A realistic representation of sea-ice deformation in models is important for accurate simulation of the sea-ice mass balance. Simulated sea-ice deformation from numerical simulations with 4.5, 9, and 18 km horizontal grid spacing and a viscous–plastic (VP) sea-ice rheology are compared with synthetic aperture radar (SAR) satellite observations (RGPS, RADARSAT Geophysical Processor System) for the time period 1996–2008. All three simulations can reproduce the large-scale ice deformation patterns, but small-scale sea-ice deformations and linear kinematic features (LKFs) are not adequately reproduced. The mean sea-ice total deformation rate is about 40 % lower in all model solutions than in the satellite observations, especially in the seasonal sea-ice zone. A decrease in model grid spacing, however, produces a higher density and more localized ice deformation features. The 4.5 km simulation produces some linear kinematic features, but not with the right frequency. The dependence on length scale and probability density functions (PDFs) of absolute divergence and shear for all three model solutions show a power-law scaling behavior similar to RGPS observations, contrary to what was found in some previous studies. Overall, the 4.5 km simulation produces the most realistic divergence, vorticity, and shear when compared with RGPS data. This study provides an evaluation of high and coarse-resolution viscous–plastic sea-ice simulations based on spatial distribution, time series, and power-law scaling metrics.

The Arctic sea ice in many respects is
an important component of the Earth's climate system, e.g., sea ice governs
the ocean-to-atmosphere heat flux, freezing and melting influences the upper
ocean salinity and density, and sea-ice dynamics act as a latent energy
transport

Here we study sea-ice deformation strain rates in the Arctic obtained from
synthetic aperture radar (SAR) satellite measurements using the RADARSAT
Geophysical Processor System (RGPS) in comparison to coupled ocean–sea-ice
simulations carried out with the Massachusetts Institute of Technology
general circulation model (MITgcm) as configured for the Estimating the
Circulation and Climate of the Ocean, Phase II (ECCO2) project

Traditionally sea-ice model performance is evaluated by comparing
satellite-derived ice area and velocities to model results

Sea-ice strain rates do not scale linearly in space and time but follow a
power law depending on the length scale

It can be shown that traditional sea-ice models using the

The main purpose of this article is to examine how model grid spacing
influences simulated sea-ice deformation representation when compared to
satellite observations. Different from previous studies, we focus on direct
comparison between the modeled and observed strain rates. Using the VP model,
we construct simulated deformation fields on the same spatial and temporal
scales as in the RGPS observations (Sect.

The remainder of this article is laid out as follows: Sect.

The model output used for this study is obtained from integrations of a
coupled ocean and sea-ice configuration of the Massachusetts Institute of
Technology general circulation model (MITgcm)

Briefly, the ECCO2 project uses a cube sphere grid projection in a
volume-conserving C-grid configuration. The ocean model has 50 vertical
levels and employs the K-profile parameterization of

The International Bathymetric Chart of the Arctic Ocean (IBCAO)

Selected sea-ice model parameters (see

Integrations with three different nominal horizontal grid spacings, 18, 9,
and 4.5

The RADARSAT Geophysical Processor System (RGPS) produces sea-ice data
products covering the Arctic Ocean derived from synthetic aperture radar
imagery acquired by the Canadian RADARSAT satellite. Details of the
analysis procedures can be found in the papers of

RGPS periods used in this study. Column 3 gives the number of monthly mean values used.

The 460 km wide swath ScanSAR Wide B
mode of RADARSAT

RGPS observations are available since November 1996 until May 2008. In this
study we use RGPS data from 20 periods (11 winter and 9 summer), or 97 months
between 1996 and 2008 (see Table

As a prerequisite for a meaningful comparison, the Lagrangian RGPS
observations and Eulerian model output have to be brought to a common
reference frame. We use the RGPS Lagrangian reference frame. This ensures
that both RGPS and model sea-ice strain rates are calculated for the same
area and time interval. This procedure avoids differences between the
datasets caused by the nonlinearity of the strain rate scaling (power-law
dependence, see Sects.

Every RGPS Lagrangian point

After this consistent RGPS and model sea-ice velocity dataset is established,
sea-ice strain rates are calculated using Delaunay triangulation. From the
triangle area

As a measure of the total sea-ice deformation rate

Erroneous cells, which might, for example, arise due to errors in the ice tracking
or from badly defined triangles from the Delaunay triangulation, are filtered
out using the following constrains: (1) the triangle cell area

We apply the anisotropic smoothing filter suggested by

This smoothing filter is applied to all partial derivatives in
Eq. (

In this section, we compare the simulated sea-ice deformation distribution to
satellite observations. Big differences between observed and modeled sea-ice
deformation fields have been reported

Examples of monthly mean November 1999 sea-ice divergence. The
divergence from

As Fig.

As Fig.

Figures

Divergence, vorticity, and shear in Figs.

In general, the large-scale sea-ice deformation patterns are reproduced by
the model for all three grid spacings. In November 1999 a pattern of high
divergence (Fig.

The RGPS data show strong sea-ice shear almost everywhere in the marginal
sea-ice zone (Fig.

We now qualitatively compare the distribution and frequency of occurrence of
LKFs followed by more quantitative comparisons in the next sections. The
model solutions for all three grid spacings do have significantly less LKFs
than the RGPS data. This is true for all three deformation variables:
divergence, shear, and vorticity. Between the three model solutions there are,
however, significant differences for the LKF distribution. While, for example, the
sea-ice shear for the 18 km model solution in Fig.

The large-scale difference in sea-ice deformation between RGPS observations
and model solutions is not evenly distributed over the Arctic Basin as can
already be seen from Figs.

Smoothed (150 km) difference in deformation rate

The main differences in

In our model configuration, we use the typical ice pressure formulation

For this study RGPS observations from all 20 available periods of RGPS
observations (i.e., 97 months, between November 1996 and May 2008) are used
(Table

The RGPS deformation rate (black) is consistently higher than all of the
4.5 km (total mean

Overview of some statistical parameters for the complete 97-month
time series of RGPS and model sea-ice strain rate invariants. All units are

The percentage

The RGPS and all model deformation time series are highly correlated
(

As seen in Sect.

The smaller the percentage

Sea-ice deformation in both the RGPS observations and all three model
solutions is very localized. The highest 15 % of all deformation rates

In summary, sea-ice deformation in the model solution with the finest grid
spacing of 4.5

Sea-ice strain rates do not scale linearly in space and time. Instead, the
scaling follows a power law. Some details about the nature of this scaling
dependence are given in, for example,

The magnitude of sea-ice strain rates and their invariants depends on the
spatial scale over which they are determined. In this section we use the
absolute divergence

All Lagrangian cells within a 5-day window are aggregated on a regular
grid with grid cell size

A filter is applied: the time interval

For each aggregate, mean strain rates (

The actual length scale

Scaling properties of absolute sea-ice divergence

Probability density function of absolute sea-ice divergence

The RGPS observations and all three model solutions follow a power-law
scaling, both during winter and during summer. Figure

For absolute divergence

For shear

Our estimates of

More importantly, for the model solutions our results do not agree with
previous studies. Our model solutions reproduce the power-law scaling
properties very well. While the

Another way to look at the power-law scaling behavior of sea-ice deformation
rates is by comparing probability density functions (PDFs) obtained from
model solutions and RGPS data. The PDFs for observed sea-ice strain rates
follow a power law. For example,

For the comparisons, the same 5-day aggregated RGPS and model datasets
described in the previous Sect.

A linear least squares regression was applied to the PDFs in log–log space
for the range 0.1–1.0

The slope of

In most cases the three model solutions show a power-law scaling behavior
over an even larger absolute range than the RGPS data (approximately

Overall the slopes of the PDF tails for simulated and observed RGPS absolute
divergence and shear rates show good agreement. The observed and simulated
power-law exponents

In this section, we examine whether sea-ice deformation rates in the three
model simulation with different horizontal grid spacing follow a similar
power-law scaling as found in observations and as discussed in
Sect.

It is a common problem when one wants to compare sea-ice deformation rates
from different model simulations. These model simulations then, in general,
have a different grid resolution, and a direct comparison is not possible due
to the different length scales involved. We will explore if the power law in
Eq. (

Due to the different averaging length scale

Figure

Comparison of filtered and unfiltered datasets using the anisotropic
smoother described in Sect.

We assume that the model deformation rate

Figure

These differences imply that a single, constant scaling exponent

From Fig.

There are additional external factors that influence

The factors mentioned in the last paragraph also explain why the scaling
exponent

In summary, the three simulations with different horizontal grid spacing,
i.e., different resolved spatial scales, follow a similar power-law scaling
as that estimated using RGPS and buoy observations. We attribute most of the
differences between simulated and observed scaling factor

The anisotropic smoothing filter described in Sect.

The goal of the anisotropic filtering is to keep the shape of the LKFs but
reduce the noise introduced by the sampling of the Lagrangian cells (see
Sect.

As a result of the smoothing, the absolute divergence (and also the magnitude
of all other strain rates) gets significantly reduced. This reduction is
50 % higher for RGPS divergence, but the shear, vorticity, and
deformation rate also decreases by about 30 % (compare
Table

This reduction in divergence magnitude can be seen in Fig.

The anisotropic filter described in

Sea-ice deformations from coupled Arctic Ocean and sea-ice simulations with
horizontal grid spacing of 18, 9, and 4.5

While RGPS sea-ice deformation data show a clear discrimination between the
thinner seasonal sea ice with more deformation and the thicker perennial sea
ice, the model deformation zones are mainly confined to a few LKFs at the ice
margins. Differences are largest for seasonal sea ice, where the model
strongly underestimates sea-ice deformation. This suggests a shortcoming of
the ice rheology, e.g., the linear dependence between ice strength and ice
thickness. Model solutions with smaller grid spacing, however, result in more
small-scale deformation features. In particular, the 4.5 km simulation has
more LKF-like features in the Central Arctic than the coarser-resolution
simulations, and, visually, the spatial distribution of these LKF-like
features agrees better with RGPS observations. This improved realism is
evaluated by computing the percentage

In Sect.

We tested if the power-law dependence can be used to compare deformation
rates obtained with model simulations using different grid spacings. The
scaling of the deformation rate in our three model solutions with different
grid spacing, i.e., different length scales, follows a similar power law as
is observed for the RGPS observations (Sect.

The anisotropic filter presented in

On larger scales the sea-ice deformation rate of all three model solutions is
very similar, with only small improvements for the 4.5 km simulation
(Fig.

A realistic representation of sea-ice deformation in models is important for
accurate simulation of the sea-ice mass balance. Multiple equilibrium flow
states (i.e., when ice growth equals ice export) can exist for the Arctic
Basin, and their characteristics are influenced by sea-ice strength and ice
rheology

An interesting future study would be to attempt to adjust sea-ice and ocean
model parameters in order to reproduce the metrics discussed in this paper.
For example, in a separate sensitivity experiment, not discussed in this
manuscript, we changed the sea-ice strength dependence on sea-ice thickness
(Eq.

The RGPS satellite data are available from the Jet
Propulsion Laboratory, California Institute of Technology, at

The authors declare that they have no conflict of interest.

The constant development and support for the MITgcm from the people involved with mitgcm.org is acknowledged. We thank Martin Losch and Pierre Rampal for constructive discussions about the model and sea-ice deformation analysis. This work was performed at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (NASA). This research has been supported by the Institutional Strategy of the University of Bremen, funded by the German Excellence Initiative. High End Computing resources were provided by the NASA Advanced Supercomputing Division. The article processing charges for this open-access publication were covered by the University of Bremen. Edited by: Dirk Notz Reviewed by: Bruno Tremblay, Amelie Bouchat, and one anonymous referee