Castro-Morales etal 2014 JGR

Castro-Morales etal 2014 JGR
JOURNAL OF GEOPHYSICAL RESEARCH: OCEANS, VOL. 119, 1–13, doi:10.1002/2013JC009342, 2014
Sensitivity of simulated Arctic sea ice to realistic ice thickness
distributions and snow parameterizations
K. Castro-Morales,1 F. Kauker,1 M. Losch,1 S. Hendricks,1 K. Riemann-Campe,1 and R. Gerdes1
Received 7 August 2013; revised 21 November 2013; accepted 21 December 2013.
[1] Sea ice and snow on sea ice to a large extent determine the surface heat budget in the
Arctic Ocean. In spite of the advances in modeling sea-ice thermodynamics, a good number
of models still rely on simple parameterizations of the thermodynamics of ice and snow.
Based on simulations with an Arctic sea-ice model coupled to an ocean general circulation
model, we analyzed the impact of changing two sea-ice parameterizations: (1) the prescribed
ice thickness distribution (ITD) for surface heat budget calculations, and (2) the description
of the snow layer. For the former, we prescribed a realistic ITD derived from airborne
electromagnetic induction sounding measurements. For the latter, two different types of
parameterizations were tested: (1) snow thickness independent of the sea-ice thickness
below, and (2) a distribution proportional to the prescribed ITD. Our results show that
changing the ITD from seven uniform categories to fifteen nonuniform categories derived
from field measurements, and distributing the snow layer according to the ITD, leads to an
increase in average Arctic-wide ice thickness by 0.56 m and an increase by 1 m in the
Canadian Arctic Archipelago and Canadian Basin. This increase is found to be a direct
consequence of 524 km3 extra thermodynamic growth during the months of ice formation
(January, February, and March). Our results emphasize that these parameterizations are a
key factor in sea-ice modeling to improve the representation of the sea-ice energy balance.
Citation: Castro-Morales, K., F. Kauker, M. Losch, S. Hendricks, K. Riemann-Campe, and R. Gerdes (2014), Sensitivity of simulated
Arctic sea ice to realistic ice thickness distributions and snow parameterizations, J. Geophys. Res., 119, doi:10.1002/2013JC009342.
models, such as our model, resolve only two thickness categories: open water (thin ice and open water) and sea ice
[Hibler, 1979]. Ice thermodynamics, however, depend
strongly on ice and snow thicknesses. These quantities can
vary considerably on scales smaller than the model’s grid
cell size. In order to parameterize these subgrid-scale variations, the mean sea-ice thickness (hi) is often replaced by
an ice thickness distribution (ITD). The ITD is represented
as a probability density function g(h) [Thorndike et al.,
[4] In practice, this distribution function is discretized.
Some sea-ice models, such as the one used here, work with
the assumption that the distribution is fixed in time. Often,
this distribution is flat, that is, it uses the same probability
for all thickness categories [Hibler, 1984] (see gray bars in
Figures 1a and 1b).
[5] It has been shown that the distribution of ice thicknesses over an ice covered area is nonuniform with one to
sometimes three modes [Eicken and Lange, 1989; Lange
and Eicken, 1991; Wadhams, 1981]. Thickness distributions also vary with regions and seasons. Bimodal distributions are found in dynamic regions such as Fram Strait, and
broad modes in regions such as north of Greenland where
new ice or open water are rare throughout the year [Haas
et al., 2010]. These observations and the sensitivity of the
ocean heat loss through a given ice thickness, suggest that a
dynamic nonhomogeneous and multicategory ice thickness
distribution is required to describe sea ice in numerical
[2] Sea ice is a complex system that forms the interface
between the atmosphere and the ocean : it insulates the
ocean against heat transfer to and from the atmosphere, and
contributes to the ice-albedo feedback mechanism. Because
of these effects, the rapid decrease of Arctic summer seaice extent and thickness in recent years [Serreze et al.,
2003, 2007b; Stroeve et al., 2008, 2011; Winton, 2011]
contributes to the polar amplification of global climate
change [Serreze et al., 2009]. Representing these changes
accurately in numerical models is still a challenge.
[3] Nowadays, most sea-ice model codes resolve both
dynamic (movement and deformation of the ice) and thermodynamic (transfer of heat or radiation) processes. Seaice momentum equations with specific rheologies
[Kreyscher et al., 2000] are solved for drift velocities that
are used to advect the ice and snow variables. Thermodynamic processes are used to determine ice growth and
decay due to melting and freezing. Many simple sea-ice
Alfred Wegener Institute, Helmholtz Centre for Polar and Marine
Research, Bremerhaven, Germany.
Corresponding author: K. Castro-Morales, Alfred Wegener Institute,
Helmholtz Centre for Polar and Marine Research, Bremerhaven 27570,
Germany. ([email protected])
©2013. American Geophysical Union. All Rights Reserved.
Figure 1. The ice thickness distributions based on airborne EM-bird measurements: (a) from a compilation of 19 campaigns (112 flights) and (b) from one field campaign (ARKXXVI/3). The canonical
seven categories uniformly distributed are shown in gray. All ITDs are scaled to give a mean thickness
of 1 m.
[7] Although dynamic ITD models appear more physical, they still require assumptions about the redistribution
between ice categories and there are hardly enough observational data available to constrain the details of the redistribution between the ice categories. This and the
additional computational cost incurred by advecting many
ice thicknesses and concentrations, may be the reason why
there are still a number of sea-ice models, including the ice
components of some of the CMIP5 models used for the
IPCC assessment report, that rely on fixed ITDs following
Hibler [1984].
[8] The heat transfer through ice (i.e., the conductive heat
flux, Fc) critically depends on its thickness, so that the form
of the prescribed ITD in the models determines to a large
extent the overall heat flux. The description of the thin ice
categories is particularly important since the heat fluxes are
the largest through these categories. Here we aim to improve
the description of the static ITD at low additional computational cost by deriving it from field measurements of ice
thickness retrieved from airborne electromagnetic induction
sounding measurements (EM-bird) [Haas et al., 2010]. The
new static ITD contains more ice categories (15) than in the
canonical configuration and follow a nonuniform distribution that resolves thin ice more accurately (Figure 1).
[9] The snow cover on top of the ice is as important as
the ice layer. Due to its low thermal conductivity and high
albedo properties, snow acts as an efficient insulator and
hence has a strong influence on the conductive heat flux. In
the presence of snow, most of the incoming shortwave radiation is reflected and sent back to the atmosphere. The
remaining shortwave radiation is attenuated further by the
ice and in the ocean mixed layer [Gerland and Haas, 2011;
Nicolaus et al., 2010].
[10] Large-scale observations of snow thickness (hs) in
the Arctic are rare. Warren et al. [1999] presented an Arctic
snow depth climatology constructed from field measurements of the Soviet North Pole drifting stations for 1954–
1991. During this time span, there was much more multiyear ice (MYI) in the Arctic than in recent years. Also, due
[6] Since both thermodynamic and dynamic processes
depend on ice thickness, it is important to have a representation of thickness variations below the grid scale in a seaice model [Hunke et al., 2010]. Consequently, more sophisticated models now evolve the ITD over time and space
and redistribute ice between categories according to redistribution functions. More recent ‘‘dynamic’’ ITD models,
e.g., CICE (Los Alamos Sea-Ice Model, sea-ice component
of the Community Earth System Model, CESM) [Hunke
and Bitz, 2009], TED (Thickness and Enthalpy Distribution) [Zhang and Rothrock, 2001], and LIM3 (Louvain-laNeuve) [Vancoppenolle et al., 2009], carry a time varying
thickness distribution with an ice concentration for each ice
category within a grid cell and hence, increase the thermodynamic resolution [Hunke et al., 2010].
Figure 2. A map with the locations of all airborne EM
sea-ice thickness surveys included in the ITDs. The color
bar indicates the year in which the survey took place and
the marker type indicates the season (inverted triangle:
spring, circle: summer, and square: autumn). Black lines
delimit different regions discussed in Table 3.
[16] In this work, we explore the sensitivity of the simulated sea-ice thickness to the treatment of snow and ice as
sketched above. The paper is organized as follows : the
model configuration is described in section 2.1, the sea-ice
thickness distributions and snow depth parameterizations
are introduced in section 2.1.1 and the heat flux calculations in section 2.1.2. Section 2.2 lists the sensitivity
experiments of this work. Section 3 presents the results to
the sensitivity of sea-ice thickness due to different ITDs
(section 3.1) and to the different snow parameterizations
(section 3.2). In section 3.3, we compare our results to the
ICESat (Ice, Cloud, and land Elevation Satellite) sea-ice
thickness derived from laser altimetry measurements. In
section 3.4, we evaluate the resulting conductive heat flux
and thermodynamic sea-ice growth. Finally, the discussion
and conclusions are presented in sections 4 and 5.
to the character of the observations on drifting ice, this climatology is limited only to snow measurements on top of
level MYI.
[11] Previous studies from observations have demonstrated that hs increases with the age of ice such as in Antarctica [Sturm and Massom, 2010]. However, various field
observations did not show a direct correlation between the
thickness of snow and ice [Eicken and Lange, 1989; Lange
and Eicken, 1991; Sturm et al., 2002; Toyota et al., 2007].
Some empirical relationships between ice and snow thickness have been proposed for different ranges of hi. For
instance, Doronin [1971] retrieved hs and hi relations (i.e.,
hs 5 0 for hi < 5 cm; hs 5 0.05 hi for 5 cm hi 20 cm
and hs 5 0.1 hi for hi > 20 cm) from satellite thermal
imagery (AVHRR) data. This relationship was later reevaluated by M€
akynen et al. [2013]. The authors retrieved the
relationship between hi and hs from the Soviet Union’s airborne Server expeditions for late winter conditions between
1950 and 1989. The only difference to Doronin’s relationships was observed when hi > 20 cm, where the slope was
10 % smaller (hs 5 0.09 hi for hi > 20 cm) than the previous
relationship for the same case. The empirical relationships
between hi and hs, proposed by M€akynen et al., were developed only for the Kara Sea and the eastern part of the
Barents Sea and they strongly rely on atmospheric forcing
data and its uncertainties particularly in air temperature and
wind speed [Doronin, 1971; M€akynen et al., 2013].
[12] In a recent work from NASA Operation IceBridge
project, hs is derived from airborne microwave snow radar
measurements along transects of thousands of kilometers.
Results from these observations suggest a higher snow
accumulation of snow over MYI [Kurtz et al., 2012; Kwok
et al., 2011]. However, the limited in situ measurements of
snow on Arctic sea ice have demonstrated the heterogeneity in the distribution of snow thicknesses with respect to
the geographical location as a consequence of environmental conditions such as humidity and wind causing erosion
and further redistribution with accumulation in depressions
and decrease in elevations [Forsström et al., 2011; Gerland
and Haas, 2011; Haapala et al., 2013; Iacozza and Barber, 2010; Sturm et al., 2006].
[13] As a result, the correlation between ice and snow
thicknesses based on Arctic snow observations is ambiguous. Hence, it is not plausible to generally expect a consistent deep snow layer over old ice, implied by long
accumulation, and over rough surfaces; and a thin snow
layer on top of young first year and level sea ice.
[14] Additionally, the complex physical processes acting
over the snow layer (i.e., variable snow density in time and
space, snow compaction due to wind effects, change in
grain size due to age) are difficult to include in numerical
models. Instead, simplified parameterizations are used
[Hunke et al., 2010].
[15] In our model, snow accumulation is parameterized
using precipitation and air temperature [Zhang et al., 1998].
The accumulated snow forms a layer of constant density on
top of the ice. When enough snow is accumulated to submerge the surface of the ice, a simple flooding algorithm
converts snow into ice until the ice-snow interface is lifted
to sea level [Lepp€aranta, 1993]. Based on this model, we
test here two different and simple methods of distributing
the snow over the different thicknesses categories of the ice.
2.1. Model Description and Setup
[17] We use the Massachusetts Institute of Technology
general circulation model (MITgcm) [Marshall et al.,
1997] in a regional coupled ocean-sea ice Arctic Ocean
configuration similar to the configuration of NAOSIM
(North Atlantic/Arctic Ocean Sea-Ice Model) [Karcher
et al., 2011]. The domain covers the Arctic Ocean region,
Nordic Seas and the North Atlantic down to approximately
50 N and has open boundaries in the North Atlantic and in
the Pacific just south of Bering Strait. The horizontal resolution is 1/4 (28 km) on a rotated grid with the grid
equator passing through the North Pole. The vertical is discretized in 33 nonequally spaced levels with depths ranging
from 10 m near the surface to approximately 356 m at maximum model depth of 4800 m. Vertical mixing in the ocean
interior is achieved by a K-Profile Parameterization (KPP)
scheme [Large et al., 1994] and tracers (temperature and
salinity) are advected with an unconditionally stable
seventh-order monotonicity preserving scheme [Daru and
Tenaud, 2004] that requires no explicit diffusivity.
[18] The dynamic-thermodynamic sea-ice model of the
MITgcm [Losch et al., 2010] uses a viscous-plastic rheology and a so-called zero-layer thermodynamics (i.e., zero
heat capacity formulation) [Semtner, 1976] with a prescribed ITD [Hibler, 1979, 1980, 1984; Losch et al., 2010].
[19] The model is forced by realistic atmospheric conditions of the Coordinated Ocean Research Experiment
(CORE) version 2 that are based on the reanalysis from the
National Center for Atmospheric Research/National Centers for Environmental Prediction (NCAR/NCEP) [Large
and Yeager, 2009]. This data set includes 6 hourly wind,
atmospheric temperature and specific humidity, daily
downward long and short-radiative fluxes and monthly precipitation fields. Surface salinity in ice free regions is
restored to a mean salinity field (also CORE data) with a
time scale of 180 days to suppress model drift. A monthly
climatology of river runoff for the main Arctic rivers follows the AOMIP (Arctic Ocean Model Intercomparison
Project) protocol based on Prange [2003].
[20] In the baseline configuration, the model is spun-up
from the first day of January 1948 to the last day of December 1978. These 30 years of spin-up allow the model to
adapt to the forcing. A control run using the baseline model
configuration and all subsequent sensitivity experiments
start on 1 January 1979 and end on 31 December 2007 (29
years). The most important sea-ice parameters used in the
model configuration are: ice strength (P ) of 27,000 Pa, a
lead closing parameter (H0) of 0.5 m and surface albedos
for ice and snow. Sea-ice and snow albedos are often tuned
for realistic simulations of sea ice [Losch et al., 2010]. In
the baseline configuration the albedos are: 0.84 for dry
snow, 0.70 for wet (melting) snow, 0.75 for dry ice, 0.66
for wet (melting) ice and 0.10 for open water, where the
surface temperature of ice determines melting conditions.
Figure 3. A schematic representation of the different
snow parameterizations evaluated in this work: (a) ‘‘snowconstant,’’ the snow thickness is the same for all ice thickness categories and (b) ‘‘snow-ITD,’’ the snow has the
same thickness distribution as the ice, so that the snow
thickness is proportional to the ice thickness.
2.1.1. Sea-Ice Thickness Distribution and Snow Depth
[21] In the sea-ice model of the baseline configuration
(control), there are seven ice thickness categories between
0 and a maximum thickness of 2hi (twice the mean thickness hi) (see gray bars in Figures 1a and 1b). These seven
thicknesses are given by hin 5hi(2n – 1)/7 and their distribution is flat, normalized and fixed in time [Hibler, 1984].
The bin width is constant with 2hi/7. All ITDs in Figure 1
are scaled for a mean thickness of 1 m.
[22] In order to add realism to this ad hoc ITD, we built
two different ITDs from frequency distributions of total ice
thicknesses (snow plus ice thickness) over level ice as
measured by an airborne EM-bird in various locations of
the Arctic Ocean. Figure 2 depicts the location of the flights
that were used to construct the ITDs. Both ITDs have 15
ice categories, a maximum thickness of 3hi and a bin width
of 3hi/15 5 0.2hi. They differ in the amount of data that we
used to construct them.
[23] For the first ITD (Figure 1a), we used a series of frequency distributions of sea-ice thickness obtained from 112
EM-bird flights of 19 field campaigns between 2005 and
2011. The data for this ITD are dominated by perennial
MYI and averages over various ice types and seasons corresponding to Arctic summer, spring, and autumn. The area
coverage of these flights includes various regions in the
Arctic Ocean such as the western marginal seas in spring
and the Transpolar Drift stream and Fram Strait in summer.
[24] For the second ITD (Figure 1b), we used the frequency distribution of sea-ice thickness from a single EMbird campaign that was carried out during the RV Polarstern cruise ARK-XXVI/3 in 2011. This cruise took place
during the sea-ice minimum in the central Arctic Ocean
(August–October) (magenta squares and circles in Figure
2). The reasoning for choosing this single campaign is the
small variation of the ice thickness distribution in the central Arctic Ocean, with the subsequent assumption that this
ITD is a suitable description for homogenous sea-ice conditions including more first-year ice (FYI). Thus, this ITD
represents the ongoing shift from MYI to younger first and
second-year ice in the Arctic Ocean. By including this ITD
in our model we aim to evaluate the response of modeled
sea-ice thickness to this condition.
[25] The choice of ITD determines a factor in the loss
term of ice concentration under melting conditions. In
Hibler’s original ITD with equally distributed ice classes
this factor is A/2h where A is the ice concentration and h
the ice thickness : A/2h, d h is the fractional area that is lost
when the thickness of the thinnest ice class is reduced by
d h. For the non-homogeneous distribution the factor 1/2 is
ðpk kÞ21Þ
replaced by
, where pk is the distribution funcn
tion and n the number of thickness classes. For the multicampaign ITD this factor is 0.334 and for the single
campaign ITD it is 0.336.
[26] Two different parameterizations for the redistribution of snow are used in this study: (1) snow depth is uniform and independent on the ice categories below, and (2)
snow is distributed proportionally to the prescribed ITD.
Our baseline model configuration follows the first type and
will be hereinafter referred to as ‘‘snow-constant’’ (Figure
3a). The second parameterization will be referred to as
‘‘snow-ITD’’ (Figure 3b). Both parameterizations are an ad
hoc solution in the absence of a clear understanding of the
snow redistribution process, and neither form is unambiguously supported by observations (see above). By using
these different snow distributions we attempt to estimate
the uncertainties introduced by our limited knowledge
about the snow distribution on the results of the sea-ice
2.1.2. Heat Flux Calculations and Thermodynamic
Growth of Sea Ice
[27] We evaluate the thermodynamic growth of sea ice
(melting and freezing rates) of our sensitivity experiments.
The thermodynamic growth is determined from the conductive heat flux (Fc in W m22) through the ice, in this case,
through each of the 15 ice categories n in the realistic
ITDs.The net growth includes a melting contribution from
warm ocean water above freezing, but this is neglected in
our presentation of the ice growth. The variability of the
thermodynamic growth depends to a large extent on the ice
and snow thicknesses. Thus, Fc is calculated according to
equation (1) [Jeffries et al., 1999]:
Tf 2Ts
Fc 5 hi
where Tf is the freezing point of seawater, Ts is the temperature at the surface of the snow, hi and hs are the mean seaice and snow thicknesses, and Ki and Ks are the sea-ice and
snow thermal conductivities. For Ks, we use a value of 0.31
W m21 K21 [Massom et al., 1998] and for Ki we use 2.16
Table 1. Characteristics of the Simulations Subject to This Study
Simulation Number
(Code Name)
1 (control)
2 (snowITD_7)
3 (snowc_15_1)
4 (snowc_15_19)
5 (snowITD_15_1)
6 (snowITD_15_19)
Number of Categories
in the Ice Thickness
Table 3. The Annual Mean Sea-Ice Thickness for All Experiments and Divided Into Regions (See Figure 2) Over the Time
Period (1990–2007) for DJF (December, January, and February),
and SON (September, October, and November)
Snow Parameterization
1 (control)
2 (snowITD_7)
3 (snowc_15_1)
4 (snowc_15_19)
5 (snowITD_15_1)
6 (snowITD_15_19)
1 (control)
2 (snowITD_7)
3 (snowc_15_1)
4 (snowc_15_19)
5 (snowITD_15_1)
6 (snowITD_15_19)
Uniformly distributed.
Obtained from one EM-bird campaign.
Obtained from 19 EM-bird campaigns.
W m21 K21 [Cox and Weeks, 1988]. Fc is defined as positive (upward) when the heat flux is directed from the ocean
to the atmosphere through the ice/snow layer. Negative
heat flux (downward heat flux warming the ocean) occurs
when the temperature at the surface of the snow is higher
than the freezing temperature of water at the bottom of the
ice layer. The distribution of the thermodynamic growth is
illustrated in section 3.4.
Canadian Basin
and Archipelago
Kara and
Barents Seas
between climatologies, from 1990 to 2007. We show results
of autumn (September–October–November) and winter
(December–January–February) since most of the Arctic precipitation falls from August to October [Serreze and Maslanik, 1997]. The maximum snow accumulation is found
during October, November and December in areas dominated by MYI [Sturm et al., 2002]. Further, autumn and winter are the only two seasons available in the satellite derived
sea-ice thickness to which we compare our model results.
The mean sea-ice thicknesses of each experiment averaged
over the entire model domain are presented in Table 2.
[31] We divided the model domain into four subareas
(Fram Strait, Canadian Basin and Archipelago, Eurasian
Basin, and Barents and Kara Seas) (see Figure 2). The mean
sea-ice thicknesses for each subarea are presented in Table 3.
2.2. Model Simulations and Sensitivity Experiments
[28] We performed six simulation experiments (Table 1).
Experiment 1 represents our control run and uses the baseline configuration of the MITgcm sea-ice model. Experiment 2 (snowITD_7) provides insight into the effect of
changing the snow parameterization to the second form
(section 3.2). Experiments 3 and 4 (snowc_15_1 and
snowc_15_19) evaluate the sensitivity of using two more
realistic ITDs than the canonical homogeneous seven-ice
categories (section 3.1) and allows also to study the sensitivity between the two realistic ITDs.
[29] Finally, a comparison between experiments 1 (control)
with 5 (snowITD_15_1) and 6 (snowITD_15_19) describes
the overall effect of combining different snow parameterizations and realistic ITDs (section 3.2). In all simulations, the
model configuration (sea-ice and ocean parameters, as well as
atmospheric forcing) and spin-up conditions are the same.
The period from 1979 to 1989 is not analyzed to allow the
model to adapt to the changes in the snow parameterization
and ITD. Thus, the results presented here are based on
monthly averages of the period 1990 to 2007 (18 years).
3.1. Sensitivity of Simulated Sea-Ice Thickness to
Different Ice Thickness Distributions
[32] First we discuss the shape of the different ITDs in
Figure 1. For the actual simulations, the ITDs are rescaled
to fit the modeled mean ice thickness in the grid cell. The
Hibler [1984] ITD is flat and all ice thickness categories
are equally frequent. The two observationally based ITDs
have a similar shape: a mode at the thin ice categories and
a tail toward the thicker ice categories. One of the differences between the ITDs is the location of the mode. The
thickness mode in the ice distribution representing one
[30] Most of the results presented in the following sections are spatial maps of climatologies, or differences
Table 2. The Annual and Seasonal Means and Their Standard Deviations of the Simulated Sea-Ice Thickness for All Experiments
Averaged Over the Entire Model Domain Over the Time Period (1990–2007): DJF (December, January, and February), MAM (March,
April, and May), JJA (June, July, and August), and SON (September, October, and November)
1 (control)
2 (snowITD_7)
3 (snowc_15_1)
4 (snowc_15_19)
5 (snowITD_15_1)
6 (snowITD_15_19)
Annual Mean
1.27 6 0.32
1.78 6 0.31
1.24 6 0.30
1.32 6 0.30
1.69 6 0.31
1.89 6 0.32
1.11 6 0.33
1.58 6 0.38
1.09 6 0.29
1.17 6 0.30
1.51 6 0.36
1.71 6 0.39
1.49 6 0.27
2.01 6 0.30
1.48 6 0.23
1.56 6 0.25
1.93 6 0.29
2.13 6 0.32
1.38 6 0.42
1.92 6 0.44
1.38 6 0.38
1.46 6 0.39
1.84 6 0.43
2.05 6 0.46
0.76 6 0.37
1.33 6 0.44
0.77 6 0.30
0.85 6 0.32
1.27 6 0.39
1.49 6 0.43
Figure 4. The spatial distribution of the sea-ice thickness in the control run for autumn (SON) and
winter (DJF).
autumn and winter (Figures 5e and 5f). We attribute this to
the fact that the thinnest ice categories are more frequent in
the multicampaign ITD of experiment 4 than in the single
flight ITD (Figure 1).
single campaign (Figure 1b) corresponds to category 4,
with a range of thickness between 0.6 and 0.8 m. Category
4 is closely followed by category 5, with a range of thickness between 0.8 and 1.0 m. The ice thickness mode in the
multicampaign ITD (Figure 1a) corresponds to category 3,
with a range of thickness between 0.4 and 0.6 m. In addition, in the multicampaign ITD the frequency between the
mode and the following thicker category is contrastingly
large compared to this difference in the single-campaign
ITD. More important for the resulting sea-ice thickness is
the distribution of the thinnest ice categories. These play a
fundamental role in setting the freezing and melting sea-ice
rates. In the single-campaign ITD, the four thinner ice categories are less frequent that in the multicampaign ITD.
[33] In the control run, the sea-ice thickness is largely
underestimated in almost the entire Arctic Ocean when
compared to remote-sensed estimates (see section 3.3). In
this baseline configuration, thin ice (<1 m) dominates in
regions such as the Eurasian Basin and Fram Strait, where
according to remote-sensed estimations, thicker ice (>1 m)
is expected to be found (Figure 4 and values per areas in
Table 3). In regions with MYI (i.e., Lincoln Sea, Canadian
Arctic Archipelago), the modeled sea-ice thickness is
underestimated by about 2 m compared to ICESat. The seaice extent, however, agrees with the satellite data (not
shown). The simulated Arctic-wide mean sea-ice thickness
over the analyzed period (1990–2007) is almost unchanged
in all seasons after replacing the 7-category ITD with the
15-category ITDs. The differences are below 0.1 m (experiment 1 (control), 3 (snowc_15_1), and 4 (snowc_15_19) in
Table 2). The largest differences (0.09 m) are found with
the multicampaign ITD in the Canadian Basin and Canadian Arctic Archipelago region during winter (Table 3).
[34] On a spatial map, the differences between experiments 1 (control) and 3 (snowc_15_1) are negligible except
near the coast of Northern Greenland in the Canadian Arctic Archipelago, and west of Svalbard (Figures 5a and 5b).
In the Canadian Basin, the changes between experiments 1
(control) and 4 (snowc_15_19) are larger than between
experiments 1 and 3 (Figures 5c and 5d). However, the differences between experiments 3 and 4 are similar for
3.2. Sensitivity of Simulated Sea-Ice Thickness Due to
Snow Parameterizations
[35] The sensitivity to different snow parameterizations
is much larger than the sensitivity to different ITDs. When
the snow parameterization is changed to the snow-ITD
parameterization in the baseline model configuration
(experiment 2) the Arctic-wide mean sea-ice thickness
increases by about 0.5 m (column 2, Table 2), whereas the
mean snow depth is almost unchanged (0.13 m with snowconstant and 0.12 m with snow-ITD) (not shown). Similar
results are obtained also for both 15-categories ITDs and
for all seasons (Table 2).
[36] Figure 6 depicts the difference in sea-ice thickness
due to the different snow parameterizations for all three
ITDs. The largest differences with respect to the snow
parameterization are obtained in all seasons with the multicampaign ITD (Figures 6c and 6d) while the differences are
slightly smaller for the original 7-categories ITD (Figures 6a
and 6b). The single-campaign ITD (Figures 6e and 6f) leads
to the smallest sensitivity to the snow parameterization. The
differences are largest in the Canadian Basin and Canadian
Archipelago in autumn and winter (from 0.7 to 0.9 m
depending on the ITD) and lowest in the Kara and Barents
Seas (0.1 m in winter and from 0.2 to 0.3 m in autumn).
Typical changes are about 0.3 m in the Fram Strait and
about 0.5 m in the Eurasian Basin (Table 3).
3.3. Comparison to Laser Altimetry-Derived Sea-Ice
[37] To evaluate our model simulations, we compare the
simulated sea-ice thickness to ice thickness maps based on
laser altimetry measurements (ICESat) [Zwally et al.,
2002]. These data are available for February/March (winter) and October/November (autumn) from 2003 to 2008.
The ICESat thickness measurements are known to overestimate thin ice (<1 m) due to the large uncertainty of 0.7
Figure 5. Spatial distribution of difference in sea-ice thickness (m) for: experiment 3 minus experiment 1
(snowc_15_1–control) during (a) autumn (SON) and (b) winter (DJF); experiment 4 minus experiment 1
(snowc_15_19–control) during (c) autumn and (d) winter; and experiment 3 minus experiment 4
(snowc_15_1–snowc_15_19) during (e) autumn and (f) winter. The results are integrated from 1990 to 2007.
terization. The differences in winter are relatively small
(0.1 m), but in autumn even the largest simulated ice thicknesses are well below the ICESat estimates (Figure 8). We
attribute the differences in autumn to the overestimation of
thin ice in the ICESat data product because we observe that
in regions where there is no presence of ice or it is very
thin, in the simulations there is implausibly thick ice of
about 1 m in the ICESat fields (see Figures 7d–7f).
m in the ice thickness estimates (within a 25 km segment)
[Kwok and Cunningham, 2008]. Therefore, the data are
only available in the inner Arctic. The March/April 2007
(Figure 7a) and October/November 2007 (Figure 7d) ICESat thicknesses are shown together with the corresponding
simulated ice thicknesses of the control run (Figures 7b and
7e) and experiment 6 (snowITD_15_19) (Figures 7c and
7f). In order to quantify the differences in sea-ice thickness
between model and satellite-derived data, we limited the
area coverage of the modeled sea ice to the area coverage
in the ICESat product. For all measurement periods the
simulated ice thickness from the experiments with the
snow-ITD parameterization are much closer to the ICESat
data than the simulations with the snow-constant parame-
3.4. Conductive Heat Flux and Thermodynamic
Growth of Sea Ice
[38] We evaluate the conductive heat flux contribution
(Fc) through the snow and ice layer for each of the 15 ice
categories of the ITDs in experiments 3–6. The total Fc in a
Figure 6. Spatial distribution of difference in sea-ice thickness (m) with different snow parameterizations for winter (DJF) and autumn (SON): (a and b) experiment 2–experiment 1 (snowITD_7–control);
(c and d) experiment 6–experiment 4 (snowITD_15_19 – snowc_15_19), and (e and f) experiment
5–experiment 3 (snowITD_15_1–snowc_15_1). The results are integrated from 1990 to 2007.
because the ice is too thick to allow any significant flux
(Figure 9).
[42] A clear distinction between the experiments with
and without snow-constant distribution (experiments 3 and
4 versus experiments 5 and 6) is visible for the first ice category. In the experiments with snow-ITD (5 and 6), the Fc
values are about three times higher than for the experiments
with snow-constant (3 and 4) due to the presence of lower
snow thickness using the snow-ITD (Figure 9).
[43] Furthermore, we evaluate the effect of the different
parameterizations on the Arctic-wide melting and freezing
rates of the sea ice. We calculated the monthly mean thermodynamic growth of ice. In Figure 10a, the annual cycle of
the thermodynamic growth for the control run is shown. In
grid cell is the sum of the flux through each individual ice
[39] In Figure 9, we show an example of the conductive
heat flux in each ice category for winter in a single model
grid cell located near the North Pole (see inset map in Figure 9) where sea-ice cover is present throughout the year.
[40] In the experiments with snow-constant (3 and 4),
the shape of the Fc over the ice categories is similar to the
shape of the ITDs (i.e., higher Fc through the ice categories
that are more frequent) while in the experiments with
snow-ITD (5 and 6) the lowest ice categories are amplified
because here thinner snow allows more heat flux.
[41] Toward the thicker ice and less frequent ice categories, the Fc decreases toward zero in all experiments
Figure 7. Comparison of sea-ice thickness (m) from the model and from laser altimetry satellite. Data
from (a and d) ICESat, (b and e) experiment 1 (control), and (c and f) experiment 6 (snowITD_15_19),
(top) for March/April 2007 and (bottom) October/November 2007.
about 150 km3 month21 from October to May over the control run with seven ice categories (experiment 1) when an
ITD with 15 categories is used (experiments 3 and 4). In
these experiments, the melting rate also increases by about
60 km3 month21 from June to September. Both effects can
be explained by a larger fraction of thin ice in the realistic
ITD with 15 categories: thin ice allows more conductive
the months between October to April, freezing dominates
with the highest freezing rate in December (1490 km3
month21). Melting dominates from May to September, with
the highest melting rate in July (23591 km3 month21).
[44] The effects of the different parameterizations on the
ice growth are illustrated by plotting the difference of the
net growth in the five sensitivity experiments and the control run (Figure 10b). The sea-ice growth increases by
Figure 9. Mean conductive heat flux (Fc in W m22)
through the ice-covered region in a model grid cell (star in
inset map) for the 15 ice categories in experiments 3–6 during
winter months (December-January-February) for 1990–2007.
Figure 8. Average sea-ice thickness for the months and
years (x axis) from the experiment simulations and from
ICESat data. Error bars represent 61r from the mean.
the distribution hi 5
ðpk hik Þ. To explore the impact of an
ITD in our model configuration, we prescribed two nonhomogeneous ITDs based on sea-ice thickness that was
retrieved from airborne measurements and we evaluate the
resulting simulated sea-ice thickness. In general, our main
result is a considerable increase in the simulated sea-ice
thickness with an ITD of higher number of ice categories
compared to the original model by Hibler [1984].
[48] We find, however, a high sensitivity to the details of
the two 15-categories ITDs. They differ in the distribution
of the thinner thicknesses, particularly in the location of the
modes. The position of the modes of thin ice is expected to
be important for energy exchange since the representation
of the thinnest ice is directly related to the thermodynamic
growth of ice.
[49] Compared to the ITD based on a single campaign,
thin ice is more frequent in the multicampaign ITD. As a
result, the simulated sea ice is thicker than using the singlecampaign ITD. In addition, there is more MYI due to the
inclusion of data collected during spring, and this is
reflected in the presence of more thick-ice categories than
for the single-campaign ITD. In contrast, in the singlecampaign ITD the mode is located in a slightly thicker ice
type and the frequency difference to the next ice category
is comparably low. The single-campaign ITD represents
the minimum sea-ice extent observed at the end of the melt
season in 2011, thus the sea ice during the sampling period
was dominated by melting first-year ice.
[50] The availability of EM-bird data provides a great
opportunity to include realistic and present sea-ice thickness measurements in sea-ice modeling. However, due to
different logistics during the sampling with the EM-bird in
spring (land-based surveys) and summer (ship-based surveys), the data are biased toward MYI in spring and toward
FYI in summer. This means that the majority of FYI is in
the melting state and there is less thin ice in the scaled
ITDs than the sum of all data, which scales typical FYI
thicknesses to thin ice due to the larger ratio of mean to
modal ice thickness of MYI.
[51] Most of the data available from observations were
collected during Arctic spring, summer, and autumn. The
absence of winter data (December–February) can lead to a
misrepresentation of the sea-ice thickness during this season in the shape of the ITD. However, we can assume that
the general shape of a winter ITD is not fundamentally different to that measured in spring because ice formation and
deformation likely have shaped a typical winter ITD
already in late autumn. Thus, the actual ITD shape in a specific region in spring depends mainly on the ice formation
and deformation history throughout winter.
[52] Currently, observations of sea-ice thickness from
field measurements, such as the ones from airborne EMbird measurements, are a valuable source of data to generate an ITD for the Arctic region with potential application
in sea-ice models. However, the use of a fixed ITD in
global climate models from observations of the past decade
must be done with caution due to the lack of representation
of the presently fast changing conditions on the Arctic sea
ice. It is also important noting that due to the nature of the
EM-bird measurements, the retrieved ice thickness
Figure 10. (a) Annual thermodynamic growth (km3
month21) of simulated Arctic sea ice integrated over the
period of analysis for the control run used as reference ; (b)
Difference between further experiments minus the control
run. Positive values indicate sea-ice freezing and negative
values indicate sea-ice melting.
heat flux (see equation (1)) and thus more freezing and
melting. The net effect is thicker ice because the influence
is larger for the freezing period, but the comparatively large
fraction of thin ice always allows ice growth and freezing.
[45] A general clustering of experiments with and without snow-constant is visible in Figure 10b. Larger freezing
and melting rates occur in experiment 6 (snowITD_15_19)
closely followed by experiment 5 (snowITD_15_1), and
experiment 2 (snowITD_7). In the latter, we observe the
second largest freezing rate and the third largest melting
rates. A second cluster of experiments is formed by experiments 3 and 4, both with snow-constant.
[46] As expected, the combined effect of a more realistic
ITD and a snow-ITD parameterization leads to a higher
sea-ice growth rate (Figure 10b). We calculated the difference in thermodynamic sea-ice growth between experiments 5 and 6 minus experiment 1 (control). A mean seaice growth of 180 km3 month21 was observed throughout
the year, with a mean from December to May of 443 km3
month21 and a mean from April to November of 282 km3
month21. The largest difference was found in January (545
km3 month21) and the lowest during June to August (mean
of 2310 km3 month21) when the melt rates are generally
larger than in the baseline experiment (Figure 10b).
[47] The mean sea-ice thickness in each model grid cell
is the convolution of the thickness in each category with
insulation with a decrease in Fc and a resulting low ice
thickness during winter. In contrast, the experiments with
snow-ITD have a thinner snow layer on top of thin ice,
allowing a higher Fc through the snow and ice layer and a
clear increase in sea-ice thickness. Because most of the
Arctic sea ice is currently dominated by first-year ice
(between 0.3 and 2 m), a prescribed ITD with better
resolved thin ice, will also lead to a higher sensitivity when
a snow-ITD is prescribed.
[57] We cannot suggest a best candidate for future simulations in numerical studies since both parameterizations
have advantages and disadvantages from a physical point
of view. A snow layer with a constant distribution can lead
to too much snow accumulation on a thin ice layer and, as
a consequence be inconsistent with the flooding algorithm
that acts on the mean ice and snow layers. On the other
hand, there is little observational evidence to suggest that
the depth of the snow layer is proportional to the depth of
the underlying sea ice.
[58] By introducing a different snow parameterization
and distributing it according to the prescribed ITD, we
observe a clear improvement in the modeled sea-ice thickness toward the satellite data during winter months. However, even with this snow parameterization the model
simulations do not compare well with ICESat data in
autumn (October/November). We attribute this bias to the
fact that ICESat data does not properly represent thin ice
(<1 m) which is present in autumn in large areas. The zero
heat capacity approximation in the modeled sea ice, however, can also be a factor that contributes to this difference.
represents the snow and ice layer for level ice. Furthermore, thick ice in the form of ridges is not well constrained
by this method and is underestimated due to footprint
[53] Besides the details of the ice thickness distributions,
our results show an even larger sensitivity of sea-ice thickness, and melting rates, to the distribution of snow on top
of the individual ice categories. This change in the model
configuration leads to ice thicknesses that are closer to ICESat values. With a nonuniform snow-ITD, a mean increase
of 0.56 m sea-ice thickness in the entire model domain and
about 1 m in the Canadian Basin and Canadian Arctic
Archipelago were found compared to using a snowconstant distribution. The larger increase in sea-ice thickness in certain regions of the model domain does not seem
to be related to the amount of the sea-ice thickness data
available to construct the ITDs (i.e., more observations
available, larger sea-ice thickness increase), but rather to
the type of ice (i.e., MYI or FYI). Thus, where there is normally thicker ice, a larger increase in thickness is found
with a snow-ITD distribution.
[54] Furthermore, the sensitivity of the snow distribution
on sea-ice thickness can be increased, or reduced, by the
selection of the ITD. We observe a higher sensitivity to the
snow parameterization for a multicampaign ITD compared
to a single-campaign ITD. This is possibly due to the different accumulation of snow relative to the different ice
[55] These results are corroborated by the melting and
freezing rates of sea ice, where we observe more sea-ice
growth during the freezing months when a snow-ITD is
used. This effect is more pronounced for the more realistic
15-category ITDs. However, the larger freezing rates go
along with larger melt rates during summer. This effect is
probably caused by more thin ice in the observation-based
ITDs allowing more heat flux and ocean warming during
summer, which in turn leads to higher melt rates.
[56] We compared our modeled thermodynamic growth
to observed values reported by Serreze et al. [2007a] who
estimated growth from net surface heat flux from ERA-40
data (1979–2001), hydrographic data for ocean sensible
heat storage, and observations of the latent heat content of
the ice divergence term. This was done over an Arctic
Ocean domain similar to our model domain. For September, Serreze et al. report ice growth of 6 cm; we obtained
for the same month a lower value for the mean model thermodynamic growth of 100 km3 (or 1.8 cm) in the control
run; and a value of 500 km3 (or 9 cm for a mean sea-ice
area of 5.5 3 106 km2) for the parameterization with snowITD, which is an ice growth 50 % bigger than the Serreze
et al. value. For February, we obtained a mean thermodynamic growth of 1200 km3, that is an ice growth of 9 cm in
the control run, and up to 16 cm (for a mean sea-ice area of
11 3 106 km2) in our parameterization of experiment 6
(snowITD_15_19). These values are both lower than the
values reported by Serreze et al. of 24 cm. The differences
between these comparisons may also fall within the uncertainties in the estimates (e.g., errors in the reanalysis data).
Our conductive heat flux calculations per ice category confirm the important role of a better description of the snow
layer. In the experiments with snow-constant a thicker layer
of snow is accumulated on top of thin ice, generating more
[59] Our results provide insight on the high sensitivity
that simulated Arctic sea-ice thickness pose to different
snow parameterizations and different descriptions of an ice
thickness distribution. These parameterizations play an
important role in optimizing simulated sea-ice cover; an
appropriate choice can improve the representation of its
energy and mass balance. Prescribing a better resolved ITD
derived from field observations leads only to a moderate
increase of simulated sea-ice thickness, but the sensitivity
of ice properties to the snow parameterizations has a larger
impact: simulated sea ice is much thicker when the snow is
distributed according to the ITD (snow-ITD), especially
when is combined with a realistic ITD with more
[60] Whenever the price for a dynamic ITD is too high,
we suggest that a more realistic distribution of sea-ice
thickness obtained from field observations be prescribed
for a better description on the current state of the Arctic sea
ice. The treatment of the snow distribution is clearly important for the simulated ice thickness, but the details of such
parameterization are still uncertain. Today, many observations of combined snow and ice thicknesses are available to
help further development of snow parameterizations, but
we encourage even more field observations at large scales
in order to find a representative and robust statistical relation between snow and sea ice. This relation will improve
the current parameterizations in models contributing to the
reduction of uncertainties. This will also help to constrain
the redistribution processes in dynamic ITD models;
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