TCThe CryosphereTCThe Cryosphere1994-0424Copernicus PublicationsGöttingen, Germany10.5194/tc-12-3949-2018Estimation of sea ice parameters from sea ice model with assimilated ice concentration and SSTSea ice parameters from a model with assimilated
dataPrasadSivaZakharovIgorigor.zakharov@c-core.caMcGuirePeterPowerDesmondRichardMartinMemorial University of Newfoundland, St. John's, CanadaC-CORE, St. John's, CanadaNational Research Council of Canada, St. John's, CanadaIgor Zakharov (igor.zakharov@c-core.ca)21December201812123949396525May20182July201823November201828November2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://tc.copernicus.org/articles/12/3949/2018/tc-12-3949-2018.htmlThe full text article is available as a PDF file from https://tc.copernicus.org/articles/12/3949/2018/tc-12-3949-2018.pdf
A multi-category numerical sea ice model CICE was used along with data
assimilation to derive sea ice parameters in the region of Baffin Bay and
Labrador Sea. The assimilation of ice concentration was performed using the
data derived from the Advanced Microwave Scanning Radiometer (AMSR-E and
AMSR2). The model uses a mixed-layer slab ocean parameterization to compute
the sea surface temperature (SST) and thereby to compute the freezing and
melting potential of ice. The data from Advanced Very High Resolution
Radiometer (AVHRR-only optimum interpolation analysis) were used to
assimilate SST. The modelled ice parameters including concentration, ice
thickness, freeboard and keel depth were compared with parameters estimated
from remote-sensing data. The ice thickness estimated from the model was
compared with the measurements derived from Soil Moisture Ocean Salinity –
Microwave Imaging Radiometer using Aperture Synthesis (SMOS–MIRAS). The
model freeboard estimates were compared with the freeboard measurements
derived from CryoSat2. The ice concentration, thickness and freeboard
estimates from the model assimilated with both ice concentration and SST were
found to be within the uncertainty in the observation except during March.
The model-estimated draft was compared with the measurements from an
upward-looking sonar (ULS) deployed in the Labrador Sea (near Makkovik Bank).
The difference between modelled draft and ULS measurements estimated from the
model was found to be within 10 cm. The keel depth measurements from the ULS
instruments were compared to the estimates from the model to retrieve a
relationship between the ridge height and keel depth.
Introduction
Regional sea ice forecasting is important for climate
studies, operational activities including navigation, exploration of offshore
mineral resources and ecological applications; e.g. the North Water Polynya in
Baffin Bay provides a warm environment for marine animals
.
Sea ice is a heterogeneous media, making it practically difficult for
remote sensing instruments to measure the ice thickness, freeboard and ridge
parameters . The climate forecast researchers and
operational ice modelling communities depend on numerical modelling techniques
implementing the physical process of atmosphere and ocean on large-scale
computational platforms along with data assimilation methods to retrieve the
information on sea ice parameters. Data assimilation methods can provide more
accurate initial conditions for forecasting systems
. The estimation of sea ice parameters
is a challenging problem in the region of Baffin Bay and the Labrador Sea due
to the high interannual variability of sea ice in this area
.
Previous sea ice modelling and assimilation studies at the Canadian Ice
Service (CIS) provided an overview of an
operational ice model coupled with atmospheric and ocean modules. The
research compared the evolution of ice thickness
distributions followed by the development of an operational ice dynamics
model for CIS . The CIS used the model developed
by to study the ice thickness
distribution in the Gulf of St Lawrence These
modelling studies were also improved by the data assimilation methods
. The Community Ice Ocean Model (CIOM)
by used the Princeton Ocean Model for the simulation of
ocean parameters and a multi-category ice model. The total ice fraction
retrieved from the Special Sensor Microwave/Imager (SSM/I) was assimilated
into CDOM using a 3-D variational (3DVAR) technique to
estimate the ice concentration. The ice concentration estimates were further
improved by assimilating information from both daily ice charts and RADARSAT
. Assimilation studies by
showed significant improvement in assimilated
ice concentration but with a large bias in the ice thickness pattern.
presented a method for ice concentration and
thickness analysis by combining the modelling of sea ice thermodynamics and
the detection of ice motion by space-borne synthetic aperture radar (SAR)
data from RADARSAT-1 and RADARSAT-2. The method showed promising results for
sea ice concentration and ice thickness estimates. In another study, Ocean
and Sea Ice Satellite Application Facility (OSI SAF) data were assimilated
into the Regional Ocean Modelling System (ROMS) for simulating sea ice
concentration and produced better results than the simulation without
assimilation . Ice concentration and extent were
overestimated in the assimilated model, probably due to the bias in
atmospheric forcing, underestimation of heat flux and over- and
underestimation of sea ice growth and melt processes.
Sea ice models can be coupled to ocean and atmosphere models, but they can
also be run in a stand-alone mode by prescribing the atmospheric and ocean
conditions. The literature does not provide details and discussion on
regional implementation and results for stand-alone models. The 3D-CEMBS is
an eco-hydrodynamic model that includes a coupled POP-CICE model for
operational forecasting implementation of the CICE model on a regional scale. The
implementation on the regional scale of the ice component and the validation
work is still ongoing . The advantage of the
sea ice model, CICE version 5.1.2 , is the stand-alone
capability. Here we use a combination of modelling using the stand-alone sea
ice model, CICE, and the combination of optimal interpolation and nudging
methods to assimilate ice
concentration. The optimal interpolation and nudging method is also used to
assimilate SST estimated by a slab ocean parameterization in the sea ice
model. The optimal interpolation method is computationally inexpensive and
was shown to provide better estimates than the non-assimilated model
. The simulated sea ice parameters are then validated
with the observations in the region of the Baffin Bay and the Labrador Sea.
This work uses a high-resolution model configuration which was previously
described in the work of . The changes in ice
concentration were taken into account to estimate the changes in the ice
volume and thereby the thickness estimates. The ice prediction models such as
Regional Ice Prediction System (RIPS) limits the
discussion on ice concentration estimates from the model. In this work, in
addition to validation of the ice concentration we also discuss the effect of
the assimilation on ice thickness, freeboard, draft and keel depth. Since
freeboard, draft and keel are functions of ice concentration and ice volume
it is reasonable to compare the model values with corresponded observations.
The work suggests a methodology to extract the level ice draft and keel depth
information from upward-looking sonar (ULS) measurements, which was then used to describe the
relationship between ridge and keel.
Model domain and forcing data
The sea ice model was implemented on a regional scale of about 10 km
orthogonal curvilinear grids with a slab ocean mixed-layer parameterization.
Density-based criteria were used as in to
compute the mixed-layer depth and thereby compute the SST and the potential
to grow or melt sea ice. The assessment of the non-assimilated model of the
sea ice concentration and its seasonal means showed that the error associated
with the model is mostly spread across the area of the North Water Polynya and
the Davis Strait where the interaction of cold and warm water is frequent. In
the present study, a data assimilation module is also introduced.
The surface atmospheric forcing is from high-resolution North American
Regional Reanalysis (NARR) data . The ocean forcing
is from various sources: currents from Climate Forecast System Reanalysis
(CFSR), salinity from World Ocean Atlas, WOA-2013 ,
and mixed-layer depth (MLD) computed from WOA-2013
. used a
density criteria of 0.2 kg m-3 at 10 m depth; the other models such
as RIPS by CIS use a density criteria of
0.01 m-3 from the ocean surface. Atmospheric and ocean forcing were
used as inputs to the model. For sea surface temperature (SST), monthly
climatology data derived from NOAA High-resolution Blended Analysis were used as input for the initial and boundary conditions.
The net heat flux from the atmosphere is the upper boundary condition for ice
thermodynamics. The heat flux from the ocean to the ice is the lower boundary
condition. Based on temperature profile and boundary conditions, the melt and
growth of ice are computed. The open boundaries are configured in the same
way as in and . For the
ice concentration and thickness, the initial condition is assumed as a no-ice
state at the beginning of September 2004. The data assimilation starts from
January 2005 and is continually assimilated whenever data are available.
Specifications of microwave radiometers used to estimate ice
concentration.
SpecificationsAMSR-EAMSR2SSMIS Center frequency (GHz)89891937Mean spatial resolution (km)6×45×369×4337×28PolarizationHVHVVHVIncidence angle (deg)555550 Swath (km)144514501700 Data availability (mm/yyyy)08/2002–10/201108/2012–present03/2005–present Remote sensing data for assimilation and validation
Ice concentrations derived from Advanced Microwave Scanning Radiometer
(AMSR-E) of resolution 6km×4km were used for the assimilation of ice concentration.
AMSR-E was developed by JAXA, and it is deployed on the Aqua satellite.
AMSR-E and AMSR2 are passive sensors that look at the emitted or reflected
radiation from the Earth's surface with multiple frequency bands. The
vertical (V) and horizontal (H) polarization channels near 89 GHz were used
to compute the ice concentration from AMSR-E . The
Arctic Radiation and Turbulence Interaction Study (ARTIST) sea ice algorithm
used to determine ice concentration from AMSR-E shows excellent results above
65 % ice concentration where the error does not exceed 10 %. With low
ice concentrations, substantial deviations can occur depending on atmospheric
conditions. The parameters of the sensor are provided in
Table . AMSR-E ice concentrations were available from January
2005 to September 2011, after which the instrument stopped functioning. From
August 2012 AMSR2 had been used for data collection. The same frequency
(89 GHz) as that of the AMSR-E instrument was used to derive information
from AMSR2. The spatial resolutions also remained the same for both AMSR-E
and AMSR2. The same algorithm was applied to derive ice concentrations from
both AMSR-E and AMSR2. The original AMSR-E/AMSR2 data with
6km×4km resolution scale were interpolated to the
model grid before assimilation.
The assimilated model results of ice concentration were compared with the OSI
SAF data. The details of the sensors are given in Table . The
OSI SAF product is derived from Special Sensor Microwave Imager Sounder
(SSMIS) . The data are available
on a 10 km polar stereographic grid and are derived from 19 V, 37 VH
channels. The erroneous data for which the ice concentration error was 100 %
or the retrieval algorithm failed were filtered out before comparison.
Measurements derived from AVHRR-only OISST analysis (Advanced Very High Resolution
Radiometer)
were used for SST assimilation. SST
data products are generated using a combination of satellite and in situ
observations from buoy and ship observations and are available on a
0.25∘×0.25∘ resolution. The analysis product
estimates SST from ice concentration only in regions where ice concentration
is greater than 50 %; otherwise it uses satellite data to retrieve SST
values.
Freeboard measurements from the CryoSat-2 altimeter were used to compare the
freeboard estimates by the model. The CryoSat-2 altimeter operating in the SAR
mode, SIRAL, has an accuracy of about 1 cm with a spatial sampling of about
45 cm . The pulse-limited footprint width in the
across-track direction is about 1.65 km and the beam-limited footprint width in
the along-track direction is about 305 m , which
corresponds to an along-track resolution about 401 m (assuming flat-Earth
approximation). Therefore, the pulse-Doppler-limited footprint for SAR mode
is about 0.6 km2. The CryoSat-2 freeboard and the ice-concentration
products were generated at the Alfred Wegener Institute (AWI)
. The products are available in a spherical
Lambert azimuthal equal-area projection of a 25 km resolution cell. The
uncertainty in freeboard measurements can arise from speckle noise, lack of
leads (which makes the estimation of sea surface height unreliable) and snow
cover. The uncertainty up to 40 cm can be observed in the region of Baffin
Bay and Labrador Sea .
For ice thickness, the data product derived from the Soil Moisture Ocean Salinity – Microwave Imaging Radiometer
using Aperture Synthesis (SMOS–MIRAS) instrument (1.4 GHz channel)
on a grid resolution of 12.5km×12.5km. The ice thickness is retrieved from observation of
the L-band microwave sensor of SMOS. Horizontal and vertical polarized
brightness temperatures in the incidence range of <40∘ are
averaged. The ice thickness is then inferred from a three-layer
(ocean–ice–atmosphere) dielectric slab model. SMOS data are available from
15 October 2010. The presence of snow accumulated over months can also
increase the uncertainty. The uncertainty in the SMOS ice thickness
(observations) shown in Table
includes the error contributions, which are caused by the brightness
temperature, ice temperature and ice salinity. The insufficient knowledge of
the snow cover also introduces a large uncertainty in ice thickness
estimates. Snow depth uncertainty can be 50 %–70 % of the mean value
. In general, the uncertainty in the thickness
observation increases with increasing ice thickness, increasing snow cover
and the onset of melt . The SMOS ice thickness
retrieval produces a large amount of uncertainty during the melt season and hence
retrieval is not conducted during the melt season. Table shows
the details on the SMOS sensor .
SMOS uncertainty.
IceUncertainty caused by a standard thicknessdeviation 0.5 K1 K ice1 g kg-1temperaturetemperatureicebrightnesssalinity0–10 cm<1 cm<1 cm<1 cm10–30 cm<1 cm1–5 cm1–13 cm30–50 cm1–4 cm2–10 cm2–22 cm>50 cm>4 cm>7 cm≤40 cm
SMOS sensor specifications.
PolarizationHVIncidence angle0–55∘Swath (km)900Center frequency (GHz)1.4 (L band)Mean spatial resolution (km)35–50Radiometric sensitivity over ocean (K)2.5 and 4.1
Ice draft measurements from an ULS instrument located on
the Makkovik Bank (see Fig. ) at 58.0652∘ W and
55.412∘ N, were used to analyze the ridge keel and the level ice
draft in the region.
The location of ULS instrument.
The ULS data measured at an interval of approximately 5.5 s are available
from the beginning of January to the end of May during 2005, 2007 and 2009. The
frequency histogram of the data yields a unimodal, bimodal or multi-modal
distribution. A sample histogram is provided in Fig. for
10 February 2007. We assume that the first mode in the histogram corresponds
to the level draft ice and the second mode corresponds to the ridge keel
measurement. The first mode of the distribution is selected by finding a
minimum between two peaks. The histogram was analyzed to derive daily
averages of ice draft and keel measurements .
The histogram of the ULS measurement, 10 February 2007, for the
estimation of draft and keel (metres).
Data assimilation
The assimilation module uses a combined optimal interpolation and nudging
technique for ice concentration
. The method can be
represented generally as Eq. () .
Xa=Xb+dtKτ(Xo-Xb),
where Xa is the final analysis of the variable, Xo is
the observed quantity (for ice concentration this is AMSR-E/AMSR2, for SST
this is AVHRR-only OISST), Xb is the background estimate of the
variable (for ice concentration and SST this is model estimate),
dt is the model time step, τ is the basic nudging timescale
as in , and K is the nudging weight with the
optimal interpolation value. K is computed as
K=σbασbα+σo2,
where σb and σo are the error standard
deviation of the model estimate and the
observations respectively. The parameters in the
weighing factor given in Eq. () are defined according to
as σb=Xo-Xb; σo=0.08 (parameter may vary
spatially), α=6.
The assimilation of the ice concentration, σo=0.08, is
calculated from a long-term standard deviation of 0.08, since the AMSR-E/AMSR2
ice concentration error is dependent on various atmospheric conditions for
values less than 65 %. The parameter α=6 is used in the
present study to ensure that the coefficients for assimilation are heavily
weighted only when there is large variation between the model and the
observation .
SST is also assimilated using the nudging and optimal interpolation scheme.
For SST assimilation, σo is fixed at 0.05 to compensate for
the assumption of zero mixed-layer heat flux. A value α equal to 6
was also used for the assimilation of SST to
ensure that only large differences between the model and observation are
weighted heavily.
The assimilation of ice concentration is then followed by a recomputation of
the estimated sea ice volume. The ice volume is subtracted or added by
including the increments or decrements with specified ice thickness. Since a
variable drag coefficient was used for the friction associated with an
effective sea ice surface roughness at the ice–atmosphere and ice–ocean
interfaces and to compute the ice to ocean heat transfer, the level ice area
is updated by assuming that the model deformed ice area and volume represent the
realistic values.
Results and validation
Three model results are discussed here: M0, the non-assimilated
model; M1, the model assimilated with ice concentration from
AMSR-E/AMSR2; and M2, the model assimilated with ice concentration from
AMSR-E/AMSR2 and SST from AVHRR-only OISST. M2 only assimilates SST
whenever there is a data gap in ice concentration from AMSR-E (e.g. from
24 March to 31 March 2005), AMSR-E data are not available and, in that case,
M2 assimilates SST instead of ice in data gaps. The AMSR-E instrument
stopped producing data from October 2011, and AMSR-E2 data have been used for
assimilation since August 2012. The model was in spin-up for 3 months before
assimilation, since it was not coupled with the ocean model. The spin-up time of
3 months is enough to estimate the ice conditions.
Ice concentration
Figure column 1 shows the absolute mean difference in ice
concentration between the non-assimilated model and the OSI SAF data,
column 2 shows the absolute mean difference in ice concentration of the model
assimilated only with ice concentration and OSI SAF data, and column 3 shows
the absolute mean difference in ice concentration of the model assimilated with
both ice concentration and SST and OSI SAF data. Model M2 shows improvement
in the ice concentration for January and March, but little improvement
between M1 and M2 for May 2010.
The absolute mean difference in ice
concentration from non-assimilated, assimilated models and OSI SAF data for
January, March and May 2010.
Figure shows the absolute mean difference in ice concentration
of the model assimilated with AMSR-E/AMSR2 and OSI SAF (SSMIS) data from
January 2010 to September 2011 and the absolute mean difference in ice
concentration from August 2012 to December 2015. The assimilation of SST and
ice concentration decreases the error between the model and the OSI SAF ice
concentration. In 2010, the non-assimilated model error of 4.624 % was
reduced to 1.939 % by assimilating ice concentration. The assimilation
of SST and ice concentration decreased the error to about 1.118 % in
2010.
The absolute mean difference in ice concentration for models M0, M1
and M2 is shown for January 2010 to September 2011 in row 1 and for August
2012 to December 2015 in row 2.
From October 2011 to July 2012, AMSR-E data are not available for a more
extended period, and model M2 was assimilated only with SST; see
Fig. . During this period, the SST assimilation decreases the
error between the model and the observation by almost 3 %.
The absolute mean difference in ice concentration from October 2011
to July 2012. Ice concentration was not available for assimilation and hence
model M2 will only be assimilated with SST during this period.
Ice thickness
In this section, we compare the ice thickness from the model
with that from the observation. The large unacceptable uncertainties in observation
data derived from SMOS create difficulties for the analysis. Also, it is
strictly recommended to not use the SMOS data with an uncertainty greater
than 1 m for practical applications. For
comparison and validation, ice thickness data are selected from both the model and
observation where the observed ice thickness has an uncertainty less than or
equal to 100 cm. The SMOS thickness has less uncertainty for
thinner ice and higher uncertainty for thicker ice; see Table
for the uncertainty in the SMOS ice thickness. In the case of SMOS-derived
thickness, the uncertainties would increase with snow accumulation and
melt onset.
Figures , and show the mean values of
the thickness estimated from models M0, M1, M2 and SMOS with the uncertainty
limits of the SMOS ice thickness (shaded grey). As ice thickness increases
through the season, so do the uncertainty limits. The values of model M2 are
within the uncertainty limits of SMOS ice thickness from October until the
end of February (except for 2014). From the comparison, during March, the
model results exceed the uncertainty limits. Figure shows the
results for the period October 2011 to April 2012 in which AMSR-E data were
missing and during which M1 was not assimilated with ice concentration but used
the initial conditions from the assimilated result. Model M2 used the initial
conditions assimilated with both ice concentration and SST but only assimilates
SST during the period. Both models, M1 and M2, show better forecasts with the improved initial
conditions in the long-term analysis. One of the
reasons why the model values exceed the uncertainty limits during March is
the choice of α=6, which considers only large differences while
weighing the coefficient K. Since the assimilation shows improvement in ice
thickness, using a value of α=2, it is expected to impose the model
values within the uncertainty limits.
The ice thickness from the models M0, M1, M2 and observation (SMOS
ice thickness) from October 2010 to April 2011 and October 2012 to April
2013. The uncertainty in the observation (SMOS ice thickness) is shaded in grey.
The ice thickness from the models M0, M1, M2 and observation (SMOS
ice thickness) from October 2013 to April 2014 and October 2014 to April
2015. The uncertainty in the observation (SMOS ice thickness) is shaded in grey.
The ice thickness from models M0, M1 (ice
concentration was not assimilated as there were no AMSR-E data available, but the initial
conditions from the model assimilated with ice concentration were used), M2
(assimilated only with SST and used model initial conditions derived from
assimilating both ice concentration and SST) and observations (SMOS ice
thickness) from October 2011 to April 2012. The uncertainty in the observation
(SMOS ice thickness) is shaded in grey.
The model M2 thickness, SMOS-derived ice thickness and the uncertainty in the
SMOS-derived measurement for 15 December 2010, 15 January 2011 and 15 March
2011 are shown in Fig. , which includes regions where observed
uncertainties are larger than 1 m.
The M2-estimated ice thickness, SMOS–MIRAS-derived ice
thickness and the observation uncertainty for 15 December 2010, 15 January
and 15 March 2011.
The thickness results for thin ice categories (<30 cm) from the model
with SMOS are shown in Figs. , and .
The shaded region shows the uncertainty in the thin ice from SMOS data. The
thin ice category thicknesses are overestimated from October to the end of November
but the values are within the uncertainty limits of SMOS from December to
March.
The ice thickness from the models M0, M1, M2 and observation (SMOS
ice thickness) and the observation uncertainty (shaded grey) for SMOS ice
thickness less than 30 cm (2010–2012).
The ice thickness from the models M0, M1, M2 and observation (SMOS
ice thickness) and the observation uncertainty (shaded grey) for SMOS ice
thickness less than 30 cm (2012–2014).
The ice thickness from the models M0, M1, M2 and observation (SMOS
ice thickness) and the observation uncertainty (shaded grey) for SMOS ice
thickness less than 30 cm (2014–2015).
Figure shows the SST from AVHRR-only OISST analysis with the
shaded regions representing the observation uncertainty and SST from models M0,
M1 and M2. In general, the SST from AVHRR-only OISST assimilation improves
the ice concentration and ice thickness results for the model M2. The
assimilated model M2 still has a systematic bias during the summer and winter,
which may be improved by decreasing α (=6, presently) and
by decreasing the nudging timescale (presently for SST, the nudging scale is
30 days). Decreasing the nudging timescale can result in the late formation
and early melt of ice (not shown here). The results can be improved by making the nudging timescale less frequent during the formation and
more frequent during the winter, until the beginning or middle of March. Frequent
nudging is also found to produce blow-up for the thermodynamic model. The
parameters in the assimilation have to be selected to maintain balance, not cause late formation and earlier melt and maintain the
stability of the model thermodynamics and dynamics. For M0, the non-assimilated
model, the results may be improved by including the mixed-layer heat flux in
a parameterization similar to . Also, note that the model
still assumes a fixed salinity profile and mixed-layer profile.
The SST from AVHRR-only OISST analysis with the shaded region
represents the uncertainty in AVHRR-only OISST analysis and SST from models
M0, M1 and M2.
Draft and keel depth
The ULS measurements were separated into level ice draft and keel depth
measurement as described in and also in
Sect. . The level ice draft, D, is computed using
Eq. () . The results are shown
in Fig. .
D=(ρivice+ρsvsno)(Aρw),
where ρi=917 kg m-3 is the density of ice,
vice is the volume of ice, ρs=330.0 kg m-3 is the density of snow, vsno is the volume
of snow, A is ice concentration, and ρw=1026 kg m-3 is
the density of seawater.
Some deviations are noticed in the comparison of level ice draft. The
estimated absolute error is about 10 cm for 2005, 2007 and 2009. The error of
10 cm on a draft of 20 cm can be accepted considering large differences in
spatial resolution between the ULS and model. Also, the analysis was done
only for 2005, 2007 and 2009 as this was when data were available. The discrepancy
occurs due to the fact that ULS gives values at a particular location with
high resolution (within the footprint of several metres), while the model
of 10 km resolution gives an averaged result close to the location of the
ULS. Moreover, the analysis of the histogram from ULS shows a multi-modal
distribution at certain time points which indicates the presence of rafted
ice. In the present study, the rafted ice is also included and considered as
the ridges which contribute towards the results achieved in this section.
The level ice draft computed from the ULS measurement and the M2
model-estimated values at Makkovik Bank for 2005, 2007 and 2009.
The keel is computed using idealized sea ice floe comprising a system of two
triangular sails and keels and a single melt pond .
The ridge height is given by Eq. () and the correlation
between the ridge height and keel depth is given by Eq. ():
Hr=2VrdgArdg(αDkmk+βCmr)(ϕrmkDk+ϕkmrC2),
where Hr is the ridge height, mr=tan(αr)=0.4; αr=21.8∘ is the
slope of the sail and mk=tan(αk)=0.5;
αk=26.5∘ is the slope of the keel;
ϕr is the porosity of the ridges; ϕk=0.14+0.73ϕr is the porosity of the keels.
Dk=5 is the ratio distance between ridge and distance between
the keels. Vrdg is the volume of the ridged ice, Ardg
is the ridged ice area fraction, α and β are the weight
functions for area of ridged ice, C is the coefficient that relates ridge
to keel, and
Hk=CHr
gives the keel depth Hk. The Makkovik Bank where the keel
measurements are estimated from ULS has high variability of ice thickness,
and frequency of the formation of keels is high due to the combined effect
of the Labrador currents and winds. Rafted ice is common in this region
. Here the model and the observation of keel depth are
used to estimate the parameter C.
The coefficient C, estimated for 2005, 2007 and 2009, shows that a value
between 3.00 and 4.50 gives a good estimate of keel measurement for January
and February, while a value between 7.00 and 8.00 gives a good estimate of
keel during March, April and May. In Fig. the values of the
coefficient C that relates ridge to keel for January and February is 3 and
C=7.00 for March, April and May; see Eq. (). These values
are derived under the assumptions in Eq. (). The
sensitivity of parameters has to be further explored to determine the
characteristics of each parameter and its effect on the ridge–keel
relationship, which may result in a different conclusion. Since the interest
lies in deriving this relationship from the assimilated model, only
results from M2 is presented. For non-assimilated models, the choice of
parameters vary.
During January to February the formation of ice and ridges occurs, and during
March the thick ice may be contributing towards the ridging, thus increasing
the value of C.
The keel depth computed from the ULS measurement and the
M2-estimated values in centimetres for 2005, 2007 and 2009.
The absolute mean difference between the model freeboard for M0, M1
and M2 and CryoSat-2 for January, February and March 2011.
The RMSE of freeboard measure for the regions where the lead
fraction is above 0 %.
The freeboard from model M2, CryoSat-2 and the uncertainty in the
observations for January, February and March 2011.
Freeboard
The uncertainty in freeboard measurements can arise due to the lack of leads.
The presence of leads was ensured by selecting the regions where the lead
fraction derived from CryoSat-2 was greater
than zero. In the model, freeboard is computed using
Eq. () . For the region, the
uncertainty in the freeboard measurements is below 40 cm
.
Df=(vice+vsno)A-D,
where vice is the volume of ice, vsno is the volume
of snow, A is the ice concentration and D is the draft; see
Eq. ().
The absolute mean difference between the model and the observations for
January, February and March 2011 is shown in Fig. . M2 freeboard
measurements are close to the observed freeboard. Figure shows
the RMSE of the freeboard from model M2 and CryoSat-2 in the areas where the lead
fraction was greater than zero. The RMSE is below the maximum uncertainty in
40 cm for the region of interest and was found to range between 4.5 and
11 cm.
The freeboard from CryoSat-2, uncertainty in the observation and the
model M2.
Figure shows the observed freeboard from CryoSat-2, the
uncertainty in the observation and the model M2. Only the model results from M2
are given, since there are only slight deviations for M0 and M1 from the
observation. Moreover, we are interested in the results of the assimilated
model and how well it performs in the estimation of freeboard. The model
values are within the uncertainty limits of the observation. Also, note that
the model results are monthly averaged, while CryoSat-2 is a mosaic of daily
measurements within a month. The spatial average of freeboard for the region,
the observed value and the uncertainty are shown in Fig. . The
average freeboard from the model lies within the uncertainty limits of the
observation.
Conclusions
The assimilated models in the literature and those
implemented in forecasting centres use a constant drag formulation and lack
details on deriving parameters other than ice concentration and ice
thickness . In this work a
variable drag formulation is used for the friction associated with an
effective sea ice surface roughness at the ice–atmosphere and ice–ocean
interfaces and to compute the ice-to-ocean heat transfer. The results from
the updated model were compared with satellite-derived measurements to
validate the model estimates of ice concentration, ice thickness and freeboard.
Moreover, the model results were used to estimate the relationship between sail
and keel depth.
The modelled ice thickness demonstrated a good correspondence with the
estimates from SMOS–MIRAS, except during the period of maximum ice extent.
The deviation in the results of ice thickness during March have to be further
explored by tuning the parameters that contribute to the ice thickness in the
non-assimilated model as well as the assimilation parameters. The thin ice
category thicknesses are overestimated from October to the end of November but the
values are within the uncertainty limits of SMOS from December to March.
The SMOS estimates are influenced by the presence of snow, and also,
during the melt seasons the uncertainties of SMOS-estimated ice thickness
might increase, in which case comparison with more reliable data would be
required. The model freeboard are compared with estimates from CryoSat-2, and
the RMSE was found to range between 4.5 and 11 cm. The estimates of
freeboard from the model are within the uncertainty values of the CryoSat-2
(below 40 cm).
The level ice draft and keel values derived from ULS were compared with the
modelled values. The coefficient that related the sail height and keel depth
for the Makkovick region lies in the range 3–8 depending on the period of the
year. Since the variable drag formulation depends on the assimilation
methodology, further sensitivity studies have to be conducted for the
optimization of the model. The model will be made operational after further
sensitivity studies.
Data used for this paper are freely
available.
The first author performed the simulation and contributed
to writing the paper. All co-authors participated in the discussions and
contributed to writing and editing the paper.
The authors declare that they have no conflict of
interest.
Acknowledgements
Funding support was provided by the Research and Development Corporation (RDC),
Newfoundland and Labrador. The authors also thank Tony King (C-CORE) and
Ingrid Peterson (DFO, Government of Canada) for providing ULS data from
Makkovik Bank. We also thank the Center for Health Informatics and Analytics
(CHIA), MUN and ACENet, Canada for providing computational resources. We
would like to thank the developers of CICE, the Los Alamos sea ice model for
public availability of the sea ice model and the users' group. The authors
would like to acknowledge the anonymous referees and editor for their fruitful
comments and suggestions.
Edited by: John Yackel
Reviewed by: two anonymous referees
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