made at specific locations using drill
holes or ground-based electromagnetic methods; however, these point
measurements are difficult to translate into area-averaged mean ice
thickness because of the highly heterogeneous nature of the ice pack.
Estimates of mean ice thickness require a large number of independent
samples. In the last 10 years or so a number of different observations of
mean sea ice thickness have been made available by different groups using a
variety of different methods. The longest historical record is from sporadic
observations made by submarines using upward-looking sonar (ULS) to measure
ice draft (Rothrock et al., 1999, 2008). These measurements are currently
available starting in 1975 and ending in 2005 and include data from
34 cruises. They have broad but incomplete spatial coverage and limited
sampling of the seasonal variations. ULS measurements from anchored moorings
have been made by a number of different groups (e.g., Vinje et al., 1998;
Melling et al., 2005; Krishfield et al., 2014; Hansen et al., 2013). Each
has excellent temporal sampling with record lengths of up to 10 years
although
only for single locations. More recently, airborne and satellite-based
observations have become available. Operation IceBridge uses lidar and radar
technology on a fixed-wing aircraft beginning in 2009 (Kurtz et al., 2012)
and electromagnetic methods from helicopters have been used to measure the
snow plus ice thickness since 2001 (Pfaffling et al., 2007; Haas et al.,
2009). Satellite-based lidar techniques began with ICESat during the years
2003–2008 (Kwok et al., 2009; Yi and Zwally, 2009). Radar altimeter
techniques are used with data from Envisat (2002–2012; Peacock and Laxon,
2004) and from CryoSat-2 beginning in 2010 (Laxon et al., 2013; Kurtz et
al., 2014). However, Envisat and CryoSat-2 estimates are not included in the
current study because there are currently few publicly available ice
thickness data from these instruments that are not preliminary products.
Observations from submarine ULS instruments have previously been used to
establish the time and space variation of sea ice draft using a
curve-fitting approach for a limited area of the Arctic Basin (Rothrock et
al., 2008). Here we extend this approach by including more recent
observations of ice thickness from multiple sources, including satellites,
and expand the area to the entire Arctic Basin. In addition, we examine if
there are systematic differences between individual data sources. This is
important because the data sources differ markedly in their methodologies
and sampling characteristics, which may result in systematic errors that can
affect the spatial and temporal characteristics of the ice thickness time series.
Differences in mean ice thickness from the various measuring systems vary on
a wide range of temporal and spatial scales and even measurements obtained
from samples nearly identical in time and space may show differences
depending on sampling error, how the measurement is made, and how the
systems record small-scale variability. The differences in the results from
different measurement systems may also depend on ice type (first-year or
multiyear), degree of deformation, ice thickness, snow depth, or season.
This study is a first attempt to characterize these differences for a broad
range of observing systems with a single number that characterizes the
difference between any two observing systems.
Approach
All available ice thickness observations are fit with a multiple regression
least-squares solution of an expression for the mean ice thickness that is a
function of time and space. The expression includes non-linear terms that
characterize the spatial and temporal variability as well as terms that
indicate which observation system is associated with each observation. The
observations can be restricted to particular observation systems, geographic
regions, or time periods to refine the analysis, with the trade-off of the
results being less general. We begin the analysis with a basin-wide
selection of all available observations for the time period 2000–2012, then
focus on specific observation systems or regions. The trend in the mean ice
thickness determined by the regression expression is compared to model-based
estimates and other observational studies. We then expand this analysis to
include data back to 1975 to compare with and update the results of Rothrock
et al. (2008) and provide an assessment of the 39-year change in ice
thickness for the central Arctic Basin from the observational record. An
assessment of errors, including sensitivity analyses that examine the role
of individual observing systems and focus on subregions of the Arctic, follows.
Locations of the observations from different data sources.
Times and ice thickness of the observations from different data sources.
The primary focus is on the years after 2000 (dashed line).
The Unified Sea Ice Thickness Climate Data Record (Sea Ice CDR) is a collection of Arctic sea ice draft, freeboard, and
thickness observations from many different sources. It includes data from
moored and submarine-based upward-looking sonar instruments, airborne
electromagnetic (EM) induction instruments, satellite laser altimeters
(ICESat), and airborne laser altimeters (IceBridge). The point observations
have been averaged spatially for roughly 50 km and temporally for 1 month.
The mooring data are averaged only in time, the submarine data only in space,
and the airborne and satellite data are averaged both temporally (1 month)
and spatially (50 km); e.g., airborne data from one campaign that are taken a
few days apart are averaged together. In all data sets except ICESat-J, open
water is included in the mean ice thickness estimates. The mean measurements
and the probability distributions for all of the sources are collected in a
single data set with uniform formatting, allowing the scientific community
to better utilize what is now a considerable body of observations. The Sea
Ice CDR data are available at the National Snow and Ice Data Center
(Lindsay, 2010, 2013; also at http://psc.apl.washington.edu/sea ice cdr).
The data sets used in this study are listed in Table 1 and
maps of the data locations and times of the observations from the various
systems are shown in Figs. 1 and 2. A short description of the eight different
data sets follows.
Submarines: ULS instruments have been deployed on US Navy
submarines using either digital or analog recording methods (Polar Science
Center, University of Washington; US Navy Arctic Submarine Laboratory; Cold
Regions Research and Engineering Laboratory; NSIDC, 1998; Rothrock and Wensnahan,
2007; Wensnahan and Rothrock, 2005; Tucker et al., 2001). The point data
are archived at NSIDC. While there are 34 cruises archived for the years 1975–2005,
only three are from after 2000: one in 2000 and two in 2005. The draft measured by
the ULS instruments is based on the first-return echo. This introduces a positive
mean bias in the measured draft that is estimated by Rothrock and Wensnahan (2007,
RW07 hereinafter) as 0.44 ± 0.09 m for multiyear ice and typical US submarine depths and beam
widths, based on work by Vinje et al. (1998). RW07
also identify an open-water detection bias of -0.15 ± 0.08 m. Combined,
the draft measurements reported for the submarines have a likely bias of 0.29 ± 0.25 m.
The error range includes the error contributions from other unbiased sources of
error (RW07). We have subtracted this bias from the US submarine draft data but
not from any of the other ice draft measurements; the bias for these measurement
types is unknown and will be accounted for in the multiple regression procedure.
Air-EM, Airborne Electromagnetic Induction: the Air-EM
measurements include an electromagnetic induction instrument that determines
the distance to the ice-water interface and a lidar to measure the distance to
the top snow surface; consequently the measurements are of the ice + snow
thickness. The method is based on measurements of the amplitude and phase of a
secondary EM field induced in the water by a primary field transmitted from the
EM instrument. Haas et al. (2009) report on the configuration of the
EM instruments and give an accuracy of 0.1 m for the ice + snow thickness over
level ice. The footprint of the Air-EM system is 40–50 m at common operational
altitudes, and as a consequence the thickness of pressure ridges are smoothed
and underestimated by as much as 50 % (Haas and Jochmann, 2003; Pfaffling and
Reid, 2009). Pfaffling et al. (2007) report mean errors compared to
drill holes of the ice + snow thickness of -0.04 ± 0.09 m over approximately
200 m of level ice in Antarctica. Haas et al. (2010) report that the
thickness distributions obtained from the instruments are most accurate with
respect to their modal thickness and less so for the mean thickness. Ice + snow
thickness samples used here are obtained from various locations around the Arctic
Basin (Alfred Wegener Institute for Polar and Marine Research and York University;
Haas et al., 2009; Pfaffling et al., 2007). In order to obtain
an estimate of the ice thickness alone, the snow depth must be subtracted. The
snow depth used here is the mean snow depth estimated from the PIOMAS ice–ocean
model, which estimates snow accumulation from the NCEP Reanalysis (Zhang and
Rothrock, 2003). The uncertainty in the snow depth from PIOMAS is not well known.
Compared to the Warren et al. (1999) climatology of snow depth, it averages
between 1 cm greater in May to 7 cm less in October. However, it potentially
offers better spatial and interannual variability than using a climatology which
may not provide the best estimate for more recent years (Kurtz et al., 2013;
Webster et al., 2014). We estimate the uncertainty in the PIOMAS snow depth to
be on the order of 0.10 m.
BGEP, Beaufort Gyre Exploration Project: this data set is comprised
of a set of three or four (depending on the year) bottom-anchored moorings with
top-mounted ULS instruments located in the Beaufort Sea (Woods Hole Oceanographic
Institute; Krishfield et al., 2014). These installations use the ASL acoustic Ice
Profiler moored at a depth of approximately 50 m below the surface. The Ice
Profiler is a 420 kHz ULS instrument with a 1.8∘ beam width,
a precision of 0.05 m, and a sample rate of 2 s. There are a total of
28 station years of data from 2003 to 2012. The data processing procedures are
outlined in Krishfield and Proshutinsky (2006) and the point data are available
at http://www.whoi.edu/page.do?pid=66566. The uncertainty
in the point ice draft estimates are estimated to be better than 0.10 m
(Krishfield et al., 2014).
IceBridge, NASA Operation IceBridge: scanning lidar altimeter,
snow radar, and cameras aboard NASA aircraft are used to determine the surface
freeboard and snow depth from an altitude of approximately 300 m. These data are
then used to determine the ice thickness distribution (Goddard Space Flight
Center; Kurtz et al., 2012, 2013; Richter-Menge and Farrell, 2013).
The IceBridge mission was initialized after the end of operations of the ICESat-1
satellite in order to partially continue the time series of sea ice and ice sheet
observations until the launch of ICESat-2. The data are available at NSIDC
(Kurtz et al., 2012) and are provided along the aircraft track at a spacing of
40 m. An estimate of the error is included for each point and is primarily a
function of the distance to a lead where the ocean water level needed to compute
the freeboard can be determined. The uncertainty in the estimated snow depth is
critical because in the freeboard–thickness relationship it is amplified into
an ice thickness uncertainty roughly 7 times as large (Kwok and Cunningham, 2008).
The mean snow depth uncertainty is not yet well characterized but Kurtz et
al. (2013) estimate it as 0.06 m for point estimates. There may also be unknown
biases in the snow depth estimates. The data for each spring campaign are
aggregated into 50 km samples, combining data from different flight days if
they are in close proximity. Points with a thickness uncertainty greater than
1.0 + 0.25 h or 2.0 m, where h is the ice thickness, are excluded.
IOS-CHK, Institute of Ocean Sciences Chukchi Sea: these are
bottom-anchored moorings with ULS instruments located in the Chukchi Sea (Institute
of Ocean Sciences; Melling and Riedel, 2008). These moorings also use the ASL
acoustic Ice Profiler. Just 2 station years are available, starting in 2003.
The measured draft uncertainty is estimated to be 0.10 m (Melling and Riedel, 2008).
IOS-EBS, Institute of Ocean Sciences, Eastern Beaufort Sea: this
collection includes data from bottom-anchored moorings with ULS instruments
located near the coast at nine different locations in the eastern Beaufort Sea
near the Mackenzie River delta and Banks Island (Institute of Ocean Sciences;
Melling et al., 2005). The data are available at NSIDC (Melling and Riedel, 2008).
We use data from 1990 to 2003. The moorings use various models of the ASL
acoustic Ice Profiler. The ice draft uncertainty for point measurements is
about 0.10 m (Melling and Riedel, 2008).
ICESat-G, ICESat measurements processed by NASA Goddard Space Flight Center:
satellite laser altimeter measurements of freeboard are used to compute ice
thickness (Yi and Zwally, 2009; Zwally et al., 2008). Snow depth is from
climatology (Warren et al., 1999). Snow density, including its time variation,
is based on Kwok and Cunningham (2008). Fifteen 1-month measurement campaigns
are included in this data set. The track data of position and ice thickness have
a resolution of about 170 m in the along-track direction. Portions of track
data from each campaign are aggregated to form nearly 30 000 50 km mean ice
thickness samples. In order to not overly fit the multiple regression procedure
to the satellite data, 900 randomly selected samples from the Arctic Basin from
all campaigns are used. This accounts for the high spatial autocorrelation of
these data and makes the ICESat data have roughly the same number of points
as the submarine data. The autocorrelation length scale of the residuals from
the regression procedure of the ICESat-G aggregated samples is about 300 km.
There are no published estimates of the expected ice thickness errors for
this system.
ICESat-J, ICESat measurements processed by the Jet Propulsion Laboratory:
these data use different processing methods from ICESat-G and cover just 10
measurement campaigns. In particular the methods of determining the freeboard
and the snow depths are different (Kwok et al., 2009). Snow depth was estimated
from daily snow accumulation data from the ECMWF Reanalysis. The data gap at
the pole due to the satellite orbital configuration is filled by interpolation.
Kwok and Cunningham (2008) find the overall uncertainty of ice thickness estimates
within 25 km track segments is ∼ 0.7 m but varies with the total
freeboard and the snow depth. In a second study, Kwok et al. (2009) find their
ICESat estimates of ice draft are 0.1 ± 0.42 m thinner than those from a
submarine cruise in 2005. For this gridded data set there is no accounting for
the overall ice concentration within a grid cell after data accumulation and
interpolation. A weighting by passive-microwave-derived ice concentration to
address this is sometimes applied to this data set (e.g., Kwok and Cuningham,
2008; Schweiger et al., 2011; Laxon et al., 2013), but this
adjustment is not made here. Weighting by ice concentration reduces the average
ICESat-J ice thickness by just 0.05 m in October/November and 0.02 m in February/March. The
data are provided on a 25 km grid for each 1-month campaign, but they have been
aggregated here to a 50 km grid to make them compatible with the other data
sets. Similar to the ICESat-G data, a subsample of 600 randomly selected points
from all campaigns (proportional to the number of measurement campaigns available)
is used in order to account for the high spatial autocorrelation (also about
300 km) of these data. This data set is not in the Sea Ice CDR but may be
obtained from JPL (http://rkwok.jpl.nasa.gov/icesat/index.html).
The submarine and mooring observations of ice draft are converted to ice
thickness following Rothrock et al. (2008) using a density of water of
1027 kg m-3, a density of ice of 928 kg m-3, and the weight of the
snow. The ice thickness h is then related to the ice draft D by
h=1.107D-f(m),
where f(m) is the monthly mean ice equivalent of the snow on the surface. We use
the monthly values of f(m) determined by Rothrock et al. (2008, RPW08
hereafter),
who found f(m) ranges up to 0.12 m in May based on the snow climatology of
Warren et al. (1999) for multiyear ice. First-year ice may have
substantially less snow than multiyear ice (Kurtz et al., 2013) but, because
the total snow accumulation depends on freeze-up dates, this difference is
likely to be variable and difficult to estimate. This uncertainty in the
snow depth plus some uncertainty in the density of the ice add to the
uncertainty of the conversion of ice draft to ice thickness.
We have little information on the absolute accuracy of the averaged samples
because we do not know the degree to which the reported measurement errors
are uncorrelated. Clearly if the errors are uncorrelated, the many thousands
of point observations that typically comprise a sample would result in very
small sample errors (Kwok et al., 2008). However, this assumption is unrealistic
(Kwok et al., 2009) since the sea ice characteristics that affect these
errors (e.g., thickness variability, snow cover, ridging) likely have spatial
autocorrelations substantially larger than the distance between samples
(Zygmontovska et al., 2014).
Methodology
Following RPW08, who developed a regression model to fit ice draft
observations from US submarine data for a sub-area of the Arctic Basin, a
smooth function of space and time, h(x, y, t), is fit to all of the selected
observations simultaneously using a least-squares multiple linear regression
procedure. We refer to this as the Ice Thickness Regression Procedure, or ITRP. This function can be evaluated
at all locations and times to yield a complete time and space record of
Arctic Basin ice thickness. However, an additional complication, the fact
that different observation systems may have unknown biases relative to each
other, needs to be accounted for. In order to do this, an indicator variable I
is included for each observation system in the multiple regression procedure
except for the reference system. I is 1 for observations from the corresponding
source and 0 otherwise. The regression equation becomes ill posed if all
systems have an associated indicator, so one of the observations systems
needs to be excluded and therefore implicitly becomes the reference system.
We chose the ICESat-G data as a reference data set in this study because of
ICESat-G's extensive spatial and temporal coverage, but we emphasize that this does
not mean it is assumed to be more accurate than the other systems. The
choice of the reference does not change the form or the goodness of fit of
the regression equation or the relative magnitudes of the indicator variable
coefficients. However, it does help determine the constant a0 so that
predictions where there are no data (all I= 0) depend on this choice and we
need to reexamine the choice after the fit is made. The regression equation
for the ice thickness is
h(x,y,t)=a0+ΣaiTi(x,y,t)+ΣbjIj+error,
where Ti(x, y, t) are the spatial and temporal terms of the regression
equation, Ij are the indicator variables for each of the observation
systems (excluding the reference), and “error” is the residual of the fit. Positive
coefficients bj for the indicator variables Ij of a particular
observation system indicate that the error in the regression is reduced if a
constant value (the coefficient bj) is added to the regression expression
(not to the observations) for all observations from that system, so positive
coefficients indicate that measurements from the system are systematically
thicker relative to the reference measurements. Different observations are
not weighted by their uncertainties because the uncertainties of the time
and space averaged observations are unknown.
The choice of terms in the regression follows the methods of RPW08. The
spatial coordinate system x, y is based on a Cartesian grid in units of 1000 km
and the time coordinate t is in years relative to 2000. Spatial and temporal
terms are included in sequence in a forward selection procedure, starting
with the one that is most correlated with the observed thickness. Additional
terms are then added one-by-one and at each step the variable that is most
correlated with the residuals is added to the list of terms. Terms
considered for the expression are up to third order in space and time,
including mixed terms involving both space and time. The seasonal cycle of
the thickness is estimated by including COS =cos(2 π year-fraction)
and SIN =sin(2 π year-fraction) as
the first harmonic of the annual period. The second and third harmonics
(COS2, SIN2, COS3, and SIN3) are also included. The linear time variable is
introduced before the quadratic and all sine and cosine seasonal terms are
always included. The partial-p values of all coefficients are assessed at each
step and any term with a value less than 0.90 is dropped unless it is one of
the indicator functions or SIN or COS. The procedure is stopped when a new
coefficient has a partial p value of less than 0.90.
The multiple regression procedure provides an estimate of the standard error
of each of the coefficients: σi for the space and time terms or σj
for the indicator terms. For the reference source we say the
coefficient is zero and the standard error is taken as the standard error of
the constant term a0. Without the indicator variables, the RMS error of
the fit for the Arctic Basin increases slightly from 0.62 to 0.64 m and the
RMS difference in the fit values at the data locations is 0.20 m, indicating
that these variables play a minor role in determining the shape of the
regression function while at the same time providing an estimate of the
relative bias of the different observational data sets.
ResultsFit for the Arctic Basin
For the entire Arctic Basin, 2000–2012, the ITRP outlined above selected
21 terms: 7 for indicator variables and 14 for time and space variability of
the ice thickness. Table 2 shows all of the terms and coefficients for this fit. The
multiple regression coefficient is Rmul= 0.84 (Rmul2= 0.70)
and the RMS error of the fit is 0.62 m. Summaries of the values of the
fit predictions at the time and location of the observations and the
residuals for the fit are depicted in Fig. 3. The observations are grouped into four types for this figure:
submarines, moorings, aircraft, and satellite. The scatter in the temporal
plot for the predictions is due to the spatial distribution of the
observations. This mixture of time and space variability is also seen in the
maps. The residuals have little temporal or spatial structure, as we would
expect, because the terms have been selected to largely account for the
systematic spatial and temporal variability.
Fit to ice thickness observation data from the Arctic Basin for 2000–2012.
(a) Map of ice thickness of the fit predictions at the data locations
regardless of time; (b) the fit predictions at the data times regardless
of location; (c) map of the residuals; (d) residuals as a
function of time. The observational sources are grouped into four different
types and color-coded as shown in (d).
ITRP coefficients for the Arctic Basin for all observational sources,
2000–2013. Sigma is the standard error of the coefficient and the p value is
the probability of being non-zero. The X and Y spatial coordinates are
oriented as in the map in Fig. 4 and are in units of 1000 km. The time T is
in years relative to 2000. The indicator coefficients are ordered by the
magnitude of the coefficients.
TermCoefficientSigmap valueIndicator variables (bj in Eq. 2) IOS-EBS-0.2040.1030.000Submarine-0.0490.0610.000BGEP-0.0450.0580.000IOS-CHK-0.0070.1300.000ICESat-G0.0000.0660.000Air-EM0.0630.0610.000ICESat-J0.4200.0341.000IceBridge0.5900.0571.000Time and space variables (ai in Eq. 2) T-0.0790.0071.000COS-0.2330.0321.000SIN0.2960.0241.000COS20.1620.0280.953SIN2-0.2260.0211.000COS3-0.1400.0300.582SIN30.0150.0250.000Y-1.7670.0381.000X2-0.3290.0171.000XY20.2530.0400.991XSIN-0.1990.0191.000Y20.6740.0371.000X2Y0.3980.0241.000XT2-0.0020.0001.000Systematic differences between ice thickness estimates
As a step towards generating a time series of sea ice thickness from
observations alone, we need to determine what, if any, the mean
differences are between the ice thickness estimates from the different
measurement systems. The ITRP provides a method to do this even when the
observations are not coincident. In this analysis the observation sources
with indicator coefficients not significantly different from zero are
Air-EM, BGEP, IOS-CHK, ICESat-G, and the submarines, indicating that these
sources are all consistent in the mean with each other over the region and
period analyzed. There is just a 0.11 m spread in the mean between the five systems. Ice thickness
data from the three submarine cruises agree in the mean with the ICESat-G
data very closely, with a bias coefficient of -0.05 ± 0.06 m (error
brackets are 1 standard deviation). Two indicator coefficients are
significantly different from zero: ICESAT-J
and IceBridge. This means they are significantly larger or smaller than the
reference data set and, in this case, from the cluster of five observation
sets that agree with each other.
The ICESat-J coefficient, 0.42, indicates that on average the JPL thickness
product is 0.42 m thicker than the Goddard product. A small portion of this
difference is due to the lack of inclusion of open water in the ice
thickness estimates but the bulk of the difference between the ICESat-G and
ICESat-J values may be related to the different techniques of determining
the sea level in order to obtain the freeboard and the different methods for
estimating snow depth. The ITRP shows the ICESat-J estimates are on average
0.47 m thicker than the submarine-based estimates. In contrast, Kwok et al. (2009)
found that the ICESat track estimates of ice draft were 0.1 m ± 0.4 m
thinner than the fall 2005 submarine ice draft data.
The estimation of the submarine coefficient is sensitive to the inclusion of
a particular cruise. The large difference between the submarines and the
ICESat-J estimates for the entire basin stems from the inclusion of the
2000 submarine cruise when there is no overlap with the ICESat data. If the
analysis period is chosen as 2001–2012 with all sources included, the
ICESat-J product is found to be just 0.05 m ± 0.09 m thicker than the
submarine-based estimates and in line with the ICESat-J validation results
reported by Kwok et al. (2009). The very sparse submarine data do not
provide a robust estimate of their mean bias relative to the other measurements.
The IceBridge data are also significantly thicker than the reference data, in
this case by 0.59 ± 0.06 m, and hence also thicker than the submarine, BGEP,
IOS-CHK, and Air-EM data. We will examine the IceBridge and Air-EM data sets
below to show that this large difference is robust. The IOS-EBS data are
estimated to be 0.20 ± 0.10 m thinner than the reference. However, we have less confidence in
this result since the IOS-EBS moorings are near the coast in the extreme
southeast corner of the Beaufort Sea and may not be well represented by the
spatial terms of the regression model. Further discussion of the
uncertainties of the indicator coefficients is found in the error assessments section.
Evaluation of ice thickness trendsArctic Basin for 2000–2012
The ITRP expression for the whole basin can be used to evaluate the
spatial and temporal patterns of ice thickness change. To do this, the
expression was evaluated at every location within the basin on a 40 km grid
with all of the indicator variables set to zero. Here it is important to
reconsider the choice of the reference system, ICESat-G.
Table 2 shows that the ICESAT-G coefficient, zero
by its selection as the reference, is very close to the median value of the
coefficients of the cluster of five observation systems that have quite
similar coefficients: submarines, BGEP, IOS-CHK, ICESat-G, and Air-EM. These
systems have a range of coefficients of 0.11 m, indicating that when spatial
and temporal variability is accounted for there is little mean difference in
the observations. The coefficients for these five are not significantly
different from each other since the sigma values are between 0.06 and 0.13 m
(Table 2). This suggests that using ICESat-G as a reference predicts an
ice thickness that is consistent with observations from these five systems
but not with the unadjusted observations from IOS-EBS, ICESat-J, or IceBridge.
(a) Mean annual ice thickness from the ITRP for the period
2000–2012. (b) Mean ice thickness for the Arctic Basin in May, in
September, and for the annual mean.
The mean ice thickness for the 2000–2012 period is shown in
Fig. 4. The map shows a maximum along the Canadian coast and a minimum in the vicinity of the New Siberian
Islands. The ITRP annual mean basin-average ice thickness has declined from
2.12 to 1.41 m (34 %) with a linear trend of -0.58 ± 0.07 m
decade-1. A quadratic time term in the fit, xT2 (Table 2), creates a slight curvature in the
basin-wide mean thickness seen in Fig. 4. The
September thickness has declined from 1.41 to 0.71 m (50 %). This
observationally based trend can be compared to that of an ice–ocean model
commonly used for ice volume estimates. The PIOMAS model (Version 2.1, Zhang
and Rothrock, 2003) has an annual mean thickness trend of -0.60 ± 0.04 m decade-1
for the same area and time period, and thus its trend is quite
consistent with that of the observations. In another observational study,
Laxon et al. (2013) computed the ice volume in the Arctic Basin from
CryoSat-2 data for 2 years, 2010 and 2011, and computed volume trends by
concatenating the ICESAT-J estimates to compute a trend from 2003 to 2011. They
found a thickness trend for fall and spring of 0.75 m decade-1. A recent
study of ice thickness measurements in Fram Strait using both surface-based
and helicopter-based EM methods (Renner et al., 2014) also found a decline
in the mean thickness. They found a decrease of 2.0 m decade-1 in late
summer for the period 2003–2012, a decline of over 50 %, for ice exiting
the Arctic Basin.
SCICEX box for 1975–2012
The regression analysis of RPW08 concentrated on submarine ice draft data
from 1975 to 2000 within the SCICEX box. They determined that the best fit
included terms up to fifth order in space and up to third order in time. The
fit showed a maximum in 1980 followed by a steep decline and then a leveling
off at the end of the period. Kwok and Rothrock (2009) used 5 years of
ICESat data to analyze the fall and winter changes in the ice draft for an
additional 5 years, to 2008; however, their regression procedure did not take
advantage of the spatial information in the ICESat data but simply
concatenated submarine and satellite records. They found the ICESat data
showed an additional modest thinning. In order to estimate the temporal
variation of ice thickness from 1975 to 2013 and to compare our results to
those of RPW08, the ITRP is extended back to 1975 in this region. The fit
procedure was performed using all of the data available from all sources
that fall within the box, 3017 observations in all. Figure 5 shows the third-order fit from
this study and the third-order curve from RPW08 that is computed for the
years 1975–2001. The ITRP fit includes indicator variables as before and
12 additional terms: T, T3, X3, Y, COS, SIN, COS2, SIN2, COS3, SIN3,
X*SIN, and T*SIN2. It explains 80 % of the variance and the RMS error is
0.49 m, while the fit in RPW08 study explained 79 % of the variance and has
an RMS error of 0.49 m as well, so the two are very similar in the fit
properties. With an additional 13 years of data it is apparent that the
annual mean ice thickness in the central Arctic Basin has continued to
decline at an approximately linear rate and the short leveling off at the
end of the RPW08 and Kwok and Rothrock (2009) time periods did not persist.
We find that the annual mean ice thickness for the SCICEX box has thinned
from 3.59 m in 1975 to 1.25 m in 2012, a 65 % decline. This is nearly
double the decline reported by RPW08, 36 %, for the period ending in 2000.
In September the mean ice thickness has thinned from 3.01 to 0.44 m, an
85 % decline. The linear trend of the annual average thickness over this
period is -0.69 ± 0.03 m decade-1. This is double the rate of ice
thickness loss computed from PIOMAS for the same area for the period
1979–2012, -0.34 m decade-1, showing that for the central Arctic
Basin and for the longer time period the PIOMAS trend in ice volume is too
conservative, as also shown by Schweiger et al. (2011). This is in contrast
to the good match for the trends from PIOMAS and the ITRP we found for the
whole basin for just the most recent 13 years.
(a) Map of the annual mean ice thickness in the SCICEX box
and (b) time series of the annual mean. The orange line is the third-order
polynomial from RPW08 for which the draft was converted to thickness with a
factor of 1.107. The green line is a third-order polynomial from this study.
The dots show the observations from within the box; red are from the submarines.
The difference in the trends between the observations and the model for the
1979–2012 period may possibly be due in part to a time-varying bias of
the submarine observations. The early part of the record has much thicker
ice in this region than the later part. The thicker ice has much larger
variability in the ice draft and hence the bias related to the first-return
correction (see also below) may be much larger for the earlier thicker ice.
If this is the case, the early ice thickness is overestimated by the draft
measurements and the magnitude of the ice thickness trend is smaller than
estimated here.
Error assessmentsLong-memory processes
Percival et al. (2008) find that the spatial autocorrelation of 1 km ice
draft measurements from submarines exhibits what is known as a long-memory
process, in which the spatial autocorrelation does not drop off as quickly as
for an autoregressive process at length scales up to 80 km. This means that
the sampling error drops off with the track length L as L-0.49 rather
than L-1. However, RPW08 found that accounting for this long-memory
correlation has only a small effect on the multiple regression coefficients
determined from submarine ice draft data. Hence we have not accounted for
this process in our analysis.
ULS first-return bias
As mentioned above, the submarine ice draft data have all been corrected
with a constant -0.29 m to account for the first-return and open-water-detection errors of
ULS draft measurements as done by Rothrock and Wensnahan (2007). This
first-return bias is a function of the roughness of the underside of the sea
ice and of the footprint width of the region insonified by the sonar beam
(Vinje et al., 1998). For the submarines, the spatial sampling is typically 2 m
and the footprint size is 2 to 5 m (Rothrock and Wensnahan, 2007),
which, according to the analysis of Vinje et al. (1998), corresponds to a
first-return correction of -0.44 m for multiyear ice. However, it is likely
an over-simplification to assume this correction is constant. It increases
as the roughness or the footprint size increases (Vinje et al.,1998; Moritz
and Ivakin, 2012). In addition, our analysis shows a strong positive
correlation for all data sources between the mean thickness and the
within-sample standard deviation determined from the point values.
Similarly, Moritz and Ivakin (2012) show a strong correlation (R= 0.81)
between the within-footprint roughness for a set of ULS observations and the
standard deviation of the sample thickness values for 256 profiles of length
50 to 150 m. Future research may show it is possible to determine a
correction for first return that is based on the sample standard deviation.
Clearly for smooth ice, for which there is no variation in the bottom
topography, it should be zero. Not accounting for this dependence on bottom
roughness may create an artificially thin bias for thin ice and a thick bias
for thick ice as was mentioned above in regards to the thickness trend.
Snow
The snow depth or snow water equivalent needs to be taken into account in
determining the ice thickness in all of the measurement systems. The error
in the estimated snow depth then contributes to the error of the thickness
estimate. However, the error in the snow depth is much less important for the
ULS observations of ice draft from submarines and moorings than for the
systems that measure the freeboard of the snow surface such as ICESat and
IceBridge. For the ULS, the snow correction for ice draft, f(m) in Eq. (1),
is based on the Warren et al. (1999) climatology and has an uncertainty on
the order of 20 %, or up to just 0.02 m. The snow depth used to correct
the Air-EM ice + snow measurements is taken from PIOMAS and has an
uncertainty of about 0.10 m, which contributes the same amount to the
uncertainty in the thickness estimate. The ICESat-J thickness estimates use
a snow depth estimated from the accumulation of snowfall from the ECMWF
Reanalysis. Kwok and Cunningham (2008) estimate that the snow depth
uncertainty is 0.05 m and contributes 0.35 m to the uncertainty in the ice
thickness while the snow density uncertainty contributes 0.10 to 0.36 m,
depending on the freeboard and snow depth. The ICESat-G thickness estimates
use the Warren et al. (1999) climatology. This climatology has an RMS error
of between 0.05 and 0.14 m, depending on the month. The associated
uncertainty in the ice thickness is a factor of 6.96 larger (Kwok and
Cunningham, 2008), or 0.35 to 0.97 m. The Warren climatology may be biased
for recent years. Webster et al. (2014) find a 0.029 m decade-1 decline
in the spring snow depth in the western Arctic now dominated by first-year
ice over the period 1950–2013. This would mean a mean decline of 0.14 m
from 1960 to 2010 or roughly one-third of the spring snow depth.
Sampling error
As we have alluded to above, sampling error can be a significant and serious
source of uncertainty in comparing different ice thickness observations. All
of the samples are from different times and/or places, so there are real
differences in the nature of the ice sampled by the different measurements.
The method used here depends on obtaining a large number of observations
from a broad range of ice conditions so that comparisons in the mean can be
made while accounting for large-scale variations in the mean ice thickness.
The error in the fit includes random measurement errors, systematic
measurement errors, sampling errors, and errors related to the inadequacy of
the ITRP expression to fully represent the thickness variability.
One way to address the robustness of the results is to randomly withhold
some of the data and repeat the fits to see if the coefficients change
significantly. A set of 100 fits were computed for the entire Arctic Basin,
2000–2012, for each of which only half of the data, randomly selected for
each system, was used. The mean of the resulting indicator coefficients is
very similar to that found using all of the data and the variability of the
coefficients from this ensemble is comparable to the standard error,
σj, of the coefficients computed as part of the fit procedure.
For example, we can conclude that the IceBridge data for the full Arctic
Basin are significantly thicker than Air-EM, BGEP, ICESat-G, IOS-EBS, and the
submarines but perhaps not thicker than ICESat-J.
Coefficients of the ITRP indicator variables for fits that leave one
data source out at a time for the Arctic Basin, 2000–2012. The coefficients
for each source are grouped together. Grey bars show the coefficients for a fit
that includes all of the observations, and bars in other colors indicate which
source has been left out as shown by the colors of the diagonal labels
(same order as the bars). The black lines give the 1σ interval for the
coefficients. ICESat-G is always the reference.
Leave one source out
The importance of the individual data sources for computing the bias
coefficients can be explored by repeating the analysis while leaving out each
of the sources in turn. Do the bias coefficients change significantly?
Figure 6 shows a bar chart of the indicator
coefficients when just one data source is left out. The coefficients for
most of the sources are quite similar for all of the ITRP fits. The largest
variability is seen for the coefficients for IOS-EBS, which is not
surprising given the isolated location of these measurements. The IOS-EBS
coefficient is particularly sensitive to the exclusion of the BGEP or
submarine data. There is also a fair amount of variability for the IceBridge
coefficients, but in all cases the coefficients are still large. However, if
both ICESat data sets are excluded and the submarines are used as a
reference, we find very large changes in the relative magnitudes all of the
remaining coefficients (not shown). This indicates the great importance of
the satellite data in establishing the spatial structure of the ice
thickness fields when performing broad analyses of observing system differences.
Regional fits
The comparisons between data sets depend very much on the nature of the
samples available for each. If they are far removed from each other in space
or time, the true variability of the ice thickness may contaminate the
difference estimates. For example, a bias between the observations could be
partially resolved by the regression procedure with a spatial term if there
is no spatial overlap. In addition, the differences between measurement
systems may not be constant because the source of the bias, for example snow
thickness or small-scale sea ice variability, is not constant. One way of
addressing these uncertainties is to examine subsets of the data to see if
differences observed between the systems are more or less robust. We look at
five different regions, all for the period 2000–2012: (1) the entire Arctic
Basin and using all measurement systems (the fit mentioned above), (2) the
so-called SCICEX box in a broad region of the central basin that includes
all submarine observations, (3) a 500 km radius circle centered on the BGEP
moorings in the Beaufort Sea, (4) a 500 km circle centered on the North Pole,
where a variety of observations are concentrated, and (5) a 300 km circle in
the Lincoln Sea to evaluate Air-EM and IceBridge observations. Table 3 lists the summary
information for each fit and Fig. 7 shows their locations. The coefficients of the indicator variables provide an
estimate of the mean difference between each set of observations and the
reference set in the sense that the RMS error of the fit is minimized if
this difference is accounted for. Table 4 lists the values of the indicator coefficients for each fit and
the RMS error of the fit for each observation source. Figure 7 shows the relative magnitudes of the
coefficients for easy intercomparison of the bias terms determined for the
different regions.
The region, time period, number of observations used,
number of terms, multiple regression coefficient, and RMS error (m)
for each ITRP fit.
(a) Locations of five regional fits for the period
2000–2012 and (b) relative magnitudes of the ITRP indicator coefficients. The
magnitudes of the coefficients are grouped by observation source and color-coded
by region (the order of the bars is the same as that of the region names).
Grey depicts the coefficients for the fit for the entire basin.
Number of observations, the indicator coefficients and their σ
values, and the RMS error for each source for each regional fit for the
period 2000–2012.
Data from US submarines are available mostly from a data release area
defined by the US Navy (RPW08), the so-called “SCICEX box” (taken from the
project name Scientific Ice Expeditions). Of the 34 submarine cruises
available since 1975, there are only three cruises after 2000. However, the
box is a convenient way to restrict the geographic extent of the data
considered to a broad region in the central basin and to also compare our
results to those of RPW08. For the 2000–2012 period the submarine data are
still in good agreement with the reference, 0.14 ± 0.05 m; however, the
coefficients for Air-EM (0.81 ± 0.08 m) and IceBridge (0.98 ± 0.07 m)
are both notably thicker than the reference and submarines when compared
to the full-basin fit. In addition, if 2000, when the first submarine cruise
of the period occurred, is excluded the coefficient for the submarines
increases to 0.42 m and the difference between it and that of ICESat-J is
greatly reduced, similar to what we found earlier for the whole basin. These
changes illustrate the fact that the differences between observation systems
are not constant and may depend on the sample populations, the region, and
the time periods included in the analysis.
Beaufort Sea
In the Beaufort Sea the four BGEP moorings provide abundant data for the
entire annual cycle, and this is a good location to further assess the mean
differences between the data sets while restricting the amount of spatial
variability that is encountered. Within a 500 km circle of the center of the
mooring array there are Air-EM and IceBridge observations as well as the
satellite-based estimates. Compared to the reference, ICESat-J estimates are
0.54 ± 0.07 m thicker and IceBridge estimates are 0.77 ± 0.10 m
thicker, similar to what we found for the full basin
(Table 4). The Air-EM and BGEP coefficients are
both substantially larger than for the full basin, 0.87 ± 0.11 m and
0.31 ± 0.07 m, respectively. The difference between the two, 0.56 m, is
much larger than the difference between them for the fit for the basin, 0.10 m,
and is likely due to regional changes in the bias of the Air-EM data.
This again illustrates that comparisons between data sets can be highly
sensitive to the particular ice conditions encountered and that caution is
recommended in assuming that intercomparisons and validation results for one
area are applicable elsewhere.
North Pole
Abundant observations from submarines, IceBridge, Air-EM, and ICESat are
available in the vicinity of the North Pole. ICESat-G has no observations
closer than 400 km because of the nadir viewing of the satellite lidar while
the ICESat-J data set has estimates within this circle based on
interpolation from adjacent data points. A 500 km circle centered on the
pole includes observations from both data sets. Note that data from a
mooring at the pole, part of the North Pole Environmental Observatory, are
still being reprocessed (Moritz personal communication) and is not included. Within
this circle 508 observations are used for the fit. In this region the
IceBridge estimates are 1.13 m thicker than the submarine estimates and 0.59 m
thicker than the Air-EM estimates. ICESat-J estimates are 0.28 m thicker
than the ICESat-G estimates. The coefficients from this fit are in general
consistent with those for the entire basin (Fig. 7b and Table 4).
Lincoln Sea
Is the large thickness bias in the IceBridge observations seen in the
previous analyses robust? IceBridge observations have a coefficient larger
than that of any of the other measurement systems in each of the fits except
for the Beaufort Sea, where it is smaller than the Air-EM coefficient.
Perhaps the IceBridge data are not well represented in the regression
equation because they are concentrated in thick ice near the Canadian coast. We
can partially address the IceBridge bias by examining only IceBridge and
Air-EM measurements in a limited region in the Lincoln Sea, where there are
50 Air-EM and 76 IceBridge measurements within 100 km and one month of each
other during the springs of 2009, 2011, and 2012. The ITRP shows that for
this sample the IceBridge data are 0.75 ± 0.13 m thicker than the Air-EM
data. This is larger than the difference computed for the entire basin where
the difference between the two is 0.59 - 0.06 = 0.53 m
(Table 4). It is also larger than for the ITRP fits
for the SCICEX box and for the Beaufort Sea where the differences between
the two are smaller, 0.17 and -0.10 m, respectively. While we cannot be
confident of the exact magnitude of the bias and indeed as we have seen it
changes considerably from place to place, it is likely that the IceBridge
estimates are systematically thicker than any of the other measurements by
up to 1.0 m (Table 4).
Conclusions
There is no gold standard for the estimation of the mean thickness of sea
ice. All of the existing measurement techniques have one or more large
sources of uncertainty. In situ measurements from the surface cannot sample
the full thickness distribution. The submarine ULS measurements depend of
the first-return echo to determine the ice draft, which is a potential
source of unknown bias that may be a function of the bottom roughness. The
mooring ULS measurements may also be subject to this same source of error.
Both have potential errors in determining the open water level and
accounting for the correct snow water equivalent. The satellite and airborne
lidar observations depend on reliable detection of the surface height of
nearby leads to accurately determine the height of the ocean surface and
hence the total freeboard. The Air-EM measurements require an independent
estimate of the snow depth, as do the satellite lidar measurements. All of
the measurements struggle with obtaining an accurate mean value when the
thickness is highly variable within the sensor footprint due to ridging. Finally, none of the measurements have been verified against other
observations over regions that encompass the full ice thickness distribution
of the area.
This study has determined some broad measures of the relative bias of the
different systems. The ITRP method is dependent on having a large number of
independent observations from each system so that a function can be fit to
the thickness observations to account for the large-scale variability of the
ice thickness. In addition to the nonlinear space and time variables, a bias
term is included for each system that can contribute to the minimization of
the error of the fit by adding or subtracting a constant value to all
observations from a given system. This bias term can only be interpreted in
a relative sense: how much thicker or thinner, in the mean, is one system
compared to another? While we have typically used the ICESat-G system as a
reference here, that does not mean it is a priori considered to be more accurate
than the others. Indeed, nothing in the study speaks to the absolute accuracy
of the measurements.
When ordered by relative magnitude of the coefficient of each system
(Table 2), we see that the coefficient for IOS-EBS
has the largest negative value relative to ICESat-G. However, because these
measurements are in a small corner of the southeastern Beaufort Sea, we have
little confidence that this result is a good indicator of the bias of the
ULS measurements in this location compared to the other measurements. Of the
others, ICESAT-G, submarines, IOS-CHK, BGEP, and Air-EM are all in broad
agreement and in the mean are within 0.11 m of each other. However, we saw
that the submarine bias coefficient is sensitive to the inclusion of the
2000 cruise. ICESat-J is 0.42 m thicker than ICESat-G but in good agreement
with the submarine measurements in 2005. Finally, the IceBridge measurements
average 0.59 m thicker than ICESat-G measurements.
It is beyond the scope of this study to determine why some of the
observation systems appear to have biases, sometimes very significant,
compared to the others. Possible sources of these discrepancies are the
interpretation of ULS echo data, assumptions about snow depth or snow water
equivalent, and methods of determination of the ocean water level for the
lidars. While it is possible that there are systematic errors in determining
the measurement differences introduced by the different times and locations
of the observations, so called sampling errors, all of the systems, with the
possible exception of IOS-EBS and the submarines, have sufficient
observations spread over large spatial or temporal ranges to make this
unlikely. Figure 7 shows the range of the
coefficients determined with various spatial subsets of the data. For the
entire basin, the experiment in which only a random half of the data from
each system was used in a large set of fits gives very similar results to
that when using the full data set. The leave-one-out experiment showed that
the satellite measurements had a greater impact on the bias coefficients
than the other systems. While our results provide an estimate of the
relative biases of the measurement systems, they also point to the fact that
more research to understand, characterize, and correct these errors is
clearly required before we can homogenize the observational ice thickness record.
The ITRP annual mean basin-average ice thickness over the period 2000–2012
has declined 34 %, a trend of -0.58 ± 0.07 m decade-1, while the
September thickness has declined by 50 %. Finally, all of the observations
in the central Arctic Basin within the SCICEX box for the period 1975–2012
indicate that the annual mean ice thickness in this region has decreased
from 3.59 to 1.25 m, a 65 % decline. In September the mean ice thickness
has declined from 3.01 to 0.44 m, an 85 % decline.
Acknowledgements
This study was supported by the NASA Cryospheric Sciences Program under
grant number NNX11AF45G and by the National Science Foundation Division of
Polar Programs under grant number 1023283. We thank all of the data
providers for sharing ice thickness observations, often obtained under
difficult conditions. We thank Harry Stern and two reviewers for a careful
review of the manuscript.
Edited by: C. Haas
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