A new algorithm for estimating sea ice age (SIA) distribution based on the Eulerian advection scheme is presented. The advection scheme accounts for the observed divergence or convergence and freezing or melting of sea ice and predicts consequent generation or loss of new ice. The algorithm uses daily gridded sea ice drift and sea ice concentration products from the Ocean and Sea Ice Satellite Application Facility. The major advantage of the new algorithm is the ability to generate individual ice age fractions in each pixel of the output product or, in other words, to provide a frequency distribution of the ice age allowing to apply mean, median, weighted average or other statistical measures. Comparison with the National Snow and Ice Data Center SIA product revealed several improvements of the new SIA maps and time series. First, the application of the Eulerian scheme provides smooth distribution of the ice age parameters and prevents product undersampling which may occur when a Lagrangian tracking approach is used. Second, utilization of the new sea ice drift product void of artifacts from EUMETSAT OSI SAF resulted in more accurate and reliable spatial distribution of ice age fractions. Third, constraining SIA computations by the observed sea ice concentration expectedly led to considerable reduction of multi-year ice (MYI) fractions. MYI concentration is computed as a sum of all MYI fractions and compares well to the MYI products based on passive and active microwave and SAR products.

Sea ice age (SIA) is one of the components of the essential climate variable
(ECV) for sea ice as defined by the Global Climate Observing System (GCOS)

Numerous studies have been focused on the estimation and evolution of the
Arctic SIA over the last decades

Sea ice age is an important parameter of the Arctic ocean system and may be a
good indicator of significant changes in the dynamical and thermodynamical
regimes that have taken place since the beginning of the current century, such
as sea ice thinning and faster ice drift. The younger seasonal ice cover
present in the Arctic nowadays is in general thinner, which makes it more
vulnerable to break up, deformation and drift under the actions of waves,
winds and currents. This has been confirmed by calculating the trends in sea
ice drift and deformation over the last 3 decades, which are significant and
respectively about 13 and 50 % per decade

It is the purpose of the present paper to describe a method and a derived
dataset that allow us to shed more light on the development of the age
distribution of the Arctic sea ice. For this purpose, we have taken advantage
of some new datasets on sea ice drift and concentration developed and
distributed by the EUMETSAT Ocean and Sea Ice Satellite Application Facility
(OSI SAF). In addition, we have developed a new Eulerian scheme of advection
supported by the Sea Ice Climate Change Initiative (SICCI) project of the
European Space Agency (ESA). These improvements have allowed us to avoid the
problem of the tracers dispersion

Information on sea ice motion was acquired from two sources. First, the
National Snow and Ice Data Center (NSIDC) sea ice drift (SID) product v.0116

Sea ice age fractions for 1 January 1985 in the Greenland and Lincoln seas. It is clearly seen that in many areas the fraction of 8YI does not exceed 20 %, but the corresponding SIA map shows that the entire pixel is assigned to contain 8YI.

The second SID product was produced by the Ocean and Sea Ice Satellite
Application Facility (OSI SAF) High Latitude Processing Center. The
low-resolution sea ice drift product from the EUMETSAT OSI SAF is operational
since 2009. It implements the continuous maximum cross-correlation algorithm
of

Sea ice concentration (SIC) product v.1.6

Sea ice types can be discriminated with PAMW satellite observations since the physical signatures of sea ice change significantly after the influence of summer melt and brine rejection. Therefore sea ice that has survived at least one summer melt is referred to as multi-year ice, and seasonal ice is referred to as first-year ice.

The algorithm of Environment Canada Ice Concentration Extractor (ECICE)

The improved MYI concentrations were provided as gridded products on polar stereographic grid with 12.5 km spatial resolution for the winter months (November–April) of 2013–2017. Compared to the MYI dataset, for which the corrections were developed, the retrievals from AMSR2 and ASCAT are much coarser (12.5 km vs. 4.45 km). The coarser resolution requires adjustment of the thresholds in the drift correction, which results in suboptimal performance of the drift correction and therefore could lead to unexpected problems in the final dataset.

The OSI SAF sea ice type is another algorithm that combines both passive and
active microwave data in a Bayesian approach

Information on SIA independent of the method introduced here
was acquired from the NSIDC portal

The SIA computation is implemented in two stages as explained in detail below. First, SIA fractions are independently advected using the satellite-derived sea ice drift and concentration observations and the Eulerian advection scheme. Second, the SIA is computed, accounting for concentration of each ice age fraction.

At each time step the observations of sea ice drift velocity components (

Scheme of Eulerian advection of sea ice. Points A and B denote start and end of drift of an ice parcel shown by the blue square.

The areal fluxes of sea ice out of the donor pixel 31 into recipient pixels
12, 13, 22 and 23 are calculated as follows:

Example of advection of an ice fraction from 1 October 2012 to 1 October 2013 shown for every third month.

When the observed sea ice drift field diverges then a gap appears between the
ice parcels (e.g., in pixel 23). If the sum of fluxes
(Eq.

When the observed sea ice drift field converges then the advected ice parcels overlap (e.g., in the pixel 12) and the sum of fluxes into a recipient pixel may exceed the concentration observed by satellites. This is interpreted as generation of pressure ridges and increase in thickness of the older fraction of sea ice. In that case the total ice concentration at the next step is assigned to be the observed ice concentration.

During the freeze-up period the observed concentration increases and becomes
higher than the sum of fluxes into a recipient pixel. This is also
interpreted as generation of young ice (YI) only and Eq. (

Advection of a SIA fraction is initiated on 10 September, the approximate date when ice extent reaches minimum in the Arctic, area of FYI is zero and all observed sea ice is MYI by definition. Initialization before this date has little impact, but initialization after this date increases risk of considering the observed FYI as MYI. The age of each ice fraction is increased by 1 year on 10 September of each consecutive year of advection.

In our study we initiated SIA calculation on 1 October 2012 when continuous high-quality observations of ice drift started to be available from AMSR2 (Fig. 3). For this date the total observed concentration was computed as the minimum concentration during the period 1 September–1 October 2002. Propagation of ice age fractions from later years started from 10 September or respective years.

We did not know the spatial distribution of ice of different age within the
pack at the first moment of time (1 October 2012), but we can postulate that
all observed ice is at least in the second-year ice (2YI) category. We have
to make a simplification: the concentration of 2YI on 1 October 2012
is assigned to be equal to the total observed concentration:

On 10 September 2013 the total ice concentration is the sum of all MYI fractions and therefore the initial concentration of the 2YI
is calculated as

At any moment of time, sea ice in each cell is characterized by a vector of
concentrations of ice fractions of various age with the sum equal to the
total sea ice concentration (Fig.

Maps of sea ice age fractions on 1 March 2015.

Maps of sea ice age on 1 March 2015 computed with different methods.

The developed advection scheme (see Sect.

In order to provide stepwise illustration of the SIA product improvements we have used four different combinations of forcings and algorithms to produce a SIA map for the 1 January 2016. First, we have implemented the NSIDC advection scheme (Lagrangian) and the SIA algorithm (age of the oldest parcel) and applied it to the ice drift product from NSIDC. Second, we have applied the NSIDC algorithms to the ice drift from OSI SAF. Third, we have applied our Eulerian advection scheme and SIA algorithm to the ice drift from OSI SAF but without accurately accounting for SIC. In this experiment all pixels with SIC below 15 % were assigned to be open water and other pixels contain 100 % ice. Finally, we have used the new advection scheme, the OSI SAF ice drift, and fully accounted for SIC.

Comparison of the generated ice age products is presented in Fig.

Comparison of SIA for the 1 January 2016 calculated with the
following combinations of forcings and algorithms:

Comparison of MYI concentration estimated from the NSIDC SIA
product

Seasonal dynamics of area of sea ice age fractions (filled plots)
and multi-year ice area (dots) derived from the NSIDC product

The change of the advection scheme does not affect the overall spatial
distribution of MYI significantly (Fig.

When the new algorithm takes SIC into account then SIA is decreasing even
more and the ice older than 4 years is observed only near the Canadian
Archipelago coast (Fig.

MYI concentration is an important indicator of abundance of
older, thicker and rougher sea ice and is readily available from several
resources including OSI SAF

Intercomparison of MYI maps from four sources indicated that the general
spatial distribution and temporal evolution is rather similar
(Fig.

Distinct features of MYI from NSIDC (Fig.

The time series of MYI areas are compared with regard to both seasonal
dynamics (Fig.

The seasonal variations of ice age fraction areas follow similar pattern for
the NSIDC and SICCI products (Fig.

Interannual dynamics of area of sea ice age fractions (bars) and multi-year ice area (dots) derived from NSIDC product (left bars), from NERSC product (right bars), from UB product (black dots) and from OSI SAF (black stars).

The MYI area is shown in Figs.

By the beginning of 2013 the SICCI product has only one fraction of MYI (2YI) because calculations were initiated in 2012 and all MYI was assigned to be 2YI. By the fourth annual cycle (in 2016) the SICCI product has five ice age fractions and the distribution can be better compared with the NSIDC product. Clearly, the fractions of the older ice in the SICCI product have lower area than in the NSIDC product.

The interannual variability can be seen on the plot of areas of the ice age
fractions for 1 January of 2013, 2014, 2015 and 2016 in Fig.

An independent validation of the SICCI MYI product was performed using a
mosaic of synthetic aperture radar (SAR) images in HH polarization from
Sentinel-1 A and B satellites acquired around 1 January 2016. MYI appears as
brighter and more homogeneous texture on SAR images which allows one to draw
an outline and compare it with outlines of MYI from the SICCI product as
shown in Fig.

Comparison of MYI extent derived by SAR visual interpretation (light blue) and from SICCI SIA product (red) on top of mosaic of Sentinel-1 SAR images for 1 January 2016. The thick red line shows 15 % threshold and thin red line shows 50 % threshold.

Comparison of sea ice age for 1 January 1985 initiated from ice
parcels with various density (1 parcel per 12

The major advantage of the new algorithm is the ability to generate individual ice age fractions or, in other words, to provide a frequency distribution of the ice age in each pixel. This allows derivation of a single number characterizing SIA using one of the statistical methods presented above. Selection of the method depends on the preferred definition of the SIA and on the eventual application. For example, in our opinion, weighted average is the optimal method for graphical representation of SIA maps as it depicts the smooth nature of SIA distribution and accounts not only for the oldest ice fractions but also for the younger ones. However, for other applications, e.g., assimilation into models, a different method may be preferred. The SIA distribution can also be used to calculate MYI concentration for various applications, including calibration/validation of the PAMW-based MYI algorithms, improvement of the freeboard to sea ice thickness conversion for altimeter data and estimation of sea ice roughness for assimilation into models.

The motivation for implementing the Eulerian advection scheme in the new
algorithm was to produce continuous and smooth spatial distributions of SIA fractions and also to prevent undersampling of the results. In the
experiments with the NSIDC algorithm it was discovered that the density of
starting points of the sea ice drift vectors indirectly influences the area
of MYI. Too low density (e.g., 1 drifter in each 12

The new sea ice drift product derived from AMSR2 also has a significant impact on the accuracy and reliability of the results. It accurately reproduces the sea ice circulation in the Arctic, is void of artifacts and produces homogeneous distribution of SIA fractions. It was discovered that the initial SID product is contaminated with high-frequency noise. Cleaning of SID with a median filter reduced small-scale deformations and prevented appearance of FYI discontinuities in artificial divergence zones. At the same time the low spatial resolution of SID (65 km) limits the algorithm from reproduction of fine-scale features in MYI distribution and may lead to over-smoothing in areas with high ice drift speed gradients (e.g., western Beaufort Sea).

The observed differences in MYI spatial distribution and total area are only
marginal for the NSIDC and the SICCI products. This happens due to a short
integration time: MYI spatial distribution is forced by observations on 15
September and then it is modified by an advection scheme (either Lagrangian
or Eulerian) and melting (in case of SICCI product) during only 1 year. In contrast, the integration over longer times and accounting for the sea
ice concentration have significant effect on the area of the older ice.
Analysis of inter-annual dynamics (Fig.

The sea ice type algorithms based on PAMW satellite observations have higher
spatial resolution than the ice-drift-based algorithms but inevitably suffer
from the unaccounted atmospheric impact or melt ponds and have to be
corrected using information on air temperature or ice motion

We have developed a new algorithm for estimating sea ice age distribution using sea ice drift and concentration products. The algorithm is based on the Eulerian advection scheme which provides smooth distribution of the ice age parameters and prevents the undersampling problem that may occur when a Lagrangian tracking approach is used. Another advantage of the selected scheme is the ability to generate not just a single age characteristic but a distribution of sea ice age fractions. First, this allows for flexibility in choosing the ice age definition and application of a statistical measure to compute SIA and, second, this provides individual spatial distributions of ice age fractions that can be assimilated into models or used for ice type delineation. For example, concentration of multi-year ice can be computed as a sum of multi-year ice fractions and used for defining ice density and snow thickness for the ice thickness algorithms, ice roughness for the ice circulation models and so on.

The new algorithm is driven by the new sea ice drift products from OSI SAF, which is void of potential artifacts due to inclusion of autonomous ice drifter buoys. This leads to a more homogeneous distribution of ice age fractions over the Arctic Ocean. The algorithm is also constrained by the observed sea ice concentration from OSI SAF, which reduces fractions of old ice and, consequently, ice age by 20–30 %. It was applied to generate time series of daily sea ice age fraction product from October 2012 to October 2017. Comparisons with the NSIDC SIA time series indicate that the fractions of MYI in the new product melt faster during the year and after a spin-up time of 3 years the area of older ice in the SICCI product is almost 20 % lower than in the NSIDC product.

The data generated with the algorithm are openly available
at FTP (for bulk download;

AK developed and applied the presented algorithm, with contributions from PR. TL provided the new sea ice drift product. SA provided the OSI SAF ice type data. YY and GH provided the new sea ice type product. LTP and RS provided the mosaic of SAR images and multi-year ice outline. All co-authors participated in fruitful discussions and writing the manuscript.

The authors declare that they have no conflict of interest.

This work has been supported by the Sea Ice Age option of the Sea Ice Climate Change Initiative project funded by the European Space Agency, contract number 4000112229/15/I-NB. Edited by: Jennifer Hutchings Reviewed by: three anonymous referees