Introduction
The evolution of Arctic sea ice towards a thinner, younger, and more seasonal
sea ice cover during the last few decades (e.g., Comiso, 2012; Haas et al.,
2008; Maslanik et al., 2007, 2011) has a strong impact on the partitioning of
solar energy between the atmosphere, sea ice, and ocean
(e.g., Perovich et al., 2007b, 2011a; Wang et al., 2014). Decreased surface albedo (Perovich et al.,
2011a), earlier melt onset, and a longer melt season (Markus et al., 2009,
updated) have contributed to the observed increases in sea ice and snow melt
(Perovich and Richter-Menge, 2009), and higher absorption and transmission of
solar irradiance within and through Arctic sea ice (Nicolaus et al., 2012;
Stroeve et al., 2014). Beyond the physical consequences of the observed
changes, strong impacts on ecological interactions and biogeochemical
processes are expected, such as changes in habitat conditions for
ice-associated organisms or changes in primary production (Arrigo et al.,
2012; Deal et al., 2011; Popova et al., 2012).
Various studies have shown the immediate link between sea ice energy and mass
balance, as well as the impact of energy fluxes on the physical properties of
sea ice (Grenfell et al., 2006; Light et al., 2008; Perovich and
Richter-Menge, 2009). These heat fluxes are composed of short-wave,
long-wave, conductive, and turbulent fluxes at the interfaces of sea ice with
the atmosphere and the ocean. Beyond these energy budget approaches, sea ice
mass balance may also be derived from direct comparisons of sea ice growth
during winter, and surface and bottom melt during summer (Perovich et al.,
2011b).
From studies on the interaction of sunlight and sea ice, it has been possible
to improve our understanding of the effects of snow cover (Perovich et al.,
2007b), melt ponds (Rösel and Kaleschke, 2012; Schröder et al.,
2014), and biological interactions (Arrigo et al., 2012; Mundy et al., 2005,
2007). In addition, the spatial variability (Perovich et al., 2011a) and
seasonal changes (Nicolaus et al., 2010a; Perovich et al., 2002; Perovich and
Polashenski, 2012) in the optical properties of sea ice and snow have been
studied by different methods. However, previous studies have not quantified
large-scale, multi-seasonal, and inter-annual changes, because these studies
were limited to different regions and/or seasons of the year. In addition,
these studies have described measurements on different ice types, which also
differ in their optical properties as a result of their growth history
(Perovich and Polashenski, 2012). One possible approach obtaining such
generalized studies on the in- and under-ice energy budgets in
sea-ice-covered oceans would be to use a radiative transfer model in
combination with surface energy budgets, as implemented by Perovich et
al. (2011a). However, such a model would require adequate knowledge about the
distribution of snow and sea ice (as forcing data) to derive the optical
properties of sea ice and snow as a function of space and time. This type of
information is not available yet, in particular not for timescales on the
order of decades. An alternative approach is to use existing remote sensing
and re-analysis data together with a parameterization of light transmittance
through sea ice. This method was developed by Nicolaus et al. (2012, 2013) to
calculate Arctic-wide radiation fluxes through sea ice. However, these
studies were restricted to 1 month (August 2011) when comprehensive in situ
measurements are available from the trans-polar cruise of German research
vessel Polarstern.
In order to improve the understanding of the ongoing change in sea ice
conditions and the associated impact on the partitioning of solar energy, we
provide an estimate of the monthly shortwave radiative transfer through sea
ice for the entire Arctic Ocean for the period 1979 to 2011. To emphasize the
changing physical properties of the Artic sea ice cover, our estimates
include fluxes through sea ice only. Therefore, we use a definition of 6
types of sea ice over the annual cycle, define 6 distinct time periods of
insolation conditions, and include the temporal and spatial variability of
melt ponds to extend and generalize the upscaling method of Nicolaus et
al. (2012, 2013). In order to investigate the reliability of the method and
to obtain a measure of uncertainty, we perform sensitivity studies by
comparing the calculated fluxes to in situ observations obtained from the
Transpolar Drift, between 86.5 and 88.5∘ N, during the drift study of
the schooner Tara from April to September 2007 (Nicolaus et al., 2010a).
Finally, it was possible to estimate transmitted heat fluxes through sea ice
and to derive trends for the entire Arctic basin for the period of 1979 to
2011. Since this study focuses on the variability of sea ice properties,
changes in sea ice concentrations are not considered.
Methods
Solar short-wave radiation fluxes (250 to 2500 nm, here also referred to as
“light”) through sea ice are calculated daily, from 1 January 1979 to
31 December 2011, for the entire Arctic Ocean (north of 65∘ N).
Building on the method and parameterization by Nicolaus et al. (2012, 2013),
which were limited to the snow-free summer season in 2011 without any
seasonal cycle of surface properties, the parameterization of light
transmittance through sea ice has been extended for all seasons. Thus,
transmittance is now estimated as a function of surface (snow) melt/freeze
state and melt pond concentration, in addition to the previous (only) sea ice
age dependence. The new parameterization was driven by satellite observations
of daily sea ice concentration and surface solar irradiance to calculate
fluxes as performed in Nicolaus et al. (2012, 2013). All data sets are
interpolated to a 10 km polar stereographic grid, using nearest-neighbor
resampling. Although daily fluxes are calculated and available, only monthly
means are shown and used to discuss the findings, because the main focus of
this extended study is on seasonal changes and long-term trends.
For the main analyses, we exclude open water areas, as those would clearly
dominate the transmitted heat flux signal (Perovich et al., 2007a).
Therefore, we consider only fluxes through ice-covered areas, as these are
crucial for the energy and mass balance of sea ice as well as for biological
processes beneath the ice cover. The solar heat input to the open ocean also
has an important impact on the ice–ocean system, but is a basic function of
sea ice concentration.
Solar heat flux equations
Solar heat input through sea ice into the ocean (ET(t,x,y)) is
calculated as the product of the downward solar radiation (Ed),
the sea ice concentration (Ci), and the total transmittance of
pond-covered sea ice (τi) for each grid cell and each day,
over the period 1 January 1979 to 31 December 1999:
ET(t,x,y)=Ed(t,x,y)⋅Ci(t,x,y)⋅τi,
with time (t) and position (x,y).
Classification of sea ice (a) types and
(b) surface properties as used in this study. The timing of each
phase results from the status of the sea ice. Depending on the season,
different sea ice types co-exist. Abbreviations: FYI: first-year ice; MYI:
multi-year ice; EMO: early melt onset; MO: melt onset; EFO: early freeze
onset; FO: freeze onset.
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Since 1 January 2000, when satellite-derived melt-pond concentrations are
available, the solar heat input through sea ice into the ocean
(ET) has been calculated as the sum of fluxes through bare ice
(EB) and melt ponds (EP):
ET(t,x,y)=EB(t,x,y)+EP(t,x,y)
ET(t,x,y)=Ed(t,x,y)⋅Ci(t,x,y)⋅1-Cp(t,x,y)⋅τb(t,x,y)+Ed(t,x,y)⋅Ci(t,x,y)⋅Cp(t,x,y)⋅τp(t,x,y),
with the transmitted solar radiation at the bottom of the ice ET,
downward solar radiation Ed, sea ice concentration
Ci, melt pond fraction Cp, transmittance of bare sea
ice τb, transmittance of melt ponds τp,
time t, and grid cell (x,y).
To obtain the total solar heat input per unit area for a certain time period
(QT(x,y)), the heat flux is calculated for each grid cell and
then integrated over the given time (Δt):
QT(x,y)=∑ET(t,x,y)Δt.
Spatial integration over the entire Arctic Ocean (north of 65∘ N)
reveals the Arctic-wide total solar heat input QT.
Assuming sea ice is at its melting point, has a density ρice
of 917 kg m-3, and has a latent heat of fusion Lice of
0.3335 J kg-1, and that there are no changes in long-wave, latent, and
conductive heat fluxes, QT(x,y) can be converted into a sea ice
melt rate meq:
meq=QT(x,y)Lmelt⋅ρice.
Seasonality of surface properties and transmittance <?xmltex \hack{\newline}?> of Arctic sea ice
To calculate solar heat fluxes under Arctic sea ice for an entire year, the
main challenge is to parameterize the seasonal evolution of
τb(t,x,y). This is mainly achieved by merging the sea ice
age information (Maslanik et al., 2007, 2011) with the melt/freeze status
(Markus et al., 2009, updated) into six surface types.
Definition of sea ice types
Figure 1 shows the annual cycle of these six sea ice classes together with
surface properties of Arctic sea ice. These classes are introduced to avoid
abrupt changes in the optical properties during the transition from spring to
summer as well as from summer to fall. After early melt onset (EMO),
melting FYI and melting MYI are introduced for sea ice
completely melting during the summer melt. Therefore, it is necessary to
classify each cell as either becoming ice free (sea ice concentration of less
than 15 %) or not. To do this, the ice concentration of each pixel is
evaluated for all days until EFO. If the pixel becomes ice free, the last day
of melting is stored for later calculations. According to Maslanik et
al. (2007, 2011), FYI surviving the summer melt turns into
MYI after week 36 of the year. As the immediate change in ice age
tagging is not associated with an immediate change in sea ice properties, we
include an additional class of new MYI that turns into MYI
at the end of the year. When sea ice concentration reaches a value greater
than 15 %, the pixel is classified as new FYI.
In the following, sea ice consisting of both bare sea ice and melt ponds is
called pond-covered sea ice.
(a) Total transmittance of sea ice during each phase
(Fig. 1). In this figure, melt pond concentrations of 26 % are assumed for
first-year ice (FYI) and 29 % are assumed for multi-year ice (MYI).
(b) Transmittance of bare ice during each phase (see Fig. 1).
Transmittance values for single ice classes are given in Table 1. The
illustrated evolution of transmittance values is based on analyses from
previous field campaigns and observations. Abbreviations: see Fig. 1.
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Transmittance of pond-covered sea ice
The seasonal evolution of surface properties and the transmittance of Arctic
sea ice is divided into six different phases (note that there are both
different ice types and different seasonal phases). The timing of these
phases is based on the melt and freeze onset data established by Markus et
al. (2009, updated). Our parameterization of seasonal variations in light
transmittance considers the transmission through both sea ice and snow, and
is mostly based on the results of two field campaigns that focused on the
understanding of ice–ocean–atmosphere processes that control the
partitioning of solar radiation between reflection, absorption, and
transmittance: the Surface Heat Budget of the Arctic Ocean (SHEBA) experiment
from 1997 to 1998 (Perovich, 2005), and measurements conducted on MYI within
the Transpolar Drift, between 86.5 and 88.5∘ N, during the drift
study of the schooner Tara from April to September 2007
(Nicolaus et al., 2010a). In addition, analyses from previous observations by
Perovich (1996), Perovich et al. (1998), and Nicolaus et al. (2010b) are
used. Figure 2a shows the seasonal total transmittance of pond-covered sea
ice (τi) for constant pond concentrations of 26 (FYI) and
29 % (MYI), respectively, used for the period 1979 to 2000, during which
time there are no available satellite melt pond coverage observations. This
combination of a given mixture of ponds and bare ice was used to develop the
seasonal cycle of transmittance, as described in the next paragraphs. All
transmittance values for the different phases are compiled in Table 1.
Phase I: winter (from FO <inline-formula><mml:math display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> 60 days to EMO)
Winter conditions are characterized by snow-covered sea ice without melt
ponds. The snow cover is assumed to be cold, dry and optically thick, which
means the snow determines the optical properties. Thus, radiative fluxes
through sea ice are small. The best available transmittance observations for
such conditions are those measured during the first days of the Tara drift,
although it was already early April. Hence, transmittance was accordingly set
to 0.002 (Nicolaus et al., 2010a).
Phase II: early melt (from EMO to MO)
EMO denotes the first significant change in optical properties. Snow depth
decreases, and surface and sea ice temperatures increase. Consequently, the
snow becomes wet and is no longer optically thick. This phase also
corresponds to formation of the first melt ponds. Here we assume a linear
increase in τi until MO.
Nicolaus et al. (2010a) calculated a transmittance of 0.02 for MYI for the
day of MO. Furthermore, Perovich and Polashenski (2012) reveal that the
surface albedo of FYI is about half that of MYI at the same time. Adapting
this albedo evolution to the transmittance, the transmittance of FYI is
assumed to be 0.04 at MO.
Melting FYI and melting MYI
After EMO, the continued melt of snow and sea ice strongly impacts light
transmittance. Starting with the summer phase (Phase IV), we assume that the
optical properties of melting sea ice differ from sea ice surviving the
summer melt. In addition, differences between melting FYI and melting MYI are
expected. Therefore, melting FYI and melting MYI are separated in the
parameterization of τi.
In order to describe these classes, laboratory studies by Perovich (1996) on
the evolution of albedo during the initial ice growth phase were applied to
the evolution of transmittance, assuming an inverse behavior of transmittance
and albedo. Therefore, the increase in transmittance of seasonal sea ice can
be described as roughly exponential (Perovich, 1996). Assuming the transition
of transmittance from melting sea ice to the open ocean is the inverse of the
albedo transition (Perovich, 1996), we use a transmittance of 0.4 for the
last remaining sea ice. Thus, an exponential increase between the first and
last day of melting for the corresponding pixel is fitted, and the maximum
transmittance of sea ice is expected to be 0.4.
Phase III: continuous melt (from MO to MO <inline-formula><mml:math display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> 14 days)
After MO, snow is assumed to melt completely within 14 days (Nicolaus et al.,
2006; Perovich et al., 2002), and pond cover fraction increases rapidly until
the maximum pond cover is reached at the end of this phase (Nicolaus et al.,
2010a). The transmittance continues to increase linearly until the beginning
of summer (MO + 14 days).
Phase IV: summer (from MO <inline-formula><mml:math display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> 14 days to EFO)
During this phase, the sea ice surface is characterized by strong sea ice
melt and culminates in the minimum ice concentration of each pixel. The
surface is a mixture of bare ice and melt ponds with a constantly renewing
surface scattering layer (Perovich et al., 2002; Barber et al., 1998). This
implies small changes in the optical properties and light transmittance of
the ice over time during Phase IV. Hence, τi is assumed to be
constant for sea ice that survives summer melt. Based on observed
transmittance values of solar radiation through FYI and MYI during TransArc
2011 (Nicolaus et al., 2012), we use summer transmittance values of 0.04 for
bare FYI, 0.01 for bare MYI, 0.22 for melt ponds on FYI, and 0.15 for melt
ponds on MYI. These values are weighted according to melt pond fractions
(Rösel and Kaleschke, 2012).
Phase V: fall freeze-up (from EFO to FO)
Air and surface temperatures drop below 0 ∘C, resulting in the
initial occurrence of surface freezing. Subsequently, snow accumulation can
begin and former melt ponds refreeze, but can still be recognized through the
new snow cover. Thus, the transmittance is decreasing rapidly. Similar to
Phase III, the transmittance of FYI decreases to 0.04 and, for MYI, to 0.02
until FO. Additionally, sea ice that survives the summer melt is promoted to
1-year older ice in weeks 36–37 according to Maslanik et al. (2007), and new
ice forms. The transmittance of new first-year ice evolves correspondingly to
the melting sea ice surface described above. From EFO until the beginning of
winter (FO + 60 days), the strong growth of sea ice (e.g., increasing sea
ice thickness) results in an exponential decrease in light transmission
through newly formed FYI.
Phase VI: continuous freeze (from FO to FO <inline-formula><mml:math display="inline"><mml:mo>+</mml:mo></mml:math></inline-formula> 60 days)
This phase is characterized by continuous freezing, increasing snow
accumulation towards an optically thick snow layer, and the gradual
disappearance of melt ponds. In addition to new sea ice formation, the
existing sea ice is getting thicker and older, and deformation is increasing.
Transmittance decreases back to 0.02 by winter. It is assumed that at the end
of the freezing phase (FO + 60 days), the surface properties of all newly
formed FYI can be considered to be equivalent. Afterwards, the accumulated
optically thick snow layer again dominates the optical properties of FYI and
MYI (Phase I).
Transmittance of bare ice and ponds
For the period after the year 2000, when satellite-derived melt pond products
are available from Rösel and Kaleschke (2012), the transmittance values
of bare ice (τb) and ponds (τp) are treated
separately (Fig. 2b). The modal transmittance of melt ponds is constant over
the entire melt season. It is set to 0.22 for FYI and 0.15 for MYI, as
measured during TransArc 2011 (Nicolaus et al., 2012). The seasonal evolution
of transmittance for bare ice (τb) follows the transmittance
for pond-covered sea ice (τi):
τb(x,y)=τi(x,y)⋅τb(summer,x,y)τi(summer,x,y).
The values of τb(summer, x, y) and τi
(summer, x, y) are the constant values during summer as given in Table 1.
Thus, the ratio of both is constant for MYI (0.20) and FYI (0.46). Finally,
those transmittance values are scaled with the pond concentrations, as given
in Eq. (2).
Deriving trends
Based on the calculated results of the solar heat input through sea ice into
the ocean, trends are analyzed for the period 1979 to 2011. The trends
(monthly and annual) are calculated by a linear least-squares fit of the
total mean (monthly or annual) heat flux for each grid cell QT(x,y). Resulting trends are normalized by trends in sea ice concentration,
because here we focus on radiative fluxes through the ice-covered part of the
ocean. Otherwise, the results would depend strongly on regional and temporal
trends in sea ice concentration, because of the high transmittance (0.93) of
open water. All trends were calculated for both the annual mean ice-covered
area in 2011 and the monthly mean ice-covered area in 2011 (sea ice
concentration > 15 %) to allow for a representative comparison. Regions
that were not ice covered at any time in 2011 are excluded from the main
analysis and discussion.
Transmittance values of different sea ice and surface types.
Abbreviations: FYI: first year ice; MYI: multi-year ice; Phase I: winter; MO:
melt onset; Phase IV: summer; FO: freeze onset; Threshold: transition from
open ocean to sea ice and vice versa.
Phase I
At MO
Phase IV
At FO
Threshold
(winter)
(summer)
FYI, pond-covered sea ice
0.002
0.04
0.087
0.04
0.4
MYI, pond-covered sea ice
0.002
0.02
0.05
0.02
0.4
FYI, bare ice/snow
0.001
0.017
0.04
0.017
0.17
MYI, bare ice/snow
0.0
0.004
0.01
0.004
0.07
FYI, melt ponds
0.22
MYI, melt ponds
0.15
Open ocean
0.93
Data sources of the different parameters used in this study.
Parameter
Time period
Source
Sea ice concentration
1979–2007
OSI SAF, reprocessed data
2008–2011
OSI SAF, operated data (Andersen et al., 2007)
Sea ice age
1979–2011
Maslanik et al. (2007, 2011)
Downward surface solar radiation
1979–2011
ECMWF (Dee et al., 2011)
Melt and freeze onset
1979–2005
SSMR
2006–2010
AMSR-E
2011
SSM/IS (Markus et al., 2009)
Melt pond fraction
1979–1999
Constant fraction as in 2011
2000–2011
ICDC (Rösel et al., 2012)
Monthly mean of total solar heat input (QT(x,y)) under
Arctic sea ice (ice-covered areas only) for the year 2011.
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Input data sets
The following satellite and re-analyses data sets were used (Table 2):
Sea ice concentration observations were obtained from the Special Sensor
Microwave Imager (SSMI/S) provided through the Ocean and Sea Ice Satellite
Application Facilities (OSI SAF, product ID OSI-401, Andersen et al., 2007).
For this study, a combination of reprocessed data (1979 to 2007) and
operational data (2008 to 2011) was used. Both data sets have systematic
differences due to processing with a different set of tie point statistics
for the ice concentration algorithm (Lavergne et al., 2010). However, within
the documented uncertainties, both data sets build the best available and
consistent time series of sea ice concentration. There is no consistent
uncertainty for the data product, but different approaches for determining
uncertainties are described in Lavergne et al. (2010).
For sea ice age, we used the updated data product by
Maslanik et al. (2007, 2011). This product has been available since 1979, and
is based on satellite-derived ice motion data calculated from different
sensors using a Lagrangian feature tracking algorithm. Although this data
product distinguishes ice ages between 1 and 10 years, here we only
distinguish FYI and MYI (2 years and older), because all MYI is assumed to
have similar optical properties. All data points with a sea ice concentration
of greater than 0 but without an assigned sea ice age class were treated as
FYI. Vice versa, all data points with sea ice concentration of greater than 15 %
but which had an assigned sea ice age class were treated as open
water. Such modifications were necessary to obtain consistent data products
from the different sources, indicating partially varying sea ice extents. The
ice age data set represents a 7-day average of either FYI or MYI without any
uncertainty estimates. However, uncertainties in sea ice concentration and
drift will have an impact on the ice age data.
Downward surface solar radiation data were obtained four times per day
from the European Centre for Medium-Range Weather Forecast (ECMWF)
Era-Interim re-analyses (Dee et al., 2011; Lindsay et al., 2014). The data
(four values per day) were averaged to daily means and have been available
since 1979. Uncertainties for the data set are not reported.
Sea ice surface characteristics were categorized by melt and freeze
onset dates from passive microwave data (1979 to 2012) (Markus et al., 2009,
updated). The data set distinguishes between the first occurrence of a melt
event (early melt onset, EMO), the following continuous melt (melt onset,
MO), the first occurrence of freeze-up conditions (early freeze onset, EFO),
and the day of persistent freezing conditions (freeze onset, FO). The
standard deviations, assumed as uncertainties, for the given dates are
reported as EMO ± 3.6 days, MO ± 3.7 days, EFO ± 4.5 days,
and FO ± 4.0 days (Markus et al., 2009, updated).
Melt pond fraction was used from Rösel et al. (2012),
retrieved from the Moderate Resolution Imaging Spectroradiometer (MODIS)
onboard NASA's Terra and Aqua satellites. As this data set has only been
available since 2000, melt pond fractions from 1979 to 1999 were set to
constant summer mean values of 26 % for FYI and 29 % for MYI, as given in
Rösel et al. (2012) for August 2011. In order to maintain the consistency
of the surface characteristics, all melt pond fractions before EMO are set to
zero. The mean standard deviation from 2000 to 2011, assumed as uncertainty,
is calculated as ±3 % for FYI and MYI.
We do not include snow depth and sea ice thickness as input data sets due to
the lack of consistent high temporal resolution and long-term data products.
Limitations of using sea ice age as an indirect proxy for ice thickness and
snow cover as well as potential other approaches for the estimation of
transmitted heat fluxes are discussed below.
Annual total solar heat input (QT(x,y)) through Arctic
sea ice. (a) Average and (b) trend from 1979 to 2011. The
trend is normalized for the trend in sea ice concentration. Purple shaded
areas were not covered with sea ice during the maximum extent in all years.
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Results
Seasonal cycle of solar radiation under Arctic sea <?xmltex \hack{\newline}?> ice in 2011
Based on the availability of all input data sets and the seasonality of
transmittance values, the solar heat input through sea ice into the ocean is
analyzed from 1979 to 2011. Figure 3 shows monthly mean heat input
(QT(x,y), Eq. 3) under Arctic sea ice (ice-covered areas only)
from April to September 2011. The exemplary year of 2011 was selected to
ensure a representative comparison with previous studies conducted in
August 2011 by Nicolaus et al. (2012, 2013). From October to March, the
monthly mean solar radiation under sea ice was less than
0.2 × 105 Jm-2, with an Arctic-wide total under-ice heat
flux (QT) of up to 0.4 × 1019 J. Since this
represents less than 1 % of the annual Arctic-wide heat flux of
53.3 × 1019 J (Eq. 3), the months October to March are omitted
from further analyses and discussion. In April, the mean heat flux increased
to 0.4 × 105 Jm-2, with a maximum of 7 to
8 × 105 Jm-2; this amount of energy is equivalent to mean
ice melt rates between 7 to 8 cm per month (Eq. 4) in the marginal ice zone
east of Spitsbergen. The transmittance triples from 0.005 in April to 0.015
in May, and together with increasing surface fluxes, the QT(x,y)
increased from 1.0 × 1019 J to 5.5 × 1019 J
during this time. The Barents Sea showed a mean transmitted heat flux of
2.2 × 105 Jm-2 for the month of May, with a maximum value
of 25 × 105 Jm-2, which corresponds to a maximum sea ice
melt of 25 cm per month. May to June showed the most pronounced monthly
increases in QT(x,y) of 9.3 × 105 Jm-2 and a
transmittance of 0.054 for the entire Arctic. The maximum QT(x,y) was 30 × 105 Jm-2 in June, with a corresponding
maximum melt rate of approximately 30 cm per month. June also had the
highest QT (20.9 × 1019 J), which was associated
with the highest surface solar irradiance over the entire Arctic Ocean
(851 × 1019 J). This increase in solar irradiance was linked
to the beginning of the melt phase (mean MO on 30 May 2011) and the
associated rapid snow melt. During this time, the difference between thin
melting sea ice along the sea ice edge and the persistent sea ice cover
became most obvious, e.g., in the Chuckchi and Beaufort seas. In July,
Arctic-wide averaged QT(x,y) reached its annual maximum of
9.8 × 105 Jm-2. This resulted primarily from the annual
maximum in mean transmittance of 0.089, and led to a
monthly flux QT of 18.4 × 1019 J. The impact of
the different optical properties (τi) of MYI and FYI became
most obvious in July, because the difference in both values is at its
maximum. In addition, the strong decrease in sea ice concentration along the
ice edge became more important for the under-ice heat fluxes, because light
transmittance increased strongly in these regions. The August decrease in
QT(x,y) by more than 50 % to
4.4 × 105 Jm-2, along with only a slight reduction in
transmittance to 0.084, can be explained by the strong decrease in surface
solar irradiance (679 × 1019 J). These surface fluxes are only
half of those calculated for previous months. August maximum QT(x,y) reached up to 19 × 105 Jm-2. In September, the
QT(x,y) decreased further to 0.6 × 105 Jm-2,
which can be related to a low transmittance of 0.039 and QT of
0.7 × 1019 J.
Arctic-wide total solar heat flux under sea ice (QT)
(black) and monthly Arctic-wide solar heat input for May to August (colored)
and its trend from 1979 to 2011. The data are corrected for the trend in sea
ice concentration. Areas that were not ice covered at any time in 2011 or
during a certain month in 2011 are excluded from the analyses.
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Light transmission from 1979 to 2011
The new data set of QT(x,y) allows quantification of annual
budgets, regional differences, and decadal trends. Figure 4a shows the
averaged annual solar heat input through sea ice into the ocean
(QT(x,y)), and illustrates therefore the strong regional
variability of QT(x,y), ranging from 20 to 100 MJ m-2 for
the given period. This range in heat fluxes is equivalent to an ice melt rate
of 24 to 120 cm yr-1. The mean total solar heat input transmitted through the
considered sea-ice-covered area (Sect. 2.3) was 46 MJ m-2. The maximum
QT(x,y) occurs at the edge of the marginal ice zone in the
Canadian Arctic Archipelago (up to 110 MJ m-2/130 cm melt per year)
and the East Siberian and Chukchi seas (up to 80 MJ m-2/94 cm melt
per year). In contrast, excluding areas characterized by a strong spring sea
ice retreat and a corresponding low sea ice concentration, the minimum
QT(x,y) was found in the central Arctic, an MYI-dominated region
of low transmittance.
The mean trend of QT(x,y) was 1.5 % a-1 (excluding areas
with a strong spring sea ice retreat), with a maximum of +4 % a-1
in the East Siberian Sea and the southern part of the North American and
Russian Arctic Basin (Figs. 4b and 5a). This trend translates to a 63 %
increase in the potential sea ice melt over the 33-year observation period.
This is likely due to the prolongation of the melt season in the same
regions. According to a linear regression from 1979 to 2011 for the entire
Arctic, the mean MO was 4 days earlier, shifting from day 145 (24 May) to
day 141 (20 May). The strongest trend of
4.8 × 1018 J a-1 was found for June, followed by May and
July with 1.8 × 1018 J a-1. August shows a comparably
weak negative trend of -0.2 × 1018 J a-1. Assuming an
identical sea ice extent in 1979 and 2011, the increase in the annual mean
solar heat flux through sea ice (QT) amounts to
22.5 × 1019 J for the entire Arctic over the full study
period. This corresponds to an average increase of 33 %. Overall, 94 % of
the total annual solar heat input through Arctic sea ice was observed during
the four key months: May to August. Furthermore, heat flux time series
(annual, June, July) show an increasing variability after 1999 (Fig. 5).
Discussion
Seasonality and trends of transmitted fluxes
The total annual solar radiation under Arctic sea ice was estimated to be
53.3 × 1019 J in 2011. Based on this, May to August are the
most important months for the radiative energy partitioning. During this
period, 96 % (51.2 × 1019 J) of the total annual solar heat
input is transmitted through the sea ice. Extending the period to April to
September amounts to 99 % (52.9 × 1019 J) of the total
annual flux being transmitted within only a 6-month period. Generalizing the
monthly fluxes, the annual cycle can be summarized in three phases: (1) the
heat input through snow and sea ice into the ocean is negligible between
October and March, (2) surface solar radiation dominates the under-ice light
conditions from April to June, because transmittance increases only slowly,
while surface irradiance determines most of the observed changes and
variability, and (3) during summer (July to September), energy fluxes depend
mainly on the sea ice type, showing large differences in transmittance
between FYI and MYI.
Comparing our results to the development of the solar heat input into the ice
presented by Perovich et al. (2011a, Fig. 2), both the solar heat input to
the upper ocean and the solar heat input to the sea ice demonstrated a
positive annual trend of 1 to 1.5 % yr-1 during the last decades. The
increasing energy in the ice and upper ocean might both lead to a stronger
sea ice melt. Therefore, the radiative heating of the upper ocean might
contribute to a higher conductive ocean heat flux to the ice. This increase
in bottom melt is affecting the sea ice mass balance. An increasing light
absorption of Arctic sea ice due to more seasonal ice and less multi-year ice
was also found by Nicolaus et al. (2012).
The trend towards more light transmission through sea ice does not only
impact the light conditions right at the bottom of the sea ice, but also
affects the horizontal and vertical light field in the ice-covered ocean.
More light at the bottom of sea ice will deepen the euphotic zone, as more
light penetrates deeper into the ocean (Frey et al., 2011; Katlein et al.,
2014). More light can contribute to an increase in mixed layer temperature,
and provide more energy for primary production and biogeochemical processes
in and beneath the sea ice. However, it has to be noted that an increase in
light availability does not necessarily increase biological activity, and
might also be harmful (Leu et al., 2010).
An increase in transmittance will accelerate internal and bottom melt, which
in turn will reduce the thickness of sea ice and increase transmittance. That
feedback process can trigger a transmittance-melt feedback.
All presented trends are normalized with the trend in sea ice concentration
(Sect. 2.3). Thus, changes related to physical properties of the sea ice are
highlighted instead of changes related to a general sea ice retreat. Fluxes
through the ice-covered ocean will be of great importance, and are much more
difficult to assess than fluxes through open water. However, including the
trend in sea ice concentration, the annual trend of transmitted solar heat
fluxes to the upper ocean decreases from +1.5 to ±1.1 % a-1.
The negative trend in the open ocean heat input is evident in areas of ice
motion causing an increase in ice concentration, which was also shown in
Perovich et al. (2007a, 2011a). This comparison emphasizes the dominance of
the albedo feedback mechanism and the strong influence of the trend in sea
ice concentration on the heat budget of the entire system.
Beyond this, it is also important to consider that the trends in sea ice
concentration differ significantly during different months. While it is
largest (-0.1 % a-1) in September, it is only -0.06 % a-1
in June, and even positive in April and May (+0.04 % a-1). This
means that the effect of increasing transmission through open water is
particularly strong in September, but less pronounced in June, when the
highest absolute fluxes are observed, or in spring, when the impact on
biological primary production is expected to be strongest (Wassmann and
Reigstad, 2011).
Comparison with field data
Validation of the calculated trends and spatial variability is nearly
impossible, as insufficient field data with adequate spatial and temporal
coverage are available. However, some comparisons with time series of light
transmission from different field studies may be performed to identify major
uncertainties.
(a) Transmitted total solar heat input and
(b) total transmittance during the drift of Tara in 2007 (Nicolaus
et al., 2010b). Compared are in situ measurements (green) with the presented
method (red) and the presented method, but using the observed dates for phase
transitions. Between 16 July and 14 August (dotted lines), a comparison is
not reasonable, since the sensor was strongly influenced by biological
processes during Tara.
![]()
Here, we compare the surface and transmitted solar irradiance of the
presented method with in situ measurements during the Transpolar Drift of
Tara from 29 April to 28 August 2007 (Nicolaus et al., 2010a).
Nearest-neighbor grid points within 0.5∘ of the daily Tara position
were extracted from the presented data set and averaged. Figure 6a (red and
green lines) shows a comparison of the time series for transmitted solar
irradiance from both data sets. Until 8 June, the transmitted solar
irradiance under sea ice varied only slightly, around 0.5 Wm-2, for
both the calculated and measured time series. Afterwards, until the end of
June, the measured transmitted fluxes increased steadily towards
10 Wm-2, whereas calculated fluxes were highly variable, with most
values below 4 Wm-2. Hence, the total solar heat input through the sea
ice to the ocean from 1 May to 16 July 2007 was 21.4 MJ m-2 for the
observed Tara data, whereas the calculated data resulted in a 17 % lower
total heat flux of 17.7 MJ m-2. The calculated underestimation is
equivalent to 1 cm of sea ice melt for this period. During summer (16 July
to 14 August 2007), under-ice fluxes cannot be reliably compared, since the
sensor at the Tara study was strongly influenced by biological processes in
ice and water, causing increased absorption and reduced transmitted fluxes.
Thus, the calculated fluxes were overestimated by 11.6 MJ m-2,
representing an equivalent sea ice melt of 4 cm during summer.
After 14 August, the measured transmitted heat flux increased rapidly to
about 6 Wm-2, comparable to the calculated value. Finally, the decrease
in solar elevation caused decreasing transmitted fluxes in both data sets,
resulting in similar heat fluxes of 0.28 × 103 MJ m-2
after 14 August.
The main reason for these differences is the timing of the phases describing
the surface characteristics. While both data sets have a coincident EMO on
9 June, large differences are evident for the later phase transitions: the
observed MO at Tara was on 21 June, whereas the calculated MO for the center
position was 17 days later on 8 July. Considering the eight neighboring cells
results in a mean MO on 13 June. This shows that there is a difference of
25 days in MO for the 10 km grid. As presented above, the transmitted heat
flux depends strongly on the timing of the different melt phases by Markus et
al. (2009). EFO was observed on 15 August during Tara, whereas the satellite
data maintain summer melt conditions until 14 September. However, the total
solar heat input through sea ice was similar for both data sets. Thus, the
solar radiation flux under Arctic sea ice depends strongly on the timing of
EMO and MO, while the timing of EFO and FO seems to be of less importance,
since the beginning of the melt season coincides with maximum surface solar
heat fluxes. The timing of melt onset also has a large influence on the total
amount of light absorption, as shown in Stroeve et al. (2014). Including the
ongoing lengthening of the melt season by up to 2 weeks per decade (by a
later EMO), Stroeve et al.'s (2014) calculations suggest an albedo decrease
of 9 % per decade.
In a second validation step, the heat fluxes were re-calculated using the
onset dates as observed during Tara instead of those by Markus et al. (2009)
(Fig. 6, black lines). This eliminated the impact of the onset dates on the
results. Nevertheless, the calculated total solar heat input through sea ice
still differed by 18 % (25.4 MJ m-2) from the Tara fluxes until
16 July (Fig. 6a), due to an unexpected peak in QT(x,y) in July.
In addition, the calculated time series still showed large day-to-day
variability, including much higher transmittance values than observed at
Tara. The main reason for this is the combination of both sea ice types (FYI
and MYI), whereas the Tara floe consisted of MYI only. Consequently, the
strong differences in optical properties of FYI and MYI, as parameterized
here, strongly contribute to the overall energy budget. To overcome this
problem, FYI/MYI fractions per grid cell (Kwok, 2004) could be used instead
of the presented discrete distinction. However, such a data set is not yet
available for the given time span.
Hudson et al. (2013) measured heat fluxes and calculated transmittance values
of Arctic FYI in July/August 2012. However, a direct comparison of energy
fluxes, as for the Tara measurements, is not possible, because the melt-pond
concentration data set ends in December 2011. August transmittance in our
study (0.087) is based on the observations by Nicolaus et al. (2012), which
is only half of the 0.16 found by Hudson et al. (2013). Hence, it may be
assumed that heat fluxes through sea ice would be larger, based on those
measurements. Differences between both studies mainly result from differences
in sea ice thickness during the respective campaigns as well as the different
methods of quantifying transmittance (mean value vs. modal value) (Hudson et
al., 2013).
Limitations
Measurements from ice-tethered profilers (ITPs) (Krishfield et al., 2008)
could be used as an alternative approach to estimate uncertainties of the new
parameterization. They allow quantifcation of the heat content of the
uppermost ocean and its changes. However, such a comparison would require a
significant extension of the present study, integrating radiation fluxes to
larger depths and through open water. Similarly, the inclusion of a radiation
transfer model is beyond the aim of this study. The advantage of this study
is the rather simplistic approach based on a seasonal parameterization of
under-ice fluxes applied to existing large-scale data products.
An improvement to this study would be the inclusion of sea ice thickness
(e.g., CryoSat-2, IceSat, OperationIceBridge) and snow depth (e.g., AMSR-E)
observations from satellites. As with all other input data, the
above-mentioned products need to be consistent over many years and reliable
during all seasons. However, this is not the case yet, and even the most
recent data sets have huge uncertainties or are not available after melt
onset (e.g., Ricker et al., 2014), which is the most important time with
respect to transmitted heat fluxes. Hence, these parameters are not
applicable for such parameterizations yet. Instead, sea ice age is used as a
proxy for ice thickness and snow depth distribution. It also includes
information about roughness and deformation of the sea ice surface. These
characteristics are crucial for the description of optical properties of sea
ice.
In addition, including data sets of different model simulations, such as sea
ice thickness, snow depth, and melt pond fraction (e.g., Flocco et al., 2012;
Schröder et al., 2014), can be considered to be an alternative approach
for the presented calculations.
Another uncertainty in the presented heat flux calculations results from
constant values for the transmittance of melt ponds on FYI and MYI. Based on
our existing data, it was not possible to include a seasonality in melt pond
transmittances, which represents the different formation and evolution stages
(Perovich and Polashenski, 2012). However, the applied transmittances of melt
ponds are modal values of a distribution function (Nicolaus et al., 2012),
representing a range of possible values. This has to be considered when
comparing our fluxes to other observations or model results. Overall, we
expect that the uncertainties resulting from the missing seasonal cycle will
have a much smaller impact than the timing of melt onset, which is discussed
in the next section.
Sensitivity studies
Based on uncertainties of the independent input variables (timing and length
of the melt season, ice age, and melt pond fraction), several sensitivity
studies have been performed to estimate the uncertainty for the presented
parameterization.
The first study studies the effect of altering the timing and duration of the
melt season on the solar heat input to the upper ocean. Three cases are
discussed: shifting the melt season dates by (Case 1a) the average
uncertainty of 4 days, as given by Markus et al. (2009), (Case 1b) 7 days
based on the temporal resolution of ice age data (once per week) (Maslanik et
al., 2011), and (Case 1c) (averaged) 14 days, as derived from comparisons
with the Tara field data (Nicolaus et al., 2010a). Based on the observed
ongoing trend towards a lengthening of the melt season, all sensitivity
studies were only performed for earlier EMO and MO, and a later EFO and FO
for the exemplary year of 2011.
Extending the melt season by 4 days (Case 1a) results in Arctic-wide mean EMO
on 12 May and MO on 27 May. This affects most regions primarily during
periods of high sea ice concentration and large surface solar irradiance. It
results in an increase in total annual solar heat input through sea ice to
the ocean (QT) of 7 %, from 53.3 × 1019 J to
57.0 × 1019 J, for the entire year of 2011. The strongest
increase of 20 % compared to the reference melt onset dates was found in
May, while the strongest absolute increase of 1.9 × 1019 J was
found in June.
Including 7 days earlier EMO and MO (8 May and 23 May, respectively)
(Case 1b) result in an additional heat input of 5.9 × 1019 J (+11 %) compared to
the reference system for the total annual heat input to the upper ocean.
Shifting the melt season another 7 days (Case 1c) backwards (1 and 16 May),
the increase in QT is more than double compared to the 7-day
shift (Table 3, 66.3 × 1019 J). The pronounced increase is
most evident in May, when 90 % more light transmission was found than in
the reference system. The strongest absolute increase of
6.2 × 1019 J (transmittance from 0.054 to 0.067) was
calculated for June. The spatial distribution in the impact of the 14-day
earlier EMO and MO showed the largest increase in solar heat input to the
upper ocean in the marginal ice zone, with increases greater than 100 %
(Fig. 7a).
Annual Arctic-wide solar heat input (and relative changes) under sea
ice (QT) in 2011 for the reference method and sensitivity
study 1: changes in melt season duration by a shift of 4 days (data
uncertainty, Markus et al., 2009), 7 days (estimated uncertainty due to the
only weekly sea ice age data by Maslanik et al., 2011),
and 14 days (derived from comparisons to field data; Nicolaus et al., 2010a).
All trends were only performed towards a prolongation of the melt season. All
numbers are in 1019 J.
Reference
Changing EMO and MO
Changing EFO and FO
system
-4 days
-7 days
-14 days
+4 days
+7 days
+14 days
Apr
1.00
1.17 (+17 %)
1.19 (+19 %)
1.45 (+45 %)
1.00 (0 %)
1.00 (0 %)
1.00 (0 %)
May
5.53
6.64 (+20 %)
7.35 (+33 %)
10.5 (+90 %)
5.53 (0 %)
5.53 (0 %)
5.53 (0 %)
Jun
20.9
22.8 (+9 %)
24.0 (+15 %)
27.1 (+30 %)
20.9 (0 %)
20.9 (0 %)
20.9 (0 %)
Jul
18.4
18.7 (+2 %)
19.1 (+4 %)
19.7 (+7 %)
18.4 (0 %)
18.4 (0 %)
18.4 (0 %)
Aug
6.33
6.34 (0 %)
6.42 (+1 %)
6.48 (+2 %)
6.46 (+2 %)
6.51 (+3 %)
6.68 (+5 %)
Sep
0.69
0.69 (0 %)
0.69 (0 %)
0.69 (0 %)
0.74 (+7 %)
0.81 (+17 %)
0.97 (+41 %)
Jan–Dec
53.3
57.0 (+7 %)
59.2 (+11 %)
66.3 (+24 %)
53.4 (0 %)
53.6 (+0 %)
53.9 (+1 %)
Changes in annual total solar heat input (QT(x,y))
through sea ice in 2011, resulting from a sensitivity study assuming an
extended melt season. (a) 14 days earlier early melt onset and melt
onset, and (b) 14 days later early freeze onset and freeze onset
than in the reference method, based on Markus et al. (2009).
![]()
Extending the melt season by 14 days later EFO and FO (Case 1c) (21 October
and 2 November, respectively) result in a 1 % increase in QT
from 53.3 × 1019 J to 53.9 × 1019 J (Fig. 7b).
Since the surface solar radiation is much less than between April and June,
the change at the end of the melt season is small during August and September
(increase of 9 % from 7.02 × 1019 J to
7.65 × 1019 J). Seven-day or rather four-day (cases 1a and 1b)
later EFO and FO have a negligible effect on the total annual transmitted
heat flux of less than 1 %.
In a second sensitivity study, the influence of the ice type was quantified.
As the sea ice type data contain no uncertainty, the study is based on the
ongoing trend towards a predominantly FYI-covered Arctic Ocean. The reference
ice cover of 2011 consists of 56 % FYI and 44 % MYI in August 2011.
Assuming that all sea ice in 2011 was MYI, the mean transmitted flux
decreased by 34 % to 35.5 × 1019 J. In contrast, assuming
that only FYI was present increased the mean transmitted flux by 18 %, to
62.7 × 1019 J. Hence, the transition from an MYI- to
FYI-dominated Arctic sea ice regime results in a further increase in solar
heat flux under Arctic sea ice.
The third sensitivity study investigates the effects of melt pond fraction
uncertainties. Here, we consider two cases: (Case 3a) Rösel et al. (2012)
give a mean uncertainty of 3 %, and (Case 3b) we estimate an uncertainty of
20 % due to the neglected seasonal cycle. Adapting these assumptions, an
increasing melt pond fraction of 3 % (20 %) results in an increase in the
transmitted heat flux of 1 % (9 %).
Uncertainties in the solar surface radiation and sea ice concentration are
not analyzed through additional sensitivity studies, because they impact the
results linearly (Eq. 2).
Summary and conclusions
The presented parameterization for light transmission through Arctic sea ice
in combination with satellite-derived time series observations and
re-analysis data allowed the quantification of solar short-wave radiation
fluxes through Arctic sea ice for the entire annual cycle over 33 years (1979
to 2011). The presented results suggest that 96 % of the total annual solar
heat input through sea ice occurs over only 4 months (May to August), with
the highest transmitted fluxes calculated for June. Over the time period 1979
to 2011, an increase in light transmission of 1.5 % yr-1 with
regional maxima of 4.0 % was found. Hence, the amount of short-wave
radiation that may contribute to sea ice bottom melt increased by 63 % over
this 33-year period. The results of our sensitivity studies show that energy
fluxes depend strongly on the timing of melt onset, sea ice types (first- and
multi-year ice), and melt pond fraction. These are the most critical
parameters for the presented calculations, and describe the most critical
uncertainties. The calculated trends are affected by most of these
uncertainties.
This study considers the fluxes through ice-covered ocean regions only. This
highlights the fact that changes in sea ice properties have a large impact on
the sea ice and upper ocean energy budget, and that this impact adds to the
obvious increase in energy input resulting from the observed decrease in
ice-covered areas (open ocean effect). However, the ongoing retreat of sea
ice will cause additional increases in radiation fluxes into the Arctic
Ocean. The additional heat will also contribute to an increase in heat stored
in the ocean mixed layer, and will impact the melt season duration and
timing, particularly during autumn freeze-up.
A comparison of trends in solar heat fluxes into the sea ice by Perovich et
al. (2011a) with our calculated solar heat fluxes through sea ice suggests
similar increases in transmitted and absorbed energy. This additional energy
input into the sea ice and the upper ocean would also impact inner sea ice
structures as well as internal and basal melting. Studies from Perovich et
al. (2011a) and Nicolaus et al. (2012, 2013) reveal that fluxes through open
water clearly dominate the transmitted heat flux signal and, therefore, the
effect of sea ice concentration becomes most obvious. Since our presented
study focuses on changes in physical properties of sea ice and its effects,
all calculated trends are corrected for the trend in sea ice concentration,
and fluxes through open water are neglected. Also, the effects of heat
convection and advection as well as lateral heat fluxes are not discussed,
due to the limited number of recent studies on that topic.
More investigations of bio-geo-physical interactions are needed to quantify
better the effects of the changing physical environment on the ecosystem and
element cycles, and vice versa. Additional work is also required to improve
Arctic-wide snow depth and sea ice thickness data products. Those products
should provide a good description of surface properties during the
spring–summer transition, when the largest uncertainties were found. Such
time series might become available from new data products that merge
observations from different satellites and sensor types (e.g., SMOS,
CryoSat-2, AMSR-E), and potentially also numerical models. The non-existence
of such reliable long-term and Arctic-wide data sets was the main motivation
for developing the presented method, based on available parameters.
Otherwise, the application of a radiation transfer model with adequate input
(forcing) data would have been an obvious alternative.