Mapping sea ice concentration (SIC) and understanding sea ice properties and
variability is important, especially today with the recent Arctic sea ice
decline. Moreover, accurate estimation of the sea ice effective temperature
(Teff) at 50 GHz is needed for atmospheric sounding applications
over sea ice and for noise reduction in SIC estimates. At low microwave
frequencies, the sensitivity to the atmosphere is low, and it is possible to
derive sea ice parameters due to the penetration of microwaves in the snow
and ice layers. In this study, we propose simple algorithms to derive the
snow depth, the snow–ice interface temperature (TSnow-Ice) and
the Teff of Arctic sea ice from microwave brightness temperatures
(TBs). This is achieved using the Round Robin Data Package of the ESA sea ice
CCI project, which contains TBs from the Advanced Microwave Scanning
Radiometer 2 (AMSR2) collocated with measurements from ice mass balance buoys
(IMBs) and the NASA Operation Ice Bridge (OIB) airborne campaigns over the
Arctic sea ice. The snow depth over sea ice is estimated with an error of
5.1 cm, using a multilinear regression with the TBs at 6, 18, and 36 V. The
TSnow-Ice is retrieved using a linear regression as a function
of the snow depth and the TBs at 10 or 6 V. The root mean square errors
(RMSEs) obtained are 2.87 and 2.90 K respectively, with 10 and 6 V TBs.
The Teff at microwave frequencies between 6 and 89 GHz is
expressed as a function of TSnow-Ice using data from a
thermodynamical model combined with the Microwave Emission Model of Layered Snowpacks. Teff is estimated from the TSnow-Ice
with a RMSE of less than 1 K.
Introduction
In situ observations of the variables controlling the sea ice
energy and momentum balance in polar regions are scarce. One way to overcome
this observational gap is to use satellites for measuring sea ice properties.
The objective of this study is to estimate key sea ice variables from
satellite remote sensing to improve current sea ice models and prediction,
sea ice concentration (SIC) mapping in the EUMETSAT Ocean and Sea Ice
Satellite Application Facility (OSISAF) project, and polar atmospheric
sounding applications.
Sea ice thermodynamics is controlled by the regional heat budget
. In general, sea ice is covered by snow, which can reach a
mean thickness of up to ∼50 cm in the Arctic . Snow on
sea ice strongly affects the sea ice energy and radiation balance, with its
high insulation of heat and reflectivity of solar radiation. Snow is a poor
conductor of heat: it insulates the sea ice and reduces the winter ice growth
. In summer, its high albedo reduces the sea ice melting
rate. The high albedo of snow on sea ice compared to open-water albedo plays
an important role in the sea ice albedo feedback mechanism and Arctic
amplification . suggest that the recent sea
ice growth has been effectively limited by the increase in snow depth on thin
ice during winter. Current sea ice models include snow schemes (e.g.
), with the snow depth and temperature gradient in the
snow pack modulating the sea ice growth and melt. Improved estimates of snow
depth (Ds), as well as snow–ice interface temperature
(TSnow-Ice) from satellite observations would provide valuable
information on the vertical thermodynamics in the snow and ice to improve
current sea ice models and therefore the prediction of sea ice growth.
Here we propose using a simple algorithm to retrieve Ds and
TSnow-Ice from passive microwave observations from the Advanced
Microwave Scanning Radiometer 2 (AMSR2), based on a large data set of
collocated in situ and satellite observations. An extensive Round
Robin Data Package (RRDP) (,
https://figshare.com/articles/Reference_dataset_for_sea_ice_concentration/6626549,
last access: 15 January 2019) has been developed
during the European Space Agency (ESA) sea ice Climate Change Initiative
(CCI) project and the SPICES (Space-borne observations for detecting and
forecasting sea ice cover extremes) project
(http://www.seaice.dk/ecv2/rrdb-v1.1/, last access: 15 June 2017). It contains in situ
data from the ice mass balance buoys (IMBs), and the Operation Ice Bridge
(OIB) airborne campaigns collocated with AMSR2 brightness temperature
measurements between 6 and 89 GHz.
Algorithms already exist to retrieve the snow depth from microwave
observations. and use the spectral
gradient ratio of the 19 and 37 GHz (GR37/19) in vertical polarization to
deduce the snow depth over sea ice. This method has been developed for dry
snow on first-year ice (FYI) in Antarctica, and it is applicable only to this
ice type. Sea ice emissivity depends on the ice type. At frequencies ≥18 GHz, the ice emissivity is higher for FYI than for multi-year ice (MYI)
. The difference of emissivity between the 19
and 37 GHz can be used to retrieve the snow depth or the sea ice type.
Therefore, the snow depth algorithms which use this gradient ratio (GR37/19)
are strongly dependent on the ice type. Improvements by
have been suggested by and . More
recently, revisit the methodology for the Arctic region,
using a new gradient ratio between 7 and 19 GHz (GR19/7) to derive snow
depths over both FYI and MYI. For their study, they use the snow depths of OIB
campaigns obtained in March and April. With the help of the RRDP, we will
extend the methodology to the full winter (from 1 December to 1 April) for
the Arctic region using the IMB snow depth data.
showed from radiative transfer simulations that there is a
high linear correlation between the TSnow-Ice and the passive
microwave observations at 6 GHz. Preliminary results from
evidenced the possibility of deriving the temperature of
sea ice from passive microwave observations using simple regression models.
This work will be extended here to estimate TSnow-Ice over
Arctic sea ice.
Passive microwave satellite observations between 50 and 60 GHz are
extensively used to provide the atmospheric temperature profiles in Numerical
Weather Prediction (NWP) centres, with instruments such as the Advanced
Microwave Sounding Unit-A (AMSU-A) or the Advanced Technology Microwave
Sounder (ATMS). For an accurate estimation of the temperature profile in the
lower atmosphere, quantifying the surface contribution is required. The
surface contribution, i.e. the surface brightness temperature (TB), depends on
the frequency, and it is the product of a surface effective emissivity
(eeff) and a surface effective temperature (Teff):
TB=eeff⋅Teff.Teff is defined as the integrated temperature over a layer
corresponding to the penetration depth at the given frequency: the larger the
wavelength, the deeper the penetration into the medium. In the same way,
eeff represents the integrated emissivity over a layer
corresponding to the penetration depth. It depends on the frequency, the
incidence angle, and the sub-surface extinction and reflections between snow
and sea ice layers . Therefore, estimating the surface
contribution is particularly complicated over sea ice due to the layering
and the vertical structure of the snowpack, which affect the microwave
emission processes
,
and to the large spatial and temporal variability of sea ice and snow cover
. The understanding of the
relationship between Teff and the physical temperature profile is
complicated, especially at microwave frequencies ≥18 GHz, when
scattering occurs, but it has been shown that from 6 to 50 GHz there is a
high correlation between the Teff and the TSnow-Ice. With TSnow-Ice estimated from the AMSR2
observations, we will deduce the sea ice Teff at AMSR2
frequencies between 6 and 89 GHz, using linear regression.
Section describes the data set and the methodology
used in this study. The snow depth retrieval is presented in
Sect. . Section reports on the
TSnow-Ice retrieval. Finally, microwave sea ice
Teff at 50 GHz is derived for application to temperature
atmospheric sounding (Sect. ).
Section discusses the snow depth and the
TSnow-Ice retrieval results over a winter in Arctic.
Section concludes this study.
Material and methodsThe database of collocated satellite observations and in situ measurements
The RRDP from the ESA sea ice CCI project is an openly available data set
(,
https://figshare.com/articles/Reference_dataset_for_sea_ice_concentration/6626549,
last access: 15 January 2019).
It contains an extensive collection of collocated satellite microwave
radiometer data with in situ buoy or airborne campaign measurements
and other geophysical parameters, with relevance for computing and
understanding the variability of the microwave observations over sea ice. It
covers areas with 0 % and 100 % of SIC and different sea ice types
(thin ice, first-year ice, multiyear ice), for all seasons including summer
melt. In our study, we will focus on Arctic sea ice during winter in regions
with 100 % sea ice cover. Two different data sets from the RRDP are used:
AMSR2 brightness temperatures (TBs) collocated with IMB measurements and
AMSR2 TBs collocated with OIB airborne campaign measurements.
AMSR2 is a passive microwave radiometer on board the JAXA GCOM-W1 satellite
(launched on 18 May 2012). AMSR2 has 14 channels at 6.9, 7.3, 10.65, 18.7,
23.8, 36.5, and 89 GHz for both vertical and horizontal polarizations and it
observes at 55∘ of incidence angle. In the RRDP, the spatial
resolution of each channel is resampled by JAXA to the 6.9 GHz resolution
(32×62 km) (see AMSR2 L1R products, )
before collocation with buoy or airborne campaign measurements (RRDP report,
).
IMBs are installed by the Cold Regions Research and Engineering Laboratory
(CRREL) to measure the ice mass balance of the Arctic sea ice cover
. Buoy components include acoustic sounders
and a string of thermistors. The thermistor string extends from the air,
through the snow cover and sea ice, into the water and has temperature
sensors located every 10 cm along the string. It measures the physical
temperature with an accuracy of 0.1 K. There are two acoustic sounders
located above the snow surface and below the sea ice. The acoustic sounders
measure the position of snow and ice surfaces (top and bottom) with a
precision of 5 mm, from which the snow depth is computed. The buoys also
include instruments that measure air temperature, barometric air pressure, and
GPS geographical position . Several IMBs are deployed by
the CRREL at different locations and times during the year. We only use
Arctic buoy data recorded during winter (1 December to 1 April) to avoid
cases where ice starts to melt. The IMBs available for this study are all
located on MYI, with an ice thickness ≥1 m. A summary of buoy
information corresponding to these criteria is given in
Table and the IMB locations are shown in
Fig. . IMB measurements collocated with AMSR2 TBs used in this
study totalize 2845 observations.
List of the IMBs used in this study, with the mean snow depth
(column 5) and the mean ice thickness (column 6) computed over the duration
of the measurements (column 2).
BuoyDuration of measurementsDeploymentPosition on 1 DecemberMean snowMean iceIDduring winterlocation(lat, long)depth (cm)thickness (cm)2012G1 Dec 2012–6 Feb 2013Central Arctic(85.79∘; -134.88∘)34.1162.82012H1 Dec 2012–6 Feb 2013Beaufort Sea(80.39∘; -129.23∘)23.2173.32012J1 Dec 2012–6 Feb 2013Laptev Sea(82.87∘; 139.09∘)25.5100.32012L1 Dec 2012–6 Feb 2013Beaufort Sea(80.36∘; -138.55∘)8.5330.12013F1 Dec 2013–31 Mar 2014Beaufort Sea(76.15∘; -146.27∘)50.3145.72013G1 Dec 2013–31 Mar 2014Beaufort Sea(75.84∘; -151.46∘)21.3249.42014F1 Dec 2014–11 Mar 2015Beaufort Sea(76.32∘; -143.10∘)16.1151.82014I1 Dec 2014–12 Mar 2015Beaufort Sea(78.52∘; -148.70∘)22.6155.3
For snow depth retrieval, we also used data from the OIB airborne campaign.
The NASA OIB project has collected ice and snow depth data in the Arctic
during annual flight campaigns (March–May) since 2009. The data are
especially valuable in this context, since they contain snow depth information
from the snow radar on board the aircraft, not only from single points but
continuously along the flight path. The vertical resolution of the OIB snow
radar is 3 cm, and the uncertainty on the snow depth is around 6 cm
compared with in situ measurements . Recent studies evidence
larger errors on OIB snow depth with issues to detect snow
depth under 8 cm . These different limitations are
summarized in . In the RRDP, the snow depth data from OIB
snow radar are averaged into 50 km sections to be collocated with AMSR2
observations. For our study we use the OIB data from the 2013 campaign. It
totalizes 408 observations over 8 d in March and April and covers FYI and
MYI areas. Figure summarizes the locations of IMBs and OIB
campaigns over the Arctic ocean.
Ice mass balance buoy and Operation Ice
Bridge (OIB) flight locations over Arctic sea ice. Squares indicate the
position of IMBs on 1 December and circles indicate the starting points of
the OIB campaigns.
It is important to note that there are discrepancies due to the scale when
comparing point measurements from buoys with the spatially averaged data from
satellites or aircrafts .
The database of simulated effective temperature and brightness temperature from sea ice properties
For the estimation of Teff, we use a microwave emission model
coupled with a thermodynamic model. The emission model uses the temperature,
density, snow crystal and brine inclusion size, salinity, and snow or ice
type to estimate the microwave emissivity, the Teff, and the TB
of sea ice. It is coupled with a thermodynamic model in order to provide
realistic microphysical inputs. The thermodynamic model for snow and sea ice
is forced with ECMWF ERA40 meteorological data input: surface air pressure,
2 m air temperature, wind speed, incoming shortwave and longwave radiation,
relative humidity, and accumulated precipitation. It computes a centimetre-scale profile of the parameters used as inputs to the emission model. The
emission model used here is a sea ice version of the Microwave Emission Model of Layered Snowpacks (MEMLS) described in
. The simulations were part of an earlier version of the
RRDP and the simulation methodology is described in . This
MEMLS simulation uses, among its inputs, the snow depth and the
TSnow-Ice and computes Teffs and TBs at different
frequencies (from 1.4 to 183 GHz). The data set contains 1100 cases and is
called the MEMLS-simulated data set in the following.
Methodology
In this study, we propose simple algorithms, using multilinear regressions,
to derive the snow depth, the TSnow-Ice, and the
Teff of sea ice from AMSR2 TBs.
The measurements from the IMB 2012G, 2012H, 2012J, and 2012L, collocated with
AMSR2 TBs, are used as the training data set for the different regressions to
retrieve snow depth and TSnow-Ice. These buoys have been
selected because they are located in different regions across the Arctic and
show a large range of snow depths. The measurements from IMB 2013F, 2013G,
2014F, and 2014I, which are all located in the Beaufort Sea, are used as the
testing data set.
First, the IMB snow depth is expressed as a function of the AMSR2 TBs using a
multilinear regression (see Sect. ). The OIB data
are used for the forward selection and the IMB training data set is used to
perform the regression. Second, the TSnow-Ice is expressed as a
function of TBs and snow depth, using linear regressions. An automated method is developed
that detects the position of the snow–ice interface on the vertical temperature
profile measured by the IMB thermistor string (see
Sect. ). Then, the IMB training data set is
used to perform the regressions (see Sect. ). For
this part there are two consecutive regressions: the first one is done
between the centred (the average was subtracted) TSnow-Ice and
TBs; the second one is done between the TSnow-Ice corrected for
the TB dependence and the snow depth. Third, the sea ice Teff at
different microwave frequencies is expressed as a function of the
TSnow-Ice (see Sect. ). This final
step uses the simulations from a thermodynamical model and MEMLS to
derive linear regression equations for the Teff at frequencies
between 6 and 89 GHz. The Teff at 50 GHz is of special interest
for atmospheric sounding applications.
Snow depth estimationMultilinear regression to retrieve the snow depth
A forward selection method is used to choose the best AMSR2 channels to
retrieve snow depth. It is a statistical method to determine the best-predictor combinations (here, AMSR2 TBs) to retrieve a variable (here, snow
depth). We use the stepwise regression . It is a sequential
predictor selection technique: at each step statistic tests are computed, and
the predictors included in the model are adjusted. Our training data set for
this forward selection is the OIB snow depth from the 2013 campaign included
in the RRDP. OIB data are chosen for forward selection because the data cover
a large area with a wide range of snow depths. In addition, the scale of the
averaged OIB data is closer to satellite footprint than buoy measurements,
increasing the consistency with the satellite observations. Forward selection
tests have also been done with the IMB training data set, but the results were
not satisfactory. We find that the best channel combination for snow depth
retrieval is the combination of the three channels at 6.9, 18.7, and 36.5 GHz in
vertical polarization (6, 18, and 36 V).
Then, a multilinear regression is conducted using the IMB training data set
(buoys G, H, J, L in 2012 collocated with AMSR2 TBs). The snow depth is given
as a linear combination of the TBs at 6, 18, and 36 V:
Ds=1.7701+0.0175⋅TB6V-0.0280⋅TB18V2+0.0041⋅TB36V,
with Ds the snow depth expressed in metres and TB in kelvin. This model was
trained with snow depths between 5 and 40 cm.
The forward selection has also been tested by constraining the number of
predictors to 2 and 4. The combinations obtained are 18 and 36 V for two
channels and 6, 18, 36, and 89 V for four channels. Then, the multilinear
regression has been performed using these combinations of two or four channels.
The results show that the three-channel combination is the best in terms of RMSE
and correlation compared to the two- or four-channel combination (see
Sect. ).
Results of the snow depth retrieval
Figure shows the comparison between the observed snow depth
measured by the acoustic sounder of IMB and the regressed snow depth computed
from AMSR2 TBs with Eq. (). The RMSE between the IMB snow
depth observations and our snow depth regression is 12.0 cm and the
correlation coefficient is 0.66, using the IMBs 2013F, 2013G, 2014F, and 2014I
(which are not in the training data set). The buoy 2013F observes a large snow
depth (> 40 cm), which is outside the bounds of our snow depth model. Tests
are conducted to improve the estimation, including the 2013F buoy in the
training data set, with equal numbers of observations for different ranges of
snow depths: it does not improve the results. Our model obtained the same
snow depth estimation between buoys 2013G and 2013F. It is consistent because
these buoys are spatially very close. Therefore, we suspect that the 2013F
buoy is located nearby a ridge or hummock, where the local snow depth is large
but not detectable at the satellite footprint scale. Without including the
buoy 2013F in the computation, the RMSE for our snow depth model is 5.1 cm
and the correlation coefficient is 0.61.
We also compare the snow depth retrievals with the measurements of the 2013
OIB campaigns (see Fig. ) with the ice type computed from the
gradient ratio between 19 and 37 GHz . Our snow depth
regression (Eq. ) RMSE is 6.26 cm and the correlation
coefficient with OIB observations is 0.87. Note that the uncertainties on OIB
data for the 2013 campaigns are between 2 and 22 cm with a mean standard
deviation (SD) of 11 cm (OIB snow depth
Dsnow provided in the RRDP). Looking at Fig. , our snow depth
regression is applicable to both ice types. The RMSEs computed for MYI and
FYI are 7.2 and 3.9 cm, and the correlations are 0.71 and 0.03.
The RMSE is smaller for FYI because the snow depth variability of FYI is also
smaller. The low correlation obtained for FYI can come from the limited
number of observations and because the snow depth variability observed is
within the signal noise.
Spatial scales are different when comparing satellite measurements or
airborne campaign measurements with buoy measurements. Discrepancies can
appear due to the spatial variability of the snow depth. It can explain that
the correlation is higher when comparing snow depth estimated from AMSR2 TBs
with the snow depth observed from OIB radar. It is also important to note
that the OIB campaign data are from late winter to beginning of spring (March
to April), while IMB measurements are from winter (December to March). With the
snow depth regression being developed on IMB measurements, this small change
in season can contribute to the larger RMSE observed with OIB data.
Time series of the comparison between snow depths from IMB
observations and our multilinear regression (Eq. ). The
beginning of the measurements with a new IMB is indicated on the x axis.
Time series of the comparison between snow depths (left y axis)
from OIB observations and our multilinear regression
(Eq. ). The beginning of the measurements with a new OIB
campaign is indicated on the x axis. For each measurement, the ice type is
indicated with a dashed grey line (right y axis).
Snow–ice interface temperature estimationAutomatic interface position detection
During winter, the air temperature is very cold, meaning that the snow surface
temperature is cold compared to ice and water temperatures. Through sea ice,
the temperature profile is piecewise linear and temperature increases with
depth (see Fig. ). In the air, the temperature
gradient is small because of turbulent mixing. In the snow, the temperature
gradient is larger due to the thermal properties of snow. Therefore, air–snow
and snow–ice interface positions can be detected by changes in the
temperature gradient. At the air–snow interface, the second derivative of the
temperature profile reaches a maximum. At the snow–ice interface, the
temperature gradient being lower in the ice than in the snow, the second
derivative of the temperature profile reaches a minimum. Using these
properties of the sea ice temperature profile, an automated method is
implemented to detect the air–snow and the snow–ice interface positions in
the temperature profile measured by the buoy thermistor string.
Figure shows an averaged temperature profile
through sea ice during winter, with the air–snow and snow–ice interface
positions detected with our automated method. This method performs best
during winter when the air is cold. It may not be applicable if the snow
depth is lower than the vertical resolution of the thermistor string
(10 cm) or if sea ice starts to melt and the temperature profile develops
gradually toward an isothermal state. The method selects the thermistor which
is located the closest to the interface. Note that the real interface
position can be located between two thermistors. Therefore, the shift between
the real interface position and the thermistor the closest to the interface
can be up to 5 cm. This can introduce uncertainties in our
TSnow-Ice regression.
Averaged temperature profile (from December to February) measured by
the IMB 2012G, with air–snow and snow–ice interface levels detected with our
automated method.
Correlation between the brightness temperature and the snow–ice interface temperature
During winter, the vertical position of the snow–ice interface is fixed with
respect to the buoy thermistor string. The thermistor string is frozen into
the ice which means that the thermistor at the snow–ice interface will stay
at that interface unless there is surface melt or snow ice formation and this
rarely happens during winter. For each IMB, the snow–ice interface is
detected with our automated method described in
Sect. .
We use a correlation analysis to select the TBs at different frequencies
describing the variability of the TSnow-Ice.
Figure shows the correlation coefficient between
TSnow-Ice and AMSR2 TBs computed using the data from all IMBs
(Table ). The 89 GHz TBs are highly correlated with
the air temperature (R>0.75). The 18.7, 23.8, and the 36.5 GHz TBs have a
low correlation with TSnow-Ice because of microwave scattering
in the snow and/or shallow microwave penetration into the snow. The 7.3 GHz
channel is ignored because it contains practically the same information as
the 6.9 GHz channel. The TBs at 6.9 and 10.65 GHz at vertical polarization
have the highest correlation with TSnow-Ice (R>0.5).
Therefore, the 10.65 and the 6.9 GHz at vertical polarization (10 and 6 V)
channels are selected as inputs to the linear regression to retrieve the
TSnow-Ice.
Correlation coefficient between the TSnow-Ice from
IMBs and the AMSR2 TBs, as a function of AMSR2 frequency.
Linear regressions to retrieve the snow–ice interface temperature
To express the TSnow-Ice as a function of the TB at 6 and
10 V, the linear regressions are calculated on centred data (i.e. the
anomaly). For each buoy, the averaged TSnow-Ice is subtracted
from the TSnow-Ice measurements and the same is done with the
TB measurements. Thus, the temperature offset between the buoys is removed
and the slope of the linear regression is unchanged:
ΔTSnow-Ice=a1⋅ΔTB6or10V⇔TSnow-Ice3=a1⋅TB6or10V+offsetbuoy,
with ΔTSnow-Ice and ΔTB describing the centred
TSnow-Ice and TB. Figure shows the
linear regression between the TSnow-Ice and the TB at 6 and
10 V, using the measurements from buoys 2012G, 2012H, 2012J, and 2012L. The
slope coefficients (a1) estimated between the TSnow-Ice and
the TB at 6 and 10 V are 1.086±0.020 and 1.078±0.019.
Centred TSnow-Ice expressed as a function of the
centred TBs at 10 V (a) and 6 V (b). Data from the IMBs
are in different colours depending on the buoy, and the linear regression is
the solid black line.
The offset (offsetbuoy) in the linear regression equations
between TSnow-Ice and the TB is different for each buoy,
because it depends on the snow depth. The TSnow-Ice dependence
on snow depth can be explained by the thermal insulation of snow
. Here, we establish an empirical
relationship between the TSnow-Ice corrected for the TB linear
dependence at 10 or 6 V, and the snow depth as follows:
TSnow-Ice-a1⋅TB10or6V=a2⋅f(Ds)+a3,
with f(Ds) a function of snow depth.
Three different linear regressions have been tested to relate the
TSnow-Ice using the snow depth directly, the inverse of the
snow depth, and the logarithm of snow depth. Figure
shows the TSnow-Ice corrected from TB dependence as a function
of snow depth. The different regressions are tested using the training
data set (IMB G, H, J, and L in 2012). The regression showing the best results
uses the logarithm of the snow depth (solid black line in
Fig. ). The linear regression using the snow depth
directly (dashed red line in Fig. ) leads to an
overestimation of the TSnow-Ice for large snow depth. The
regression using the inverse of the snow depth (red dotted line in
Fig. ) leads to an underestimation for small snow
depth. The RMSEs obtained on the TSnow-Ice are compared and the
relation using the logarithm of snow depth shows the lowest RMSE. Based on
these results, the final equations to relate the TSnow-Ice to
the snow depth and the TB at 10 and at 6 V are as follows:
TSnow-Ice=1.078⋅TB10V+5.67⋅log(Ds)-5.13TSnow-Ice=1.086⋅TB6V+3.98⋅log(Ds)-10.70,
where TSnow-Ice and TB are expressed in kelvin, and Ds
is expressed in metres.
TSnow-Ice corrected for the 10 V TB (a) and
of the 6 V TB (b) dependence as a function of snow depth. Data from
the IMBs are represented by different colours, the regression using the snow
depth is shown by the dashed red line, the regression using the inverse of snow depth
by the dotted red line, and the regression using the logarithm of the snow
depth by the solid black line.
Results of the snow–ice interface temperature retrieval
Figure shows the comparisons between
the observed TSnow-Ice and the regressed
TSnow-Ice using the 10 and 6 V TBs (Eqs.
and ), and the in situ snow depth measured by the
acoustic sounder of IMB. The RMSEs are computed using the IMB 2013F, 2013G,
2014F, and 2014I. The regression of the TSnow-Ice using the
in situ snow depth with the 10 V TBs (Eq. ) is
slightly better (RMSE =1.78 K) than the regression with the 6 V TBs
(Eq. ) (RMSE =1.98 K). The variability due to the snow
depth is better described with the regression using the 10 V TBs.
Figure is the same as
Fig. but with our snow depth estimation
(Eq. ). The RMSEs are 2.87 K for the 10 V regression and
2.90 K for the 6 V regression. The results are degraded because of the snow
depth regression, especially for the buoys with thick snow (∼50 cm) or
thin snow (∼5 cm) (e.g. buoy 2013F and buoy 2012L). Note that the
regression is tested with IMBs, which are all located on MYI. However, using our
algorithm to derive the TSnow-Ice is also applicable over FYI
areas, as our snow depth algorithm is applicable to both ice types and our
TSnow-Ice algorithm uses the channels 10 or 6 V, which have
limited sensitivity to the ice type .
Time series of the comparisons between TSnow-Ice
observations from IMBs (black line), and TSnow-Ice regressions
with TBs at 10 V (blue line) and at 6 V (red line). The snow depth used in
Eqs. () and () is the snow depth observed by
the IMB sounder. The beginning of the measurements with a new IMB is
indicated on the x axis.
Same as Fig. , using the
regressed snow depth (Eq. ) in place of in situ snow
depth
Sea ice effective temperature estimationBias between the model and the observations
Teff is related to the frequency and the incidence angle of the
satellite observations. It is not a geophysical variable that we can measure
directly as an in situ parameter. A microwave emission model has to
be used to computed the Teffs from the geophysical parameters.
The Teff used here is available from a simulated data set using a
thermodynamical model and the microwave emission model, MEMLS. The model
set-up and the simulations are described in . In this
data set, the TBs and the Teffs are simulated using the
TSnow-Ice and the input snow and ice profiles from the
thermodynamical model. Even though the simulated TB data are comparable to
observations in terms of mean and standard deviation, both the
thermodynamical model and the emission model are based on physical equations
and are not tuned to observations. TBs simulated with MEMLS are not fitted to
AMSR2 TBs, meaning that a bias is expected between the TSnow-Ice
of the MEMLS-simulated data set (TSnow-IceMEMLS) and the
TSnow-Ice estimated with our regression.
The bias obtained is the mean value of the difference between the
TSnow-IceMEMLS, and the TSnow-Ice regressed
from Eqs. () and () using the TBs of the MEMLS-simulated data set as inputs. Biases of 3.97 and 4.01 K are estimated for
the regressions with 10 and 6 V respectively. The RMSEs computed between the
TSnow-IceMEMLS and the TSnow-Ice regressed
and corrected for the biases at 10 and 6 V are 2.7 and 2.07 K.
Figure shows the TSnow-Ice from the MEMLS-simulated data set as a function of TB at 10 and 6 V, and the
TSnow-Ice computed from our regressions (Eqs.
and ), with and without the bias correction. We can see that
the slopes of our linear regressions are consistent with the data simulated
from MEMLS.
Comparisons between the TSnow-IceMEMLS from the
MEMLS-simulated data is shown with blue points, the regressed TSnow-Ice
(Eqs. and ) with a dashed black line, and the
regressed TSnow-Ice debiased to fit the MEMLS simulations with
a solid black line at 10 V (a) and 6 V (b)
channels.
Linear regression between the effective temperature and the snow–ice interface temperature
The Teff near 50 GHz in vertical polarization is correlated with
the TSnow-Ice and it can be expressed as a
linear function of the TSnow-Ice:
Teff(freq,pol)=b1(freq,pol)⋅TSnow-IceMEMLS+b2(freq,pol),
with Teff, b1, and b2 depending on the frequency (freq)
and on the polarization (pol). We use the MEMLS-simulated data set to
calculate the linear regression between the TSnow-Ice and the
Teff at 6.9, 10.65, 18.7, 23.8, 36.5, 50, and 89 GHz in vertical
polarization. Teffs at vertical and horizontal polarizations are
about the same. Only the vertical polarization is considered here, because
TBs measurements are noisier at horizontal polarization due to the
variability of sea ice emissivity at this polarization.
Figure shows the Teff at 50 V as a
function of TSnow-Ice. The linear regressions between the
TSnow-Ice and the Teff at different frequencies are
computed. The coefficients b1 and b2 of Eq. () are
given in Table . The slope coefficient of the regression
increases with frequency, meaning that the sensitivity of the
Teff to the TSnow-Ice is increasing with frequency
between 6 and 89 GHz. A slope coefficient lower than 1 means that the
penetration depth at the given frequency is deeper than snow–ice interface.
At 50 GHz the slope coefficient is near to 1, meaning that the penetration
depth is close to the depth of the snow–ice interface. The RMSEs are below
1 K, with the regression of Teff at 50 V showing the lowest
RMSE (0.33 K), and at 89 V showing the highest RMSE (0.92 K).
Regressions of the Teff for different frequencies at
vertical polarization as a function of the TSnow-Ice (see
Eq. ) using the MEMLS-simulated data set.
These linear regressions between the Teff and the
TSnow-IceMEMLS (Eq. ) are the final step in
retrieving the Teff of sea ice at microwave frequencies as a
function of TBs, using the work in the previous sections to express the
TSnow-Ice as a function of TBs (Eqs. ,
and or ). The biases between the AMSR2
observations and the MEMLS-simulated data set are taken into account, replacing
TSnow-IceMEMLS by TSnow-Ice estimated from
AMSR2 TBs with a bias correction (see Table ):
Teff(freq,pol)=b1(freq,pol)⋅TSnow-Ice-3.97+b2(freq,pol),8for the regression using 10 V TBTeff(freq,pol)=b1(freq,pol)⋅TSnow-Ice-4.01+b2(freq,pol),9for the regression using 6 V TB.
Regression of the Teff as a function of
TSnow-Ice at 50 GHz in vertical polarization. The data from
the MEMLS simulations are in blue points and the linear regression is the
solid black line.
Discussion
For days in November, January, and April, Fig. shows the maps
of the snow depth estimated with our multilinear regression
(Eq. ), the TSnow-Ice estimated with our
multilinear regression (Eq. ), and the MYI concentration
products from the University of Bremen (https://seaice.uni-bremen.de,
last access: 1 November 2018).
Maps of the MYI concentration from University of Bremen are derived from
AMSR2 and from the Advanced SCATterometer (ASCAT) with the method of
. To perform our regressions, we use the AMSR2 TBs
(Level L1R) provided by JAXA and the SIC from the European Centre for
Medium-Range Weather Forecasts (ECMWF) Reanalysis Interim (ERA-Interim)
data. Only the areas with 100 % SIC are considered to compute the snow
depth on sea ice and the TSnow-Ice with our method.
Maps of the snow depth (a, b, c) and the
TSnow-Ice(d, e, f) estimated from our multilinear
regression using AMSR2 TBs, with multi-year ice (MYI) concentration products
(g, h, i) from the University of Bremen on 5 November
2015 (a, d, g), 5 January 2016 (b, e, h), and 5 April
2016 (c, f, i).
The results show that the snow depth is larger (40 cm) in the north of
Greenland due to the presence of drift snow
caused by the numerous pressure ridges present in this area
, as anticipated. We can observe that the snow depth is
larger in areas with larger MYI concentrations. The variability of the snow
cover is low during winter, as the snow depth reaches a maximum by December
and remains relatively unchanged until snowmelt .
For TSnow-Ice, in January and April when the air temperature is
cold (between -20 and -30∘C over the whole Arctic, on 5 January
and 5 April 2016 from ERA-Interim air temperature), the areas with large snow
depth show larger TSnow-Ice because of the thermal insulation
power of the snow. It is different in November: the air temperature is warmer
(∼-5∘C near Kara Sea, ∼-15∘C near
Laptev Sea, and ∼-25∘C in the central Arctic and Beaufort seas,
on 5 November 2015 from ERA-Interim air temperature) and the areas with
thinner snow show larger TSnow-Ice which are close to the air
temperature . Note that we can observe low
TSnow-Ice in some locations near the sea ice margins due to the
presence of open ocean in the satellite footprint. As the brightness
temperature of open water is low, the total brightness temperature measured
is decreased and it impacts our TSnow-Ice estimation.
Visually the TSnow-Ice shows a high correlation with the
distribution patterns of multiyear ice concentration on the same days: the
highest values are found in the north of Greenland and in the Canada Basin,
with some branches of higher values extending from there towards the Siberian
coast, marking the Beaufort Gyre of the Arctic sea ice drift (see the
animations for the same year at
https://seaice.uni-bremen.de/multiyear-ice-concentration/animations/,
last access: 1 November 2018).
The main differences between FYI and MYI are, on average, the higher
thickness of MYI and its higher snow load. Both effects will influence the
TSnow-Ice. Under the same conditions, a higher ice thickness
will lead to a lower TSnow-Ice. In contrast, it will be higher
if only the snow depth is increased. The positive correlation between MYI
concentration and TSnow-Ice suggests that the influence of the
higher snow depth on MYI outbalances that of the higher ice thickness on the
TSnow-Ice, emphasizing the important role of snow on sea ice in
its thermodynamic balance.
The similar patterns observed between the maps of the TSnow-Ice
and the MYI concentration on Fig. are encouraging and give
confidence in the methodology developed here, as these MYI concentration
products are from independent work done at the University of Bremen and
distributed daily to users. However it should be noted that the input
channels of both methods overlap in some AMSR2 channels, and even different
channels show some covariance .
Conclusions
We derive simple algorithms to
estimate sea ice parameters such as the snow depth, the
TSnow-Ice, and the Teff of sea ice at microwave
frequencies, from AMSR2 channels. This is achieved using the ESA RRDP, which
contains AMSR2 data collocated with IMB data and OIB campaign data. In
addition, simulated TB outputs from a sea ice version of MEMLS are used for
the regression of the Teff. All the equations used to retrieve these
sea ice parameters are derived using several linear and multilinear
regressions.
Our regression to retrieve the snow depth over winter Arctic sea ice uses the
TBs at 6.9, 18.7, and 36.5 GHz in vertical polarization. A RMSE of 5.1 cm is
obtained between the estimated and the IMB snow depths using an independent
IMB test data set. This snow depth retrieval is applicable to FYI and MYI,
with lower uncertainties for FYI than for MYI (3.9 cm compared to 7.2 cm).
To retrieve the TSnow-Ice, two relations are derived using two
different AMSR2 channels (10 or 6 V) and the estimated snow depth. The two
regressions show similar results. The errors are 2.87 and 2.90 K
at 10 and 6 V. This TSnow-Ice retrieval has been
tested only for MYI. It can also be applied to FYI, as the 6 and 10 V
channels have limited sensitivity to the ice type
. Finally the Teffs at 6.9, 10.65,
18.7, 23.8, 36.5, 50, and 89 GHz in vertical polarization are retrieved as a
function of TSnow-Ice using linear regressions. At the final
step, the RMSEs of the linear regressions between the simulated
TSnow-Ice and the Teff for all channels are lower
than 1 K, with a minimum value of 0.33 K at 50 GHz, which is a key
frequency for atmosphere temperature retrieval. The methodology used to estimate
snow depth and TSnow-Ice has been applied to several days
during winter. It shows consistent results with MYI concentration
estimates obtained independently.
These algorithms can be used to create snow depth and TSnow-Ice
products which can improve the study of sea ice variability (e.g. sea ice
growth). Information on the TSnow-Ice may help in sea ice
models by constraining the sea ice temperature gradient and the
thermodynamical ice growth. The Teff estimations can be used in
atmospheric radiative transfer calculations and to reduce noise in SIC
retrieval algorithms (e.g. EUMETSAT OSISAF global SIC
product).
Data availability
The round robin data package used for this study is publicly
accessible at https://figshare.com/articles/Reference_dataset_for_sea_ice_concentration/6626549.
Author contributions
This study was conducted by LK and supervised by RTT and
CP. GH contributed to the analysis and to the correction of the draft.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
This research was funded by EUMETSAT OSISAF (OSI VS17 03) and the PNTS
(Programme national de télédédtection spatiale). The authors
acknowledge the support from the EUMETSAT OSISAF visiting scientist programme
and the Danish Meteorological Institute for its welcome. We also acknowledge
the reviewers for their precious comments, which improved this
manuscript a lot.
Review statement
This paper was edited by John Yackel and reviewed by Leif
Toudal Pedersen and one anonymous referee.
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