TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-10-2745-2016Benefits of assimilating thin sea ice thickness from SMOS into the TOPAZ systemXieJipingjiping.xie@nersc.nohttps://orcid.org/0000-0002-8602-2774CounillonFrançoisBertinoLaurenthttps://orcid.org/0000-0002-1220-7207Tian-KunzeXiangshanKaleschkeLarshttps://orcid.org/0000-0001-7086-3299Nansen Environmental and Remote Sensing Center, Bergen, NorwayInstitute of Oceanography, University of Hamburg, Hamburg, GermanyJiping Xie (jiping.xie@nersc.no)16November2016106274527619May20166June201615October201623October2016This 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://tc.copernicus.org/articles/10/2745/2016/tc-10-2745-2016.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/10/2745/2016/tc-10-2745-2016.pdf
An observation product for thin sea ice thickness (SMOS-Ice) is derived from
the brightness temperature data of the European Space Agency's (ESA) Soil
Moisture and Ocean Salinity (SMOS) mission. This product is available in
near-real time, at daily frequency, during the cold season. In this study, we
investigate the benefit of assimilating SMOS-Ice into the TOPAZ coupled ocean
and sea ice forecasting system, which is the Arctic component of the
Copernicus marine environment monitoring services. The TOPAZ system
assimilates sea surface temperature (SST), altimetry data, temperature and
salinity profiles, ice concentration, and ice drift with the ensemble Kalman
filter (EnKF). The conditions for assimilation of sea ice thickness thinner
than 0.4 m are favorable, as observations are reliable below this threshold
and their probability distribution is comparable to that of the model. Two
parallel Observing System Experiments (OSE) have been performed in March and
November 2014, in which the thicknesses from SMOS-Ice (thinner than 0.4 m)
are assimilated in addition to the standard observational data sets. It is
found that the root mean square difference (RMSD) of thin sea ice thickness
is reduced by 11 % in March and 22 % in November compared to the daily
thin ice thicknesses of SMOS-Ice, which suggests that SMOS-Ice has a larger
impact during the beginning of the cold season. Validation against
independent observations of ice thickness from buoys and ice draft from
moorings indicates that there are no degradations in the pack ice but there are some
improvements near the ice edge close to where the SMOS-Ice has been
assimilated. Assimilation of SMOS-Ice yields a slight improvement for ice
concentration and degrades neither SST nor sea level anomaly. Analysis of the
degrees of freedom for signal (DFS) indicates that the SMOS-Ice has a
comparatively small impact but it has a significant contribution in
constraining the system (> 20 % of the impact of all ice and
ocean observations) near the ice edge. The areas of largest impact are the
Kara Sea, Canadian Archipelago, Baffin Bay, Beaufort Sea and
Greenland Sea. This study suggests that the SMOS-Ice is a good complementary
data set that can be safely included in the TOPAZ system.
Introduction
The Arctic climate system has undergone large changes during the last 20 years: increase of temperature (Chapman and Walsh, 1993; Serreze et al.,
2000; Karl et al., 2015; Roemmich et al., 2015), decrease of sea ice extent
(Johannessen et al., 1999; Comiso et al., 2008; Stroeve et al., 2012), sea
ice thinning, and loss of sea ice volume (Rothrock et al., 1999; Kwok and
Rothrock, 2009; Laxon et al., 2013). The interpretation of such changes is
severely hampered by the sparseness and the complexity of the observational
network. A reanalysis database can combine the sparse observations with a
dynamically consistent model and is becoming an important tool.
While observations of sea ice concentrations (SIC) have been available for
the past 30 years, observations of sea ice thickness (SIT) are comparatively
sparse. An improved knowledge of SIT would be greatly beneficial, both for
model developments and for improving the accuracy of operational ocean
forecasting system. The initialization of SIT is also expected to improve
predictability on seasonal timescale (Guemas et al., 2014). Until the last
decade, observations of SIT were mostly limited to field campaigns or
submarine measurements. Major efforts in remote sensing have been proposed
to monitor the spatiotemporal evolution of SIT, and they gradually obtained
various products from different satellite retrieval algorithms. Measurements
of thick sea ice freeboard on basin-wide scales have been derived from laser
altimeters on board ICESat (e.g., Forsberg and Skourup, 2005; Kurtz et al.,
2009; Kwok and Rothrock, 2009) or from radar altimeters on ERS, Envisat, and
CryoSat-2 (e.g., Laxon et al., 2003; Giles et al., 2007; Connor et al.,
2009). Still, large uncertainties remain in the accuracy of the resulting
SIT estimates (larger than 0.5 m) due to uncertainties in the snow depth and
the sea ice density (Zygmuntowska et al., 2014). A new database based on
CryoSat-2 has been provided (Laxon, 2013; Ricker et al., 2014) and has been
made available in near-real time (Tilling et al., 2016). Finally, methods for
SIT retrieval based on measurements of the brightness temperature at a low
microwave frequency of 1.4 GHz (L-band: wavelength λa= 21 cm)
have been developed in preparation for the European Space Agency's (ESA)
Soil Moisture and Ocean Salinity (SMOS) mission (Heygster et al., 2009;
Kaleschke et al., 2010, 2013). It has been shown that SMOS
can be used to retrieve level SIT up to half a meter under cold conditions
(Kaleschke et al., 2012; Huntemann el al., 2014).
An improved retrieval method based on a radiative transfer model and a
thermodynamic sea ice model has been further proposed by considering the
variations of ice temperature, salinity, and a statistical SIT distribution
(Tian-Kunze et al., 2014). An operational product has been derived from this
method and is available at daily frequency (hereafter referred to as
SMOS-Ice). The SMOS-Ice has been validated during a field campaign in the
Barents Sea (Kaleschke et al., 2016; Mecklenburg et al., 2016). It provides
daily estimates of SIT and is available from October 2010 (Tian-Kunze et
al., 2014). In this study, we are testing the benefits of assimilating
SMOS-Ice into the TOPAZ system.
The TOPAZ forecasting system (Sakov et al., 2012) is a coupled ocean–sea ice
data assimilation system and is the main Arctic Marine Forecasting system in
the Copernicus Marine Services (http://marine.copernicus.eu/). It provides a
10-day coupled physical–biogeochemical forecast every day and a long-term
reanalysis from 1990 to 2015 (Sakov et al., 2012; Xie et al., 2016). At
present, TOPAZ assimilates several data types jointly with the ensemble
Kalman filter (EnKF): sea surface temperature (SST), along-track sea level
anomalies (SLA) from satellite altimeters, in situ temperature and salinity
profiles, and SIC and sea ice drift from satellites. The
reanalysis product of the TOPAZ system has been widely used in studies about
ocean circulation and sea ice in the North Atlantic Ocean or in the Arctic
region (Melsom et al., 2012; Johannessen et al., 2014; Korosov et al., 2015;
Lien et al., 2016). Although the capability for assimilating SIT has been
demonstrated in Lisæter et al. (2007), TOPAZ does not yet assimilate SIT
nor apply post-processing for this variable. The reanalysis in the period
1991–2013 has been compared to available observations at different periods
of time (Xie et al., 2016). It was found that TOPAZ underestimates the sea
ice draft compared to in situ drafts from sonar of the US Navy submarines
for the period 1993–2005 (Lindsay, 2013). In spring and autumn of 2003–2008,
the SITs in TOPAZ are in good agreement with those of ICESat data (Kwok and
Rothrok, 2009) with a spatial correlation 0.74 and 0.84 respectively.
However, the SIT in TOPAZ is too large (by more than 0.2 m) in the Beaufort
Sea and too low in the rest of the Arctic (up to 1 m). When compared against
the IceBridge SIT (Kurtz et al., 2013) for the period 2009–2011, it was
found that the thick SIT in the central Arctic is underestimated by 1.1 m in
TOPAZ. Such inaccuracies in the SIT are a common limitation of coupled
ice–ocean models in the Arctic (Johnson et al., 2012; Schweiger et al.,
2012; Smith et al., 2015).
The first demonstration of assimilating SMOS-Ice has been presented by Yang
et al. (2014) for the period from November 2011 to January 2012. The system
assimilates both SIT (thinner than 1 m) from SMOS-Ice and SIC from
Special Sensor Microwave Imager/Sounder (SSMIS) in a nested Arctic
configuration of the Massachusetts Institute of Technology general
circulation model (MITgcm). It uses the Localized Singular Evolutive
Interpolated Kalman (LSEIK; Nerger et al., 2005) data assimilation method
with a 15-member ensemble. It was found that assimilation of SMOS-Ice leads
to improvement of the SIT forecasts and to a small improvement for sea ice
concentration. A comparison of SIT from three moorings from the Beaufort
Gyre Experiment Program (BGEP) and from one autonomous ice mass balance
(IMB) buoy shows that the overestimation of SIT is reduced. The present
study follows up the work from Yang et al. (2014) but it further explores
the impact and relative importance of SMOS-Ice in the perspective of an
ice–ocean forecasting system:
the impact of assimilating SMOS-Ice is
tested both during the onsets of the melting and freezing seasons;
SMOS-Ice is tested together with a more complete observations network and
its relative contribution is quantified;
the results are tested with a
different model at slightly higher resolution, with a comparable
assimilation method but with a larger ensemble size.
This paper is organized as follows: Sect. 2 introduces the main components
of the TOPAZ system including the model, the assimilation scheme, and the
observations assimilated. In Sect. 3, we compare SMOS-Ice data to the
TOPAZ reanalysis for the period 2010–2014 and investigate potential biases
and whether conditions are favorable for data assimilation. In Sect. 4,
two Observing System Experiment (OSE) runs are conducted, consisting of two
assimilation runs with and without the SMOS-Ice data during 2014. In Sect. 5,
we compared the contributions of SMOS-Ice relative to other types of
observations for controlling the degree of freedom of the system during
assimilation.
Descriptions of the TOPAZ data assimilation systemThe coupled ocean and sea ice model
The ocean general circulation model used in the TOPAZ system is the version 2.2
of the Hybrid Coordinate Ocean Model (HYCOM) developed at University of
Miami (Bleck, 2002; Chassignet et al., 2003). HYCOM uses hybrid coordinates
in the vertical, which smoothly shift from isopycnal layers in the
stratified open ocean to z level coordinates in the unstratified surface
mixed layer. This feature has been demonstrated in a wide range of
applications from the deep oceans to the shelf (Chassignet et al., 2009).
The NERSC-HYCOM model is coupled to a one-thickness category sea ice model,
for which the ice thermodynamics are described in Drange and Simonsen (1996)
and the ice dynamics are based on the elastic–viscous–plastic rheology
described in Hunke and Dukowicz (1997) with a modification from Bouillon et
al. (2013). In the model, there is a minimum thickness of 0.1 m for both new
ice and melting ice. The model grid is produced using conformal mapping
(Bentsen et al., 1999) and has a quasi-homogeneous horizontal resolution of
12–16 km in the Arctic as shown in Fig. 1.
TOPAZ model domain and horizontal grid resolution (km) with color
shading. The blue line delimits the Arctic region (north of 63∘ N)
and other color lines delimit the three marginal seas discussed in this
study.
The temperatures and salinities at the model lateral boundaries are relaxed
to a combined climatology of the World Ocean Atlas of 2005 (WOA05, Locarnini
et al., 2006) and the version 3.0 of the Polar Science Center Hydrographic
Climatology (PHC; Steele et al., 2001). A seasonal inflow is imposed at the
Bering Strait with a transport that is following the observed estimate from
Woodgate et al. (2012). A balanced outflow of similar mean transport is
imposed at the southern boundary of the model. The TOPAZ system uses
atmospheric forcing from ERA-Interim (Dee et al., 2011).
The EnKF data assimilation
The analysis with the standard EnKF, is expressed as follows:
Xa=Xf+KY-HXf,
where X is the ensemble of model state vector, and the superscripts
“a” and “f” refer to the analysis and the forecast respectively. The
ensemble consists of 100 dynamical members. H is the observation
operator and Y is the perturbed observation matrix. The term
innovation refers to the misfits between the observations and the model:
i.e., the term in brackets in Eq. (1). The Kalman gain K in
Eq. (1) is calculated as
K=PfHTHPfHT+R-1,
where R is the matrix of observation error variance and
Pf is the matrix of background error covariance, which can be
calculated by an ensemble anomalies with N members – P=
(1/N-1) ⋅AAT. The superscript T denotes a matrix
transpose, and A is the ensemble of anomalies. The ensemble
anomalies is calculated as
A=X-x‾IN,
where x‾ is the ensemble mean vector, and
IN=[1,…,1] is the vector with all components equal
to 1.
The TOPAZ system uses the deterministic EnKF (DEnKF; Sakov and Oke, 2008),
which is a square-root filter implementation of the EnKF that solves the
analysis without the need for perturbation of the observations. The DEnKF
overestimates the analyzed error covariance by adding a semi-definite
positive term to the theoretical error covariance given by the Kalman
filter, which mitigates the need for inflation (Sakov and Oke, 2008).
In the DEnKF, the ensemble mean is updated by assimilating the unperturbed
observation y:
xa‾=xf‾+K(y-Hxf‾).
The analyzed ensemble anomaly is calculated as follows:
Aa=Af-12KHAf.
The full ensemble is reconstructed by adding the two terms as follows:
Xa=Aa+xa‾IN,
where Xa is the matrix of the updated model states after
assimilation.
Overview of observations assimilated in TOPAZ system in the official run.
All observations are retrieved from http://marine.copernicus.eu
and assimilated weekly.
Conditional expectations of TOPAZ versus SMOS-Ice (with bin of
5 cm) for each month calculated over the period 2010–2014. The cyan
error bars correspond to the RMSD against observations within each bin. The
red error bars correspond to the averaged standard deviations of observation
error. The gray dashed line denotes the line y=x.
An overview of the observations assimilated in the present TOPAZ system is
given in Table 1. Observations are quality controlled and the super-observation algorithm is used
(i.e.,
the process of combining observations falling within the same model grid
cell) as in Sakov et al. (2012). TOPAZ assimilates the following data sets
on a weekly basis: the gridded SST from the Operational Sea Surface
Temperature and Sea Ice Analysis system (OSTIA, Donlon et al., 2012); sea
ice concentration from the Ocean & Sea Ice Satellite Application Facility
(OSISAF); along-track sea level anomaly by Collecte Localisation Satellites
(CLS); delayed-mode profiles of temperature and salinity from Ifremer; and
the sea ice drift during the 3 days prior to the analysis f rom the CERSAT
(Centre ERS d'Archivage et de Traitement) of IFREMER (French Research
Institute for Exploitation of the Sea). All these standard measurements are
retrieved from http://marine.copernicus.eu. The SLA data and
the sea ice drift data are assimilated asynchronously (see Sakov et al.,
2010).
Bias analyses for thin ice thickness
The TOPAZ system has computed a reanalysis at daily frequency for ocean and
sea ice variables. Its sea ice thickness has been validated against in situ
data and satellite observations in Xie et al. (2016). Data assimilation
assumes that the model and observations errors are unbiased. In this
section, we investigate the bias by analyzing the thickness misfits for thin
sea ice during five cold seasons from 2010 to 2014.
SMOS-Ice products (version 2.1) are available during the cold season (from
15 October to 15 April) at daily frequency from 2010 and up to
near-real time. The data set is provided by University of Hamburg (Kaleschke
et al., 2012, 2013; https://icdc.zmaw.de/1/daten/cryosphere/l3c-smos-sit.html).
Here, the daily averaged SITs of TOPAZ are compared to the observations. The
spatial or temporal bias and root mean square difference (RMSD) are
calculated as follows:
Bias=1n∑i=1n(Hx‾if-yi),RMSD=1n∑i=1n(Hx‾if-yi)2,
where x‾if is compared to observations at
similar time, H is the observation operator (see Eq. 1), and n is
the number of available observations within the calculation period. Note
that we compare the TOPAZ SITs to imperfect observations, which contains
error and may also be biased. As such, the bias as formulated in Eq. (4)
refers to the difference between the model and observation biases calculated
against an unknown truth. Still it is reasonable to assume that the bias in
the observation is smaller than in the model and that the bias obtained with
Eq. (4) mainly accounts for model bias.
Figure 2 shows the simulated SIT from the TOPAZ reanalysis as conditional
expectations with respect to SMOS-Ice data sorted into bins of 5 cm. Again,
the SITs from TOPAZ in Fig. 2 are selected at the same locations and time as
observations. Overall, the SIT in TOPAZ tends to be overestimated. The
overestimation varies from month to month and with the amplitude of SIT
(more pronounced for thick ice). For SIT lower than 0.4 m, the match between
the observations and TOPAZ is relatively good through the cold season. There
is no clear bias between October and December but a slight increasing thick
bias from January to April. For SIT larger than 0.4 m, TOPAZ clearly
overestimates SIT compared to observations during October and
February–April, while it underestimates it in November. The penetration
depth for the L-Band microwave frequency into sea ice is about 0.5 m
(Kaleschke et al., 2010; Huntemann et al., 2014), and the effect of ice
melting leads to saturation beyond 0.4 m (see Heygster et al., 2009). For
these reasons, assimilation of SITs thicker than 0.4 m appears as
problematic because the large bias from observations or models may be
transferred to other variables (e.g., in the ocean) via the multivariate
properties of our data assimilation method (note that TOPAZ uses strongly
coupled data assimilation between the ocean and sea ice). In the following
we will only assimilate the SIT observations less than 0.4 m.
We now investigate whether there is an interannual, seasonal, and spatial
variability in the bias of SIT. Figure 3 shows the yearly bias (as defined
in Eq. 4) for SIT thinner than 0.4 m during the period 2010–2014. After
2011, the thick bias is increasing, reaching a maximum of 0.1 m in 2014.
There is some seasonality in the bias, and the thick bias is larger in March
than in November. There is a large spatial variability in the distribution
of the bias (right panel of Fig. 3), with the bias being largest in the
Beaufort Sea and in the Kara Sea. We therefore select the periods of March
and November 2014 to set the assimilation system in the most difficult
situations.
Yearly thickness biases of thin sea ice from TOPAZ compared to
SMOS-Ice observations (Eq. 4). The black line represents the yearly mean
bias. Left: the green (red) line represents the mean bias for March
(November) months. Right: the colored lines represent the biases in the
Barents Sea, the Kara Sea, and the Beaufort Sea.
Observing System Experiment of SMOS-IceDesign of OSE runs for SMOS-Ice
The SMOS-Ice ice thickness data are gridded at a resolution of approximately
12.5 km and are available at daily frequency during the cold season. For the
reasons explained in previous section, we only used the observations with
thickness lower than 0.4 m and with a distance of at least 30 km away from
the coast (see Sect. 3). The related innovations in Eq. (1) are
expressed as sea ice volume:
ΔSIT=ysmos-H(h‾mod×f‾mod),
where ysmos is the observed SIT for thin ice from SMOS,
H is the same observation operator as in Eq. (1),
h‾mod is the ensemble mean of ice thickness within the
grid cell, and f‾mod is the ensemble mean of SIC. Note
that the model has a minimum thickness of 0.1 m, but SIT observations of ice
thinner than 10 cm can be assimilated quantitatively because the ensemble
mean from 100 ensemble members can take values as low as 1 mm. To highlight
the additional impact of SMOS-Ice observations, two OSE runs are carried
out:
The “official run” uses the standard observational
network of the TOPAZ system. It assimilates every week the SLA, SST, in situ profiles of temperature and salinity, sea ice
concentrations, and sea ice drift data (listed in Table 1).
The “test run” assimilates the SMOS-Ice data in addition to the
observations assimilated in the official run. In this study, the observation
errors are assumed to be spatially uncorrelated. The observation error
variance (diagonal term of R term in Eq. 2) for SIT is set as
recommended by the provider. It is estimated based on a priori estimate of
the maximum uncertainty of different input parameters: surface air
temperature, bulk ice temperature, and bulk ice salinity (Tian-Kunze et al.,
2014). We consider an observation error variance of 25 m2 to be the
threshold beyond which observations are assumed fully saturated and are not
assimilated in our system; this, however, generally does not occur for SIT
values lower than 40 cm (see Fig. 4).
Figure 4 shows the uncertainties of the observations as function of the
observed thickness from SMOS in March and November of 2014. There is a
linear increase of the observation error with SMOS-Ice SIT with a slope of
approximately 2.6. There is no visible seasonal variation in this relation
(not shown).
In the following, the two parallel OSE runs are carried out at two typical
time periods of the cold season: at the onsets of the ice melting from
15 February to 31 March and at the freezing time from
15 October to 30 November 2014.
Scatter plot of the uncertainty of the observation as function of
the observed thickness from SMOS in March and November of 2014.
Validation against assimilated measurements
The error analysis focuses on the following target quantities: SIT, SIC, SST,
and SLA. All quantities are derived from the ensemble mean daily averages
that are compared to observations at same locations and time. The bias is
calculated as specified in Eq. (4) and the RMSD as in Eq. (5).
The spatial distribution of selected SMOS-Ice data for thin sea ice is shown
in the top panels of Fig. 5 during March and November of 2014. In March, the
available observations in the Beaufort Sea are very few and unevenly
distributed – mainly located in the coastal areas. Hence, most of the
observations are unreliable (close to the error saturation threshold at 5 m)
or too thick (> 0.4 m) to be assimilated. Therefore in the
following, the results for the Beaufort Sea are only presented for November.
In the middle panels of Fig. 5, the differences of RMSD for sea ice
thickness between the official run and the test run are shown (red
color indicates an improvement due to assimilation of SMOS-Ice and blue a
degradation). In March, the improvements are mainly found to the east of
Franz Josef Land and to some extent near the ice edge in the Greenland Sea.
In November, the reduction of RMSD is larger than 0.2 m in the Beaufort Sea,
the Greenland Sea and to the North of Svalbard. Finally, the differences of
monthly ice thickness between the official run and the test run are shown in
the bottom panels of Fig. 5. They suggest that assimilating SMOS-Ice leads
to a reduction of sea ice thickness both in March and November 2014.
Top row: number of the valid SMOS-Ice data in March (left) and in
November (right) of 2014. The trajectories of the buoys 2013F and
2013G (2013F and 2014F) from IMB are the blue lines in
March (November). Their first positions are marked by circle and triangle
respectively. In March (November), the mooring locations from BGEP –
2013a, b, and d (2014a, b, and d) – are marked
by diamond, square, and pentagram respectively. Middle row: difference of
RMSDs for the thin SIT between official run and test run. The black line
denotes the 0.2 m isoline. Bottom row: difference of SIT between official run and test run. The black line denotes the 0.2 m isoline, and the green
(magenta) line is the 15 % concentration isoline from OSISAF (official run).
Daily time series of the bias (marked with crosses) and the RMSD
(marked with circles) calculated for the Arctic region in the official run
(magenta) and the test run (blue) for different variables in March (left)
and November (right).
Daily time series of the mean SIT for thin sea ice in the Kara Sea
(top row), the Barents Sea (middle row), and Beaufort Sea (bottom row) in
March (left) and November (right). The light (dark) gray
shading is the daily spatial RMSD of thin sea ice in the test run (official run).
Based on Eqs. (4) and (5), the time series of daily bias and RMSD for thin
ice thicknesses in the OSE runs are shown in the top panels of Fig. 6. The
bias of thin SIT is reduced from 16 to 12 cm in March and from 7
to 4 cm in November, when SMOS-Ice data are assimilated. The RMSD of thin SIT is
reduced from 35 to 31 cm in March and from 27 to 21 cm in November.
This corresponds to a reduction of the bias of 25 % in March and 43 % in
November, and a reduction of the RMSD of about 11 % in March and 22 % in
November. In the other panels of Fig. 6, the bias and RMSD of SIC, SST, and
SLA are presented. There is a slight benefit for the bias and RMSD of SIC
(i.e., the reduction of the SIC RMSD is about 0.001), but the statistics for
SST and SLA are unchanged.
Daily time series of SITs from official run (crossed magenta line)
and test run (dashed blue line) compared to the buoy measurements from IMB
(squared black line). The daily standard deviations of the observations are
shown with error bars. The buoy locations and their drift trajectories in the
month are shown in Fig. 5. Upper row covers the period 15 February to
30 March 2014 by (a) Buoy 2013F and (b) Buoy 2013G.
Bottom row covers period 15 October to 30 November 2014 by
(c) Buoy 2013F and (d) Buoy 2014F.
Comparison of sea ice drafts from the official run (square magenta
line), the test run (dashed blue line), and the bottom-tethered moorings
of BGEP. The left (right) panels are for March (November) 2014. The daily
histograms of sea ice draft (frequency percents for 0.1 m bins) are shown
with shading colors. The positions of the moorings are marked in Fig. 5.
The averaged thicknesses of thin sea ice in the marginal seas – in the Kara
Sea, Barents Sea, and Beaufort Sea – are shown with marked lines in the
panels of Fig. 7. The corresponding daily RMSDs of ice thickness relative to
thin SMOS-Ice data are added with shading. In each month, there are four
assimilation steps marked with vertical lines.
In the Kara Sea, the thickness observed in March is very stable with a
slight gradual increase. There is a relatively uniform reduction of RMSD by
about 21 %, which is mainly the result from a correction of the large (too
thick) bias in the model. In November, the bias is much smaller and the
resulting improvement is small (8 %), but the performances
improve slightly throughout the month for RMSD.
In the Barents Sea, the observations of SIT in March show an increasing
trend. The official run shows initially a large (thick) bias that reduces as
SIT increases in the observations. Assimilation of SMOS-Ice data reduces
the initial bias well, but the bias converges towards the official run at
the end of the month and so does the RMSD. On average, the RMSD of SIT is
decreased by approximately 27 % from the test run. In November, the
observations show large variability that is well captured in the official run but the ice is initially too thick. The RMSD reduction of the test run
compared to the official run is about 19 % and both the bias and the RMSD
are reduced.
In the Beaufort Sea, there are too few observations to provide a
representative estimate of the system performance in March (top panels of
Fig. 5) and the statistics are not presented. In November, the observations
show an increasing trend and the official run shows once again a relatively
large thick bias initially. The RMSD in the test run is reduced by about
51 %, which is mainly caused by a reduction of the bias. The increasing
trend in the test run is in relatively good agreement with the observations.
Validation against independent observations of SIT and sea ice draft
Three IMB buoys (Perovich et al., 2009;
http://imb.erdc.dren.mil/buoyinst.htm) are available for independent
validation during our period of study (2013F, 2013G, and
2014F). Their drift trajectories are shown in Fig. 5 for March and
November 2014. On 1 March 2014, the buoys of 2013F and
2013G are located at 150.8∘ W, 74.8∘ N and
157.9∘ W, 75.3∘ N. And on 1 November 2014, the
buoys 2013F and 2014F are located at 158.4∘ W,
77.6∘ N and 146.3∘ W, 76.7∘ N respectively. In
Fig. 8, the daily SIT of the OSE runs are compared to those of the buoys
along their trajectories. Between 15 February and 30 March, the SITs
of the two runs are identical and are increasing from 1.6
to 1.9 m while the observations show a more moderate increase from 1.5 to
1.65 m. It should be noted that the increase in the model is not necessarily
caused by thermodynamic growth only since the modeled ice motions may differ
from the buoys trajectories. Between 15 October and
30 November (buoys 2013F and 2014F), the SIT in the test run
is slightly improved compared to the official run (with an improvement of
2 cm). It is expected that the impact of SMOS-Ice on the two buoys is small
because they are located far away from the locations where SMOS-Ice data are
assimilated (shown in the top panels of Fig. 5). The TOPAZ system uses
localization, meaning that the impact of observations during assimilation is
limited to a certain radius and their influence reduces as function of
distance. In the TOPAZ system, the effective localization radius is 90 km.
Still, it is encouraging to see that the improvements seem to be increasing
with time, suggesting that the region influenced by SMOS-Ice is gradually
spreading across the domain.
Monthly averaged DFS from the test run in
March (upper) and in November (lower) for sea ice thickness
from SMOS-Ice (left column), sea ice concentration from OSISAF (middle
column), and the total DFS of all assimilated observations (right column).
The black line denotes the isoline of DFS equal to 2.
Observations of sea ice drafts from moored sonar data are another source of
independent observations. There are in total six moorings: 2013a, b, and
d in March 2014 and 2014a, b, and d in November 2014, the
locations of which are shown in Fig. 5. These measurements are available from BGEP
(Kishfield et al., 2014; http://www.whoi.edu/page.do?pid=66559). They use
moored upward-looking sonar instruments and collect year-round time series
measurements of the sea ice draft distribution (into 0.1 m bins) at daily
frequency. These data are processed to filter out wave action in the summer
months that may lead to the removal of thin draft measurements (Krishfield
et al., 2014). This can be problematic if the model estimates are lower than
the observed values. The sea ice draft from TOPAZ is diagnosed as proposed
in Alexandrov et al. (2010), i.e.,
di=hiρiρw+hsnρsnρw,
where di is sea ice draft, hi is ice thickness, and hsn is the
modeled snow depths. The constant ρi, ρw, and
ρsn are the densities for ice, water, and snow (respectively
900, 1000, and 300 kg m-3). In March 2014, the
observed sea ice drafts are mostly distributed between 0.8 m and 1.6 m (see
Fig. 8). Both OSE runs overestimate the sea ice drafts in March and perform
identically. In November 2014, the observed sea ice drafts are thinner
(< 1 m). The sea ice drafts from the OSE runs are again
overestimated in all three locations. The averaged draft difference in the
two runs is about 1 cm at the two moorings 2014a and b and about 16 cm
at the mooring 2014d, which is located closest to locations where SMOS-Ice has
been assimilated (see Fig. 5). We have also compared the two OSE runs in
March 2014 with the NASA IceBridge SIT Quick Look (QL) data set available
from National Snow and Ice Data Center. The analysis leads to similar
conclusions (not shown), which is that assimilation of SMOS-Ice only yields
improvements of SIT near the ice edge near the location where SMOS-Ice is
assimilated but does not yield degradation in other places.
Relative contributions of each observational data set in the total
DFS during March 2014. (a) Sea ice concentration from
OSISAF; (b) sea ice thickness from SMOS-Ice;
(c) temperature profiles; (d) SST; (e) along-track
sea level anomaly (SLA); (f) salinity profiles. The black line is the
20 % isoline.
Relative impact of the SIT from SMOS-Ice
In this section, the quantitative benefit of assimilating SMOS-Ice into the
TOPAZ system is compared to other observations assimilated. To do so, we
evaluate a performance metric calculated during the analysis, the degree of
freedom for signal (DFS), which is widely used for such purposes (Rodgers,
2000; Cardinali et al., 2004). During the assimilation, one can calculate the
DFS as follows:
DFS=tr∂y^∂y=tr∂HXa∂y=trKH.
Here, the matrix H is the observation operator as in Eq. (1),
and tr defines the trace, applied to the matrix (KH). The DFS
measures the reduction of mode that can be attributed to each observation
type. A value of DFS close to 0 means that the observation has no impact,
while a value of m means that the assimilation has reduced the number of
degree of freedom of the ensemble by m. Note that the reduction cannot exceed
the ensemble size, i.e., 100 here. In Sakov et al. (2012), it was recommended
that the DFS should not exceed 10 % of the ensemble size to avoid a
collapse of the ensemble spread.
Same as Fig. 11 for November 2014.
In the following the term DFSij denotes the DFS of the assimilation at
time i, of the jth type of observations, as calculated by Eq. (7).
The averaged DFS over a specific time period is calculated as follows:
DFS‾j=1m∑i=1mDFSij,
where the subscript j represents the jth type of the assimilated
observations, the subscript i is time, and m is the total number of
assimilation steps within the considered time period (e.g., four for a monthly
estimate with weekly assimilation). The DFS values are calculated at each
model grid cell. In Fig. 10, we are plotting the averaged DFS maps (as
defined in Eq. 8) for the different observation data sets assimilated in
March and November. In the Arctic the total DFS is dominated by the ice
concentration that reaches large value (approximately 6) near the ice edge.
The DFS for SMOS-Ice is comparatively small and is larger in March than in
November. In some regions, the monthly DFS of SMOS-Ice reaches values larger
than 2.
Furthermore, based on the sum of the DFS of all observation types
assimilated in TOPAZ, we can estimate the relative impact of the jth
type of observations (RDFSj):
RDFSj=DFS‾j∑l=1ODFS‾l×100%,
where O is total number of observation types. Figure 12 shows the relative
contribution of each observational data set in March. As expected, the
assimilation of ice concentration dominates the total DFS, while the impacts
of SST and SLA are limited to the region that are not ice covered. Profiles
of ocean temperature and salinity near the North Pole in the Arctic are
collected by the Ice-Tethered Profiler Program (Krishfield et al., 2008;
Toole et al., 2011). They have a very large impact but are very sparse.
In March the SMOS-Ice data have a significant impact (> 20 % of
the total DFS) in the northern Barents Sea, the western Kara Sea, Baffin
Bay, the Greenland Sea, and Hudson Bay. In November, the relative
contribution is still significant in the Barents Sea, the Kara Sea, and
the Greenland Sea, but it is also significant in the Beaufort Sea and in the
Canadian Archipelago.
Summary and discussion
The thickness observations of thin sea ice in the Arctic can be derived from
SMOS brightness temperature at 1.4 GHz (Tian-Kunze, et al., 2014; Kaleschke
et al., 2016). This data set is available in near-real time since 2010 at
daily frequency. The study in this paper investigates the impact of
assimilating this data set within the TOPAZ system, which is the Arctic
component of the Copernicus Marine Services. It is shown that for thin ice
(less than 0.4 m), the TOPAZ reanalysis and the SMOS-Ice have comparable
distributions (though TOPAZ slightly overestimates the thin ice thickness
from January to April) and that conditions are favorable for assimilating
this data set.
We investigate the impact of assimilating SMOS-Ice (thinner than 0.4 m) in
TOPAZ that already assimilates ice concentration, ice drift, SST, SLA, and
temperature and salinity profiles. The comparison is carried out for two
periods: February–March and October–November 2014. The study shows that
the assimilation of SMOS-Ice data reduces the thickness RMSD of thin sea ice
in March and in November by about 11 and 22 %, respectively, mainly
caused by the reduction of the bias (too thick sea ice that seems larger in
2014 than in previous years). There are also some small improvements for
SIC. The RMSDs for SST and SLA remain unchanged but are not degraded.
When compared to independent observations of SIT (IMB buoys) and sea ice
draft (BGEP moorings) it is found that assimilation of SMOS-Ice yields
improvements near the ice edge next to where SMOS-Ice has been assimilated
but does not lead to improvements nor degradations in the rest of the
Arctic.
In this study, the DFS is used to evaluate the relative contributions of
assimilated observations to the reduction of error in the TOPAZ system. The
SMOS-Ice data have a smaller impact than ice concentration but also a
significant contribution (defined as larger than 20 % of the total impact
from all observations) in some areas, namely in the Greenland Sea, the Kara
Sea, the Barents Sea, Baffin Bay, and Hudson Bay in March and in the
Greenland Sea, the Kara Sea, the Barents Sea, the Beaufort Sea, and the
Canadian Archipelago in November.
These studies follow from the first attempt of assimilation of SMOS-Ice with
the LSEIK in a regional MITgcm configuration (Yang et al., 2014). Compared to
this study, it is found that assimilation of SMOS-Ice has a more moderate
impact. This may be related to the fact that TOPAZ uses a more complete
observation network and that the assimilation has been spun up over a longer
period of time (from 1989). We also find that assimilation of SMOS-Ice is
comparatively larger in October–November than in February–March the time
period when Yang et al. (2014) tested assimilation of SMOS-Ice. We also
verified that assimilation of SMOS-Ice does not degrade ocean variables (SST
and SLA), which could happen with a strongly coupled data assimilation
scheme. Finally, we quantified the relative influence of SMOS-Ice for
constraining the mode of variability in TOPAZ compared to a standard
observation network.
To conclude, our study suggests that SMOS-Ice can be assimilated without
degradation of other skills in our operational forecasting system. The
benefits are generally small but can be significant for some regions near
the ice edge. However, further work needs to be done to better understand
the uncertainty of the assimilated SIT from the SMOS-Ice. Recently, Yang et
al. (2016) tested the sensitivity of assimilating the SMOS-Ice data with the
LSEIK during the winter of 2011–2012, and they found that perturbations of the
atmospheric forcing is important for improving the performance of
assimilation, in agreement with Lisæter et al. (2007).
In the future, we may use the “saturation ratio” that is defined by the
relationship of the variable L-band penetration depth and the maximal
retrieval thickness as a function of temperature and salinity with which we
can better identify the valid observations of sea ice thickness from SMOS.
In addition, the satellite CryoSat-2 provides freeboard height data in thick
ice that can complement the observations from SMOS (Kaleschke et al., 2010).
The new sea ice thicknesses derived from a combination of SMOS and CryoSat-2
will be soon available (Kaleschke et al., 2015). Incidentally, the
US Navy Arctic Cap Nowcast/Forecast System (ACNFS) is currently testing the
assimilation of a combined sea ice thickness product (personal communication
from David Hebert) where the sea ice thickness is blended from SMOS-Ice and
CryoSat-2 based on each satellite retrieval error.
Data availability
The official run used in this
paper is available from CMEMS (http://marine.copernicus.eu) with
the name ARCTIC_REANLYSIS_PHYS_002_003. The test run assimilates
SMOS-Ice data in addition to the data set assimilated in the official run.
The model outputs from the test run are available from
10.11582/2016.00005. The SMOS-Ice data are available at
https://icdc.cen.uni-hamburg.de/thredds/catalog/ftpthredds/smos_sea_ice_thickness/v2/catalog.html.
The assimilation code is available at https://svn.nersc.no/enkf and the
coupled ocean and sea-ice code is available at
https://svn.nersc.no/repos/hycom/. The simulations were processed with
the supercomputer hexagon.bccs.uib.no, a Cray XE6 distributed memory
system that consists of 696 nodes interconnected with a high-bandwidth,
low-latency switch network (Gemini, 2.5D torus). Each node has two 16-core
AMD “Interlagos” processors (2.3 Ghz) and 32 GB memory. The total number
of cores is 22272. The file system is Lustre.
Acknowledgements
The authors are grateful to two anonymous reviewers and Jennifer Hutchings
for their insightful comments that were helpful in improving the paper.
Thanks to Y. Wang for useful discussions. We thank to the US National
Snow and Ice Data Center (NSIDC) for providing the IceBridge data. This
study was supported by ESA contracts 4000101476/10/NL/CT and
4000112022/14/I-AM and CPU time from the Norwegian Supercomputing Project
(NOTUR II grant number nn2993k).Edited by: J. Hutchings
Reviewed by: two anonymous referees
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