Introduction
The variability of the Arctic sea ice has received increasing attention from the scientific community over the past years
e.g.,. The main
reason lies in the fact that Arctic sea ice plays a key role in the Earth's climate system .
Among other contributions, it has been suggested that a decline of the Arctic sea ice extent and volume leads to a weakening of the
Atlantic Meridional Overturning Circulation and, therefore, potentially impacts the global distribution of
heat . At the same time, the Arctic is one of the most sensitive regions to climate changes
due to a phenomenon known as Arctic amplification .
For instance, the current observed warming in the Arctic is reported to be nearly twice as large as other
regions of the globe .
Other multiple specific interests from different stakeholders have reinforced the importance of sea ice
projections, both at regional and larger scales, which include shorter shipping lanes ,
travel and tourism industry , hunting and fishing activities ,
mineral resource extraction , potential impact on the weather at midlatitudes ,
environmental hazards , and loss of weather predictive power by indigenous
communities . In this context, the sea ice thickness (SIT) is likely the most relevant state variable
for monitoring, forecasting, and understanding recent and future changes of Arctic sea
ice, first, because this parameter provides predictive information for the sea ice extent anomalies
and, second, due to the fact that SIT anomalies persist longer than
sea ice extent anomalies, the former being reported as a forcing of the latter .
However, direct observations of SIT and/or related parameters, namely draft and freeboard,
are still sparse in time and space, despite the continuous efforts for compiling former and recent datasets from a range of
sources . Some recent observational programs, such as the Year Of Polar
Prediction (YOPP) and the MOSAiC International Arctic Drift Expedition (https://www.mosaicobservatory.org/; last access: 15 July 2018),
aim to enhance the Arctic observational system, being
especially useful for improving our future modeling and forecasting skills.
Due to this lack of direct measurements in the past and present day, the ocean–ice reanalyses deserve special attention.
A reanalysis product consists of models' outputs, which are generated over a certain time span by the same model,
configurations, and procedures, and so are distributed onto regular grids, evenly stepped in time. These products are often built with assimilation of
observational dataset(s) in order to improve the estimate of a certain parameter. For instance, SIT is often
estimated by assimilating atmospheric, oceanic and, eventually, sea ice concentration data. The ocean–ice reanalyses are
likely the main and more robust source of SIT data in terms of spatiotemporal resolution, being also broadly used for initialization
and assimilation in other climate models e.g.,. Additionally, long-term reanalyses are crucial for
understanding the past Arctic sea ice characteristics, in a period when in situ observations of ice parameters were inexistent.
In this work we make use of 14 state-of-the-art reanalyses in order to study two important aspects
of the SIT predictability: the timescale (or persistence) and the length scale of SIT
anomalies (see Sect. ). Their importance is reinforced by the fact that the predictability of the SIT field depends
on how long the anomalies persist over time and on how these anomalies spread in space.
Notice that, hereafter, besides the traditional definition of time predictability,
we adopt this term also for the spatial scale.
In addition, timescales and length scales may also be useful for designing an optimal observation system when
selecting ideal locations for deploying instruments as well as for defining a frequency
sampling strategy .
reported SIT anomalies with typical timescales and length scales of about 6–20 months and 500–1000 km, respectively. These results reinforce the fact that
the SIT anomaly persists longer compared to the sea ice area anomaly, which is reported with a timescale
of 2–5 months .
suggested that the SIT anomalies from models characterized by a thinner mean ice state tend to present shorter persistence
but larger spatial scales. reported
a decline in the timescale of sea ice volume anomalies, as a result of the ice thinning induced by
recent climate changes.
The first aim of this study is to evaluate the performance of different reanalysis products regarding their
SIT realism by comparing these reanalyses against observational datasets. A point of main interest is to
identify whether or not the assimilation of sea ice concentration by the reanalyses improves the representation of SIT.
Second, we seek to characterize the timescales and length scales of the Arctic SIT anomalies. Again, we verify whether or not sea ice data assimilation
plays a role in the temporal and spatial scales of SIT anomalies. Furthermore, we investigate the long-term
evolution of timescales and length scales, as well as the relationship between these two parameters.
The paper is organized as follows: Sect. introduces the reanalysis products, the
observational datasets, and the respective methods applied in this research; Sect.
compiles all results, including the comparison between observations and reanalyses (Sect. ),
the comparison of reanalyses themselves (Sect. ), and the patterns of
timescales (Sect. ) and length (Sect. ) scales. Lastly,
Sect. draws discussion and conclusions on the findings reported in
the previous sections.
Sea ice volume anomalies estimated from all reanalyses. Anomalies are calculated by excluding the trend and
the seasonal cycle. Tick labels are placed at the first day of the respective year. Reanalyses labeled in blue and red
highlight whether the datasets were built with or without sea ice data assimilation, respectively.
Data and methods
Sea ice reanalyses
Monthly fields of SIT from 14 state-of-the-art ocean–ice reanalyses
are used in this work. All but one were compiled in the context of the ORA-IP
project .
The ORA-IP reanalyses
(and their respective author/provider institution) are
C-GLORS05 (CMCC; ),
ECCO-v4 (JPL/NASA, MIT, AER; ),
ECDA (GFDL/NOAA; ),
G2V3 (Mercartor Océan; ),
GECCO2 (University of Hamburg; ),
GloSea5 (UK Met Office; ),
GloSea5-GO5 (UK Met Office; ),
MERRA-Ocean (GSFC/NASA/GMAO; ),
MOVE-CORE (MRI/JMA; ),
MOVE-G2 (MRI/JMA; ),
ORAP5 (ECMWF; ),
TOPAZ4 (ARC MFC; ) and
UR025-4 (University of Reading; ).
The 14th reanalysis is the Pan-Arctic Ice-Ocean Modeling and Assimilation System, PIOMAS
. For the abbreviations, the reader is referred to Appendix A.
The original horizontal grids present different resolutions (Table 1), but for comparison, all reanalyses are interpolated onto a common grid
of 1∘×1∘ spatial resolution following .
Specific characteristics of each reanalysis regarding horizontal resolution, ocean–sea ice model, atmospheric forcing data,
subgrid-scale ice thickness distribution, ice dynamics (VP, viscous–plastic, or EVP, elastic–viscous–plastic), parameters for the ice strength
formulation, air–ice drag coefficient, ocean–ice drag coefficient, and the presence (and respective method) of ice data assimilation are summarized in
Table . For additional information the reader is referred to and/or to the respective providers.
Ensemble of reanalyses, their respective configurations and set of selected parameters.
Reanalysis/
C-GLORS05
ECCO-v4
ECDA
G2V3
GECCO2
GloSea5
GloSea5
MERRA-
MOVE-
MOVE-
ORAP5
PIOMAS
TOPAZ4
UR025-4
parameter
-GO5
Ocean
CORE
G2
Nominal
0.5∘
0.4∘–1.0∘
1.0∘
0.25∘
∼40 km in
0.25∘
0.25∘
0.5∘
0.5∘×1.0∘
0.3–0.5∘×1.0∘
0.25∘
∼22 km in
12–16 km
0.25∘
horizontal
the Arctic
the Arctic,
resolution
Barents, and
GIN Seas
Ocean–sea
NEMO3.2–
MITgcm
GFDL–
NEMO3.1–
MITgcm
NEMO3.2–
NEMO3.4–
MOM4.1–
MRI.COM3–
MRI.COM3–
NEMO3.4
POP–
HYCOM2.2–
NEMO3.2
ice model
LIM2
MOM4.4.1–
LIM2
CICE4.0
CICE4.1
CICE4.0
Mellor and
Mellor and
–LIM2
TED
Drange and
LIM2
SIS
Kantha (1989)
Kanta (1989)
Simonsen (1996),
+ CICE4.0
+ CICE4.0
Hunke and
Dukowicz (1997)
Atmospheric
ERA-
ERA-
Coupled run
ERA-
NCEP/
ERA-
CORE2
Coupled run
CORE
JRA55
ERA-
NCEP/
ERA-
ERA-
forcing data
Interim
Interim
constrained to
Interim
NCAR
Interim
constrained
Interim
NCAR
Interim
Interim
NCEP/NCAR–
to MERRA
NCEP/DOE
Number of
1
1
5
1
2
5
5
5
5
5
1
12
1
1
ice thickness
categories
Dynamics
EVP
VP
EVP
EVP
VP
EVP
EVP
EVP
EVP
EVP
VP
VP
EVP
VP
P*
P*=2.0
P*=2.754
P*=2.5
P*=2.0
P*=0.5
Cf =17
Cf =17
P*=2.75
P*=2.0
P*=2.0
P*=1.5
Cf =17
P*=2.75
P*=1.0
(104; N m-1)
or Cf (–)
Drag air–
1.63
2.00
1.21
1.50
1.2
1.63
1.63
1.63
3.00
1.00
1.63
2.00
1.6–2.14
1.63
ice (10-3)
Drag ocean–
10.00
1.00
3.24
10.00
5.5
5.36
5.36
5.36
5.50
5.50
10.00
5.50
5.50
5.00
ice (10-3)
DA sea ice
Linear
Adjoint
None
2-D local
None
3D-VAR
3D-VAR
EnOI
None
None
3D-VAR
Nonlinear
EnKF
OI
system
nudging
analysis
FGAT
nudging
SEEK filter
DA sea ice
NSIDC
NSIDC
None
CERSAT
None
OSI-SAF
OSI-SAF
NSIDC
None
None
OSTIA
NSIDC
OSI-SAF
OSI-SAF
data
P* and Cf are parameters for the ice strength formulations following respectively Hibler (1979) and
Rothrock (1975).
Observational references
We use a compilation of 16 observational datasets available in the Unified Sea Ice Thickness Climate Data Record
(Sea Ice CDR; ; http://psc.apl.uw.edu/sea_ice_cdr; last access: 15 July 2018). The Sea Ice CDR is a concerted effort to bring together
a range of datasets in a consistent format but is originally sampled by different methods and spatiotemporal scales as well
as being stored in a variety of formats. We use the post-processed version of the Sea Ice CDR data, which is distributed by monthly mean for
moored upward-looking sonar (ULS) point measurements or 50 km averages for submarine, airborne, and satellite observations.
If applicable, the Sea Ice CDR already provides the files corrected for data biases e.g.,.
From these 16 datasets, 11 provide draft measurements, while the remaining 5 provide sea ice thickness data.
Seven draft datasets were sampled by means of moored ULSs, namely North Pole Environmental
Observatory
(NPEO; ), Beaufort Gyre Exploration Project (BGEP),
Institute of Ocean Science (IOS) – Eastern Beaufort Sea (IOS-EBS) and – Chuck Sea (IOS-CHK), Alfred Wegener Institute – Greenland Sea (AWI-GS; ),
Bedford Institute of Oceanography Lancaster Sound (BIO-LS; ),
and Polar Science Center – Davis Strait (Davis_St; ). Four other draft datasets are also based on ULS measurements
but are installed on US and UK submarines: US Navy Submarines – Analog (US-Subs-AN), US Navy Submarines – Digital (US-Subs-DG; ),
UK Navy Submarines – Analog (UK-Subs-AN), and UK Navy Submarines – Digital (UK-Subs-DG; ).
From the ensemble of sea ice thickness datasets, the Ice Thickness Program run by Environmental Canada
(CanCoast) is the only dataset providing direct measurement of ice thickness by means of ice boreholes. The NASA Operation
IceBridge datasets (IceBridge-V2 and IceBridge-QL; ) are derived from an aircraft-mounted laser altimeter.
Finally, two datasets come from satellite campaigns: the laser-altimeter-derived ICESat Mission-Goddard (ICESat1-G; )
from National Aeronautics and Space Administration (NASA) and the radar-altimeter-derived
CryoSat satellite data (CryoSat-AWI; ) from the European Space Agency (ESA).
Methods
Reanalyses are compared against observations by selecting SIT values from the nearest grid points to the respective
observational sites, during the same respective months. Complementary metrics are employed to evaluate the relationship between
observations and reanalyses. When directly comparing SIT from reanalyses and observations, we estimate the root mean square error (RMSE),
the correlation coefficient (R), and the mean residual sum of squares (MRSS) from the linear fit between both datasets,
by having the reanalysis values as predictors and the observational values as predicted variables.
Since SIT and draft are different variables, here we evaluate the strength of the linear relationship between them.
Thus, when comparing SIT from reanalyses against draft from observations, we only estimate R and MRSS.
In this work we do not account for snow variation in order to avoid adding uncertainties to the SIT fields.
SIT anomalies are derived by eliminating the trend and the seasonal cycle present in the time series. To do so, the
trend is estimated separately for every month by means of a second-order polynomial fit and
subtracted from the respective month. A second-order fit seems to better reproduce the trends when compared to the
linear fit, although the results are very similar (not shown).
The same method is applied for the analyses conducted with the pan-Arctic sea ice
volume anomaly, derived from the SIT data, as illustrated in Fig. .
Grid point comparisons of SIT anomalies among all reanalyses are performed by means of RMSE and R maps,
calculated over an overlapping period of 15 years, from January 1993 to December 2007. This time span corresponds to the period
during which data are available from all reanalyses. Furthermore, as adopted by ,
only grid points wherein the mean ice thickness at the time of summer minimum is greater than 0.1 m are taken into account.
This condition is valid for all reanalysis-based results, unless otherwise stated.
The timescale (or persistence) is derived from individual time series by calculating the lagged autocorrelation stepped
forward by one measurement, equivalent to 1 month. The e-folding reference is used so that the persistence is assumed
to be the time when the lagged autocorrelation curve crosses the 1/e (∼0.3679) value, as proposed in previous works
e.g.,. As an example,
Fig. displays the timescale derived from the mooring-based draft anomaly sampled in the
framework of the BGEP at 150∘ W, 75∘ N, from August 2003 to August 2013 . Figure
also shows the timescales from the allocated reanalysis-based SIT anomalies. For this geographical location and time span,
the draft anomaly from BGEP persists for about 3.7 months, while the SIT anomalies from the different reanalyses persist from
2.4 to 8 months. The persistence is estimated both from a regional and pan-Arctic perspective. First, it is calculated
at each grid point, for all SIT anomaly time series. Second, it is estimated for the long-term (GECCO2 and MOVE-CORE)
pan-Arctic ice volume anomalies. For the latter case, we evaluate how stable the e-folding timescale is over time by applying
a moving (stepped by 1 month) and length-variable window (from 5 to 59 years). Here, we also investigate whether the moving
timescale is marked by significant band(s) of variability. To do so, we applied wavelet analysis as proposed by
.
Autocorrelation curves for the draft time series sampled in situ by upward-looking sonars deployed in the
BGEP oceanographic mooring (black line). This mooring was placed at 150∘ W, 75∘ N
(see location in Fig. c), and the data span from August 2003 to August 2013. The blue and red lines
display the autocorrelation estimated from the SIT anomalies time series for the ORA-IP reanalyses, at the nearest
grid point to the mooring and same time span, for the reanalyses built with and without sea ice data assimilation,
respectively. The cyan line indicates the autocorrelation estimated for the PIOMAS reanalysis. The time in which the
curves cross the black dashed line is defined as their respective e-folding timescales.
(a) The e-folding length scale estimated from the CryoSat seasonal data of sea ice thickness. This dataset contains
14 spring (March–April) and autumn (October–November) fields, starting in autumn 2010 and finishing in spring 2017. (b) Same as (a), but using the equivalent temporal
averages from the PIOMAS data. The difference between the fields shown in (a) and (b) is plotted in (c). The black circle
in (c) indicates the location of the mooring from which data are used in Fig. .
The length scales of the SIT anomalies are estimated for the reanalysis datasets. The first step is to determine one-point
correlation maps. In other words, we calculate the cross-correlation between the SIT anomaly from each grid point with the anomaly
from all other points. Subsequently, we make use of the e-folding reference and, for every map, we select all grid cells
with a correlation coefficient higher than 1/e. The radius of a circle that yields the area covered by these selected cells is
defined as the length scale of the SIT anomaly. This methodology is detailed and graphically presented by
. Figure a shows an example for which the length
scale is calculated for the SIT anomalies from CryoSat seasonal data: spring (March–April) and autumn (October–November), from autumn 2010 to
spring 2017. In turn, Fig. b–c reveal that a similar length scale pattern is also present
in PIOMAS. It is worth mentioning that this illustrative example allows a first assessment of how length scales from
observations and reanalyses compare to each other. However, it can not be compared to the spatial scales of monthly
anomalies further studied in Sect. .
Results
Comparison of reanalyses with observations
The scatter plots shown in Fig. combine SIT from each reanalysis and the observational datasets
from all sources. The latter are separated into two parameters: draft (black dots) and SIT (green dots). The comparisons indicate that all
reanalyses are significantly correlated to the observations, whether these are draft or SIT. By comparing SIT and draft, four reanalyses
have correlation coefficients larger than 0.7: TOPAZ4 (R=0.76), C-GLORS05 (0.74), MOVE-CORE (0.74), and UR025-4 (0.73). On the other hand,
GECCO2 (0.17) and MERRA-Ocean (0.10) are marked by the weakest correlations. If we evaluate the reanalyses' statistical capability for predicting the
observational values, the MRSS from the linear fit indicates that TOPAZ4 (MRSS =0.39 m2), UR025-4 (0.42 m2) and C-GLORS05 (0.49 m2)
are the best predictors, while MERRA-Ocean (1.42 m2) and GECCO2 (1.27 m2) provide the lowest agreement.
When comparing SIT from both datasets, the reanalyses with higher correlation coefficients are
PIOMAS (R=0.66), GECCO2 (0.64), and TOPAZ4 (0.61), while ECDA (0.43), ECCO-v4 (0.40), and MOVE-G2 (0.30) are the reanalyses
with poorest correlation. In terms of linear fit, PIOMAS (MRSS =0.41 m2), TOPAZ4 (0.41 m2), GECCO2 (0.42 m2), ORAP5
(0.46 m2), and C-CGLORS05 (0.49 m2) are the best performing predictors (MRSS <0.5 m2), while MOVE-CORE (0.71 m2) and ECCO-v4 (0.7 m2) provide
the lowest prediction capability. In addition, a direct comparison by means of RMSEs indicates which reanalyses are
closer to the ensemble of observations, as follows: PIOMAS (RMSE =0.7 m), C-GLORS05 (0.8 m), GloSea5-GO5 (0.8 m), ORAP5 (0.8 m),
GECCO2 (0.9 m), GloSea5 (0.9 m), MOVE-CORE (0.9 m), TOPAZ4 (0.9 m), ECCO-v4 (1.0 m), ECDA (1.0 m), MERRA-Ocean (1.0 m), G2V3 (1.1 m),
MOVE-G2 (1.1 m), and UR025-4 (1.1 m).
For a detailed overview on how each reanalysis is linked to each observational dataset, in terms of RMSE, MRSS, and R, the reader is referred
to the tables presented in Appendix B.
Comparison between sea ice thickness from reanalyses and sea ice thickness (green points) or draft (black points) from observational datasets.
The lines represent the linear fits having the reanalysis as the predictor and the observations as predicted variables. The mean residual sum of squares
(MRSS) from the fit, the correlation coefficient (R), and the root mean square error (RMSE) are also displayed for each comparison.
RMSE is calculated only when comparing SIT from both sources (green) but not when comparing SIT and draft (black).
Reanalyses labeled in blue and red highlight whether the datasets were built with or without sea ice data assimilation, respectively.
Comparison of reanalyses to each other
As a first assessment of how well the reanalyses compare to each other, we estimate the RMSE and
R between time series of the SIT anomaly, at every grid point, and between all pairs of products. The results are organized
as a square matrix in Fig. , in which the number at the top of each panel represents
the respective global value estimated by considering the data from all grid points. The lower triangular part of the matrix
reveals that the smallest RMSE is found for the pair ECDA–UR025-4 (RMSE =0.21 m). Only four other pairs
present RMSE ≤0.25; they are the match between the two GloSea5 products (0.23 m) and the combination of UR025-4
with C-GLORS05 and ECCO-v4 (0.25 m). The largest RMSE is found when comparing GECCO2–MOVE-G2 (0.61 m).
From Fig. (lower triangle), the averaged RMSE for each individual reanalyses
indicates that UR025-4 is the reanalysis closer to the ensemble, while MOVE-G2 has the largest errors compared to its
counterparts:
UR025-4 (0.30±0.06 m),
ECCO-v4 (0.33±0.06 m),
ECDA (0.33±0.06 m),
GloSea5 (0.34±0.07 m),
C-GLORS05 (0.35±0.06 m),
PIOMAS (0.35±0.06 m),
MOVE-CORE (0.36±0.06 m),
GloSea5-GO5 (0.36±0.07 m),
TOPAZ4 (0.37±0.06 m),
ORAP5 (0.38±0.06 m),
G2V3 (0.41±0.06 m),
MERRA-Ocean (0.44±0.04 m),
GECCO2 (0.45±0.06 m), and MOVE-G2 (0.47±0.06 m).
Square matrix plot displaying the root mean square error (RMSE) (a) and
the correlation coefficient (R) maps (b), estimated from the sea ice thickness time series,
at every grid point, and between all pairs of reanalyses. The numbers at the top of each panel indicate the
respective value calculated with data from all grid points. All maps have the 0∘ longitude placed at
06:00, while the bounding latitude is 67∘ N. Reanalyses labeled in blue and red highlight whether the
datasets were built with or without ice data assimilation, respectively.
At the regional scale, most of the pairs of reanalyses have larger differences off the coast of northern Greenland and to the north of the Canadian
Archipelago, which are more pronounced in the MERRA-Ocean product. Almost all systems present minimum errors in the central Arctic Basin.
In turn, the upper triangular part of the matrix in Fig. displays the linear relationship between
pairs of reanalyses, quantified by the correlation coefficient. The strongest pan-Arctic correlations are observed for GloSea5–GloSea-G05 (R=0.69),
ORAP5–UR025-4 (0.67), and G2V3–ORAP5 (0.65). MOVE-CORE and MOVE-G2 present a marked anti-correlation with several other reanalyses, mainly in the
central Arctic Ocean. Such anti-correlation is also reflected in the sea ice volume anomalies shown in Fig. .
Notice that negative anomalies in MOVE-CORE and MOVE-G2, for instance from 2001 to 2004, occur at the same time that strong positive anomalies
in reanalyses such as GECCO2, G2V3, and ECDA do, as well as C-GLORS05, ORAP5, PIOMAS, TOPAZ4, and UR025-4, though in a less pronounced way
(Figs. and ). We do not have a clear understanding of why these anti-correlations take place.
The e-folding timescales (or persistence) estimated for the SIT time series. Only grid cells in which the time mean
(for the January 1993–December 2007 period) SIT at the time of summer minimum is greater than 0.1 m are taken into
account for the computations. Averages for the systems with ice data assimilation and no data assimilation are
represented by the DA and NA panels, respectively. All maps have the
0∘ longitude placed at 06:00, while the bounding latitude is 67∘ N. Reanalyses labeled in blue and
red highlight whether the datasets were built with or without ice data assimilation, respectively.
Timescales
An important property inherent to time series in general concerns their timescale and/or persistence, as defined in Sect. .
In other words, we aim to infer how long the SIT anomaly maintains a good correlation with future
measurements at the same grid cell. Persistence can also be perceived as the skill of a self-prediction scheme, for which past data are used
to predict future values. In addition, it is a relevant variable to be taken into account when designing
the sampling frequency of observational programs, especially if these programs target the understanding
of the SIT time variability.
Figure displays the e-folding timescales for the SIT anomaly at every grid point, and for
all reanalyses. The area weighted mean (AWM) timescales (in months) sorted in ascending order are
2.5 (GloSea5),
2.6 (GloSea5-GO5),
3.6 (PIOMAS)
3.7 (ECCO-v4),
3.8 (MERRA-Ocean),
4.0 (UR025-4),
4.3 (TOPAZ4),
4.4 (C-GLORS05),
4.7 (ORAP5),
4.9 (MOVE-CORE),
5.0 (G2V3),
6.0 (ECDA),
7.2 (MOVE-G2), and
7.8 months (GECCO2).
These values were calculated only taking into account grid points with a valid SIT value from all reanalyses.
The results reveal that the thickness anomalies from reanalyses with no ice data assimilation
(NA; Fig. , red labels) present a longer persistence, mainly distinguished in
MOVE-G2 and GECCO2. Potential reasons to explain why the thickness anomalies persist longer in NA systems
are suggested and discussed in Sect. .
In contrast, the thickness anomalies from the GloSea5 systems (GloSea5 and GloSea5-GO5) have a much shorter
persistence.
(a) Moving e-folding timescales estimated for the ice volume anomaly time series from the GECCO reanalysis. The window length
varies from 5 to 59 years, and it is stepped forward by 1 month over a total period of 64 years (January 1948–December 2011).
(b) Moving e-folding timescales for the 15-year window length case. The red stars in (a) and (b) indicate the 15-year overlapping
period (January 1993–December 2007, center time mid-June 2000).
(c) Wavelet power spectrum of (b), with Morlet as the mother wavelet. The black lines denote the 95 % significance levels above a red noise background spectrum,
while the crosshatched areas indicate the cone of influence, in which the edge effects become important. The color bar is omitted
in panel (c) since we are not interested in the power's magnitude but in the frequencies outstanding as significant in the spectrum.
(d) Time-integrated power spectrum from the wavelet analysis, where the dashed line corresponds to the 95 % significance level.
The bands of significant periods (4.4–6.1 years and >10.7 years) are highlighted by the gray horizontal bars.
(e)–(h) Same as (a)–(d), respectively, but for the MOVE-CORE ice volume anomaly which has a spanning period of 60 years
(January 1948–December 2007).
The horizontal gray bar in (h) highlights the only period band of significant variability, defined by periods longer than 12.7 years.
From a regional point of view, Fig. shows that GloSea5 and GloSea5-G05 are the only
reanalyses in which the SIT anomaly persistence is remarkably short all over the Arctic, presenting e-folding timescales higher than 4 months only in a few, not evenly distributed, grid points.
By contrast, the SIT from GECCO2 has a marked longer persistence (>15 months)
extending from the region off the northern coast of Greenland to the north of the Canadian Archipelago and mid-Arctic Ocean.
The ECDA product presents a relatively similar pattern of the timescale over the region mentioned above but persisting for a
shorter period (∼8 months).
SIT anomalies from MOVE-G2 also indicate long persistence off the coast of northern Greenland, extending to the central
Arctic and East Siberian Sea. For the remaining reanalyses, there is no common regional pattern of persistence outstanding
from their respective timescale maps.
Nevertheless, the results above should be interpreted with caution.
The e-folding timescale is a metric that depends on the shape of the lagged autocorrelation curve,
which in turn may differ according to the period and time span of the original time series being analyzed.
In order to evaluate how stable the timescale is by varying the time span and also by allowing it to evolve over time,
we applied a time-moving and length-variable window to calculate the e-folding timescale of the ice volume
anomaly (detrended in the same way as the SIT time series) from the two longest reanalyses
(GECCO2 and MOVE-CORE), as shown in Fig. a and e. The window length varies
from 5 to 59 years (stepped by 1 year) and it moves in time, stepped forward by 1 month. Here, we use
the ice volume anomaly, rather than the SIT anomaly, for two reasons, first, because it is computationally more
efficient than calculating the timescale for the SIT anomalies at every grid cell, considering the large
number of interactions for a time-moving and length-variable window, and second, because the volume provides a pan-Arctic
perspective of the SIT persistence.
Notice in Fig. a and e that the persistence overall grows to longer than
∼20 months when taking into account long time spans,
remarkably for GECCO2 in which the ice volume anomaly persists for longer than 25 months at several center times.
As for the thickness anomalies, MOVE-CORE presents a shorter persistence compared to GECCO2.
As a measure of stability, we estimate the standard deviations for all computations displayed in
Fig. a and e. Results show that
MOVE-CORE has a more stable timescale, with standard deviation of 3.0 months from its mean (9.7 months), while GECCO2
presents the average and standard deviation of 15.0±6.5 months.
The e-folding length scales estimated for the SIT time series. Only grid cells in which the time-mean
(for the January 1993–December 2007 period) SIT at the time of summer minimum is greater than 0.1 m are taken into
account for the computations. Averages for the systems with ice data assimilation and no data assimilation are represented by the DA
and NA panels, respectively. All maps have the 0∘ longitude
placed at 06:00, while the bounding latitude is 67∘ N. Reanalyses labeled in blue and red highlight
whether the datasets were built with or without ice data assimilation, respectively.
Figure b and f show the case where the window length is 15 years, as it is for the overlapping period
January 1993–December 2007. For this case, the average (standard deviation) timescales for GECCO2 and MOVE-CORE are 11.4±2.6 and 9.1±2.5 months,
respectively. Minimum to maximum ranges are 6.2–16.5 months for GECCO2 and 4.9–13.5 months for MOVE-CORE. If we take into account the
same center time of the time span January 1993–December 2007, that is mid-June 2000, the ice volume anomaly persistence
is 13.6 and 9.2 months (red stars in Fig. b and f, respectively). Note that the
timescales of the ice volume anomalies are a few months longer compared to the persistence of the AWM thickness anomalies
(9.2 months, GECCO2; 5.4 months, MOVE-CORE).
We make use of wavelet analysis to evaluate whether the time series displayed in Fig. b and f
exhibit a significant band(s) of variability. Figure c and d reveal that the ice volume anomaly from GECCO2
presents two bands of significant variability, as highlighted by the horizontal gray bars in Fig. d.
The first spans from 4.4 to 6.1 years, and it is present in the first half of the time series but does not persist over time
(black contours in Fig. c). The second is marked by periods longer than 10.7 years, which seems
to be recurrent over time but should be interpreted with caution since it is placed near the “cone of influence”,
in which edge effects become important, as indicated by crosshatched areas overlapping the black contours in
Fig. c.
The ice volume anomaly from MOVE-CORE, in turn, is marked by a single band of significant variability, with periods longer than 12.7 years
(Fig. g, h). Again, this band should be interpreted with caution since it is also placed
near the cone of influence.
Length scales
The e-folding length scale is a metric used for indicating how well a variable from a certain grid cell compares
to the neighboring cells. In other words, it shows how the anomalies spread in space.
As for the timescale, the length scale is a promising parameter to be explored when designing observational systems,
but in terms of spatial coverage of instruments. Simplistically, regions marked with high length scales
would require fewer instruments to be monitored better.
Figure shows the length scales for the SIT anomaly at every grid point.
The AWM length scales, in kilometers and ascending order, for each system are
337.0 (GloSea5),
420.7 (GloSea5-GO5),
544.6 (C-GLORS05),
681.5 (MERRA-Ocean),
724.3 (TOPAZ4),
728.2 (G2V3),
596.9 (ORAP5),
597.4 (UR025-4),
730.2 (PIOMAS),
732.5 (ECCO-v4),
846.7 (MOVE-G2),
835.8 (MOVE-CORE),
934.0 (ECDA), and 935.7 km (GECCO2).
A similar pattern to the timescale is observed here, with GloSea5 and GloSea5-GO5 presenting the minimum length scales, rarely higher than
500 km, while the reanalyses without sea ice data assimilation are characterized by higher length scales, sometimes higher than
1200 km. In all systems the length scales are relatively longer near the central Arctic. This suggests that higher length scales could
be somehow associated
with thicker ice. The relationships between mean ice thickness, timescale, and length scale will be
explored in detail in Sect. .
The stability of the length scale over time (Fig. ) was tested by means of a moving window with 15 years length, as follows:
first, we calculate the one-point correlation maps for every grid point;
second, we estimate the length scale for each one-point correlation map;
third, the AWM length scale was calculated taking into account only grid points with a valid SIT value from all reanalyses;
fourth, the process was repeated by stepping forward the 15-year window by 12 months.
It is worthwhile mentioning that, computationally, it is much more expensive to calculate the length scale than the timescale.
This is the reason why, here, we just use a time-moving but not length-variable window. The results suggest that the length scale
is relatively more stable than the timescale (Fig. b and f), as further discussed in Sect. .
(a) Moving e-folding length scales estimated for the ice volume anomaly time series from the GECCO reanalysis. The window length
is 15 years, and it is stepped forward by 12 months over a total period of 64 years. (b) Same as (a), but for the MOVE-CORE reanalysis,
which has a time span of 60 years.
Discussion and conclusions
The first aim of this study was to evaluate how the SIT from the reanalyses compares against observational datasets, either draft or SIT.
We have used three different metrics to perform this comparison: the correlation coefficient (R), as a measure of the linear
correlation between datasets; the mean residual sum of squares (MRSS), as an indicator of whether reanalysis values are good predictors
for the observations; and the root mean square error (RMSE), which directly compares how the SIT from the reanalyses approaches the SIT from
observations. The results show that some of the reanalyses have a relatively good correspondence either comparing SIT and draft or SIT from both
sources of data. This is the case, for instance, for the TOPAZ4 product. A direct comparison between SIT from all reanalyses and observations
indicates RMSEs ranging from 0.7 to 1.1 m. PIOMAS has the best agreement with the observational datasets. A particular case is GECCO2, which
presents a relatively small RMSE and a good correlation with the SIT observational datasets, as well as a linear relationship. However, this same
product is weakly correlated with the draft observational datasets as well as having poor predictive skill.
One of our main goals in performing such a comparison was to identify whether or not systems built with assimilation of sea ice concentration
data are closer to observations, compared to the products built with no sea ice data assimilation. The results suggest that reanalyses with
sea ice data assimilation do not necessarily perform better. One could speculate that some reanalyses do not reflect the
covariances between sea ice concentration and SIT well.
We have compared the mean state (mean SIV) and respective variability (SD SIV) of all reanalyses against the specifications and parameters
displayed in Table . Nevertheless, for such a comparison, where each system has its own configuration with several varying
parameters, we were not able to distinguish the effect that the selected parameters may have on the mean state and variability. The comparison
among SIT from the different reanalyses (Sect. ) is not straightforward and does not necessarily improve
due to common specifications and key parameters from the two systems being compared. For instance, the pair C-GLORS05–G2V3 shares a set of
common assumptions (ocean–sea ice model, atmospheric forcing, vertical discretization, number of ice thickness
categories, EVP dynamics, ocean–ice drag coefficient, analysis window, and both assimilate sea ice data), but this pair still presents a relatively
high RMSE (0.39 m) and not such a strong correlation (R=0.4), as shown in Fig. . Only a few different assumptions and parameters, as well as
their nonlinear interactions, may result in systems with considerably distinct mean state and variability. Although the pair C-GLORS05–G2V3
shares several common aspects, these two systems assume different air–ice drag coefficient and also assimilate the sea ice data in a different
way, for instance. The same statement could be applied to other pairs of systems, e.g., G2V3–ORAP5, which also share some similarities but
are still distinct in terms of mean state and variability.
The pair with the smallest RMSE (Fig. ), ECDA–UR025-4, at the same time has a weak linear relationship (R=0.21).
This reinforces the importance of looking at different metrics when comparing different products. If we average the RMSEs that one specific
reanalysis presents against all the others (Fig. ), thus comparing with the pan-Arctic mean ice volume of this same reanalysis, it becomes
clear that products with relatively low sea ice volume (i.e., thin ice) present small RMSEs when compared with their counterparts
(Fig. ), although MERRA-Ocean is an outlier in this pattern by presenting thin sea ice but a large RMSE compared
to the other reanalyses (Fig. , left upper corner). Figure helps to explain why ECDA and
UR025-4 have a small RMSE, though their anomalies are marked by a relatively weak correlation, as suggested in Fig. . This is also evident in the
respective sea ice volume anomalies from these two reanalyses shown in Fig. . In the same way, Fig. also
indicates that the large differences in the SIT field take place near the coast of northern Greenland and the Canadian Archipelago, which are regions
marked by the thickest sea ice over the studied domain.
Time-mean sea ice volume vs. the mean RMSE. This last parameter is an average of the RMSEs that each reanalysis has when
its SIT field is compared individually to the other 13 reanalyses, as shown in Fig. . Shades of blue and purple indicate the reanalyses
which do assimilate sea ice data, while shades of red indicate the reanalyses without sea ice data assimilation.
Another main goal of this work was to characterize the timescales and length scales of the sea ice thickness anomaly as well as to report whether
these parameters are influenced by the fact that a respective reanalysis assimilates sea ice data or not. In this case, sea ice data
assimilation plays a clear role in the scales referred to: systems with sea ice data assimilation are characterized by shorter timescales and length scales compared to the systems which do not assimilate sea ice data. Nevertheless, a comparison between the same system but built with
(G2V3) and without (G2V1; not included in the 14 reanalyses of the present study) assimilation of sea ice concentration data
(Fig. )
suggests that this finding is valid in terms of pan-Arctic averages but not necessarily at every grid cell. This may explain why in the specific
location addressed in Fig. the reanalyses with data assimilation showed relatively longer timescales
compared to the reanalyses without data assimilation. The pan-Arctic AWM timescale and AWM length scale from G2V3 are 5 months and 728.2 km, respectively. Without sea ice data assimilation (G2V1),
the AWM timescale and AWM length scale increase to 5.5 months and 745.3 km, respectively.
Grid-point differences (G2V3–G2V1) of timescale (a) and length scale (b) between two versions of the GLORYS system: G2V3
which assimilates sea ice data and G2V1 which does not assimilate sea ice data.
Histograms showing how the AWM timescale (left-hand panels) and AWM length scale (right-hand panels) are related to different reanalysis
specifications: (a–b) whether or not the system assimilates sea ice data, (c–d) the source of atmospheric forcing
data, (e–f) the sea ice model used, and (g–h) the dynamics used (viscous–plastic or elastic–viscous–plastic) for ice–ice
interactions that control ice deformation. Shades of blue and purple indicate the reanalyses
which do assimilate sea ice data, while shades of red indicate the reanalyses without sea ice data assimilation.
Likely, the main reason why the assimilation of sea ice concentration data impacts the timescales and length scales of the SIT field is linked to the fact that
when a reanalysis assimilates sea ice information, the system is forced towards the assimilated conditions, different from what occurs
with free-running models. Eventually, data assimilation introduces SIT increments that are not necessarily physical and so contributes to
an attenuation in the correlation of this variable at a certain grid cell both in time, with their future estimations, and in space, with the
neighboring grid points.
We have shown that timescales and length scales are clearly influenced by whether or not the reanalyses assimilate sea ice data, as represented graphically in Fig. a–b. However, are these two properties also clearly influenced
by other specifications and parameters? Figure c–h show how timescales and length scales are linked to the choices of atmospheric forcing, sea ice model, and dynamics for ice–ice interactions that control ice deformation
(VP or EVP). Even though the atmospheric forcing fields are reported to play a major role in the
sea ice simulations , we could not identify distinguished patterns between
the two main sources of atmospheric forcing used by the
ensemble of reanalyses: ERA-Interim and NCEP/NCAR (Fig. c–d). Likewise, timescales and length scales are
not clearly linked to the choices of sea ice model (Fig. e–f) and ice deformation dynamics
(Fig. g–h), although a certain coherence in the timescales and length scales is observed for the systems
that use the Louvain-la-Neuve sea ice model (LIM; Fig. e–f).
Scatter plots showing how the (a, c, e) AWM timescale and (b, d, f) AWM length scale are related to the (a, b) mean state,
(c, d) mean sea ice (SI) drift, and (e, f) drag air–ice coefficient. (g) Relation between drag air–ice coefficient and mean state.
(f) Relation between drag air–ice coefficient and mean sea ice drift. Black dashed lines indicate the linear fit, while the
coefficient of correlation R (and its respective p value) is also displayed in each panel. The black cross in panels (e)–(h) indicate
that MOVE-CORE was not used in the respective regressions (black dashed lines), since this reanalysis adopts a much higher
drag air–ice coefficient compared to the other 13 reanalyses. Shades of blue and purple indicate the reanalyses
which do assimilate sea ice data, while shades of red indicate the reanalyses without sea ice data assimilation.
Scatter plot of the average weighted mean (AWM) timescale vs. the AWM length scale. The black dashed line
indicates the linear regression between both parameters, while the coefficient of correlation (R) is also displayed in the plot.
The gray rectangle compares the two GLORYS systems: G2V1, built without sea ice data assimilation,
and G2V3, built with sea ice data assimilation
Besides the spread among the points, the scatter plots displayed in Fig. a–b
indicate a certain correlation between the time-mean SIV (mean state) and the studied scales, where relatively thin ice
leads to shorter scales, in agreement with . In contrast, the timescales have
a marked anti-correlation with the sea ice drift as shown
in Fig. c: reanalyses with faster sea ice present a short timescale. Such
correlation is less pronounced for the length scale (Fig. d). Different parameters
from the reanalyses could potentially influence the sea ice velocity. For instance, high air–ice and low ocean–ice drag
coefficients each contribute to faster ice velocities . As an example, ECCO-v4 has the second
highest air–ice (smaller only compared to MOVE-CORE) and the smallest ocean–ice drag coefficients (see Table ).
This may explain why ECCO-v4 has relatively high ice velocities (Fig. c) and, therefore,
low timescales and length scales (Figs. and ). For our ensemble
of reanalyses, Fig. e shows a close correlation between sea ice velocity and
the drag air–sea coefficients. Again, this correlation is less pronounced for the length scale
(Fig. f).
The ice strength formulation is a major player in the sea ice velocity . All reanalyses follow the linear
parameterization proposed by , except the GloSea5 products and PIOMAS, which employ the ice strength formulation
following . A higher ice strength parameter P* in Hibler's formulation leads to thicker and slower-moving ice,
which would potentially lead to larger scales. Nevertheless, a relation between P* and the scales is not so clear for the ensemble
of reanalyses (not shown). In addition, presented a detailed study
comparing Hibler's and Rothrock's methods and showed that, for systems characterized by relatively thinner ice, model simulations
with Rothrock's formulation result in lower ice strength, and therefore faster ice velocities, compared to
Hibler's formulation. We do not have a clear understanding of why the GloSea5 products present such short timescales and length scales; however, we could
speculate that the combination between relatively thin ice (Fig. a) and the use of
Rothrock's ice strength formulation could support this result.
The discussion above indicates that timescales and length scales are mainly driven by the fact of whether or not the reanalyses
assimilate sea ice data, but that they are also influenced by the air–ice drag coefficient and sea ice drift.
Figure shows a strong correlation between both timescales and length scales, whereby long timescales are
associated with large length scales. Notice in this plot the difference in the timescales and length scales from G2V1 and G2V3 systems,
highlighted by the gray rectangle placed near the center of the figure.
As mentioned before, the ice thickness timescales and length scales are interesting properties to be explored
when designing and planning an optimal observation system both in terms of temporal sampling and spatial placement
of instruments. Nevertheless, these properties also vary over time (Figs. and ). The stability over
time of timescales and length scales can be estimated by the coefficient
of variation (Cv= SD/Mean).
The Cv is a non-dimensional metric used to evaluate the extent of a certain variability in
relation to its mean, allowing different properties to be compared. The Cv for the GECCO2 and MOVE-CORE moving timescales,
estimated from the time series shown in Fig. b and f, is 0.23 and 0.27, respectively,
while the Cv for moving length scales (Fig. ) is 0.13 and 0.07.
Lastly, it is worthwhile mentioning that both timescales and length scales are promising properties to
support the design of an optimal observing system. As suggested by the Cv presented above, and by the
fact that the timescale is more sensitive to the reanalysis specifications and parameters
(see Fig. c–f), the length scale is considerably more stable
than the timescale; therefore it is a more reliable variable to be taken into account for deploying observing systems.
For instance, the multiple linear regression model used by , for determining optimal
locations to predict sea ice extent from SIT, could be combined with the length scale information, thereby avoiding two
or more stations placed into the same radius of correlation (length scale) being selected. The timescale would be more useful
if used in combination with the knowledge of its variability. Further studies are required to evaluate the
performance of timescales and length scales in providing support for the optimal design of observational programs,
though this work already shows some promising results in that direction.