We use model simulations from the CESM1-CAM5-BGC-LE dataset to characterise the Arctic sea ice thickness internal variability both spatially and temporally. These properties, and their stationarity, are investigated in three different contexts: (1) constant pre-industrial, (2) historical and (3) projected conditions. Spatial modes of variability show highly stationary patterns regardless of the forcing and mean state. A temporal analysis reveals two peaks of significant variability, and despite a non-stationarity on short timescales, they remain more or less stable until the first half of the 21st century, where they start to change once summer ice-free events occur, after 2050.
In the recent decades, Arctic sea ice has retreated and thinned significantly (Notz and Stroeve, 2016).
The annual mean Arctic sea ice extent decreased by
The mean spatial distribution of the Arctic SIT is relatively well documented (Stroeve et al., 2014). But there are some uncertainties around its interannual variability and its spatial modes of variability.
Some studies (Lindsay and Zhang, 2006; Fuckar et al., 2016; Labe et al., 2018) already analysed the spatial distribution of Arctic sea ice variability by applying empirical orthogonal functions (EOFs) (
Apart from Olonscheck and Notz (2017), the studies cited above used data covering a few decades under historical forcing. In this work we use a long climate model control run under pre-industrial conditions from the CESM1-CAM5-BGC-LE dataset, which enables us to study only the internal variability of the Arctic SIT. We study the internal variability both temporally and spatially by applying a wavelet analysis and an EOF decomposition to the pan-Arctic SIV and gridded SIT anomaly time series, respectively. We also determine whether or not the SIV and SIT variability is stationary by analysing the model outputs under historical and future climate conditions with 30 ensemble members.
This paper is organised as follows. The model and its outputs are briefly described in Sect. 2. In Sect. 3, the spatial and temporal internal variability of Arctic sea ice is analysed, as well as its persistence through historical and future climate conditions. Then we explore the drivers of the main modes of internal variability. Conclusions are finally given in Sect. 4.
We use the CESM1-CAM5-BGC-LE dataset (Kay et al., 2015). The Community Earth System Model Large Ensemble (CESM-LE) was designed to both disentangle model errors from internal climate variability and enable the assessment of recent past and future climate changes in the presence of internal climate variability. The CESM1(CAM5) is a CMIP5 participating model. It consists of coupled atmosphere, ocean, land and sea ice component models. It also includes a representation of the land carbon cycle, diagnostic biogeochemistry calculations for the ocean ecosystem and a model of the atmospheric carbon dioxide cycle (Moore et al., 2013; Lindsay et al., 2014). While it is not possible to validate the data in terms of SIT and SIV variabilities due to the lack of continuous observational data, the model was well validated in terms of mean state of the ice thickness and extent, as well as regarding the recent trends in the latter. Jahn et al. (2016) showed good agreement between observations and CESM1(CAM5) simulations for mean Arctic sea ice thickness and extent in the early 21st century. Barnhart et al. (2016) demonstrated that CESM1(CAM5) captures the trend of declining Arctic sea ice extent over the period of satellite observations. Based on these validation studies, we consider that the CESM1-CAM5-BGC-LE time series is a fair proxy to study the variabilities of the Arctic SIT and SIV under different forcing conditions.
In this paper, we use the monthly averaged Arctic SIT and SIV provided over the three periods (pre-industrial, historical and future). The pre-industrial period is represented by a single 1700-year control simulation with constant pre-industrial forcing. The ocean model was initialised from a state of rest (Danabasoglu et al., 2012), while the atmosphere, land and sea ice models were initialised using previous CESM1(CAM5) simulations. This experimental design allows the assessment of internal climate variability in the absence of climate change. In practical terms, we will use the last 200 years of this simulation. The historical period has one ensemble member covering the 1850–2005 period and 30 ensemble members over 1920–2005. Also with 30 ensemble members, the future climate period (2006–2100) follows the Representative Concentration Pathway (RCP) 8.5 scenario, corresponding to a total radiative forcing of 8.5 W m
For the variability analysis, the trend and seasonal cycle are removed from the time series (pan-Arctic SIV and gridded SIT) so that we focus on the interannual variability. Since the spatial variability analysis uses 30 ensemble members, the SIT anomaly fields are computed by removing the ensemble mean to each member. When only one ensemble member is used, as for the temporal analysis, the anomaly is calculated by excluding the individual trend (provided by a second-order polynomial fit) of each month.
To characterise the internal variability of the Arctic sea ice, we aim at inspecting how the SIV variability evolves in time and how SIT variability is characterised in space. For addressing the temporal variability, we make use of wavelet analysis, with Morlet as wavelet mother, following the methodology proposed by Torrence and Compo (1998). The wavelet analysis has the advantage of taking into account possible non-stationarity of the time series. In this paper, we show the results for one of the historical (1850–2005) members and one of the future (2006–2100) members, although we tested the robustness of the results over the 30 ensemble members as discussed later (Sect. 3.1 and 3.2).
The spatial variability is analysed by computing the EOFs on the SIT anomaly time series. This decomposition reduces the large number of variables of the original data to a few variables, but without compromising much of the explained variance. Each EOF represents a mode of SIT variability that provides a simplified representation of the state of the SIT at that time along that EOF. In other words, the EOFs themselves are fixed in time but their weighting coefficients are time-varying; the associated time series (one for each mode) indicate in which state the SIT is at any time (Hannachi, 2004). The analysis is made on the gridded SIT anomaly time series for the three periods. For the historical and future periods, the EOFs are computed over 30 ensemble members, all appended together over time (as done by Labe et al., 2018).
By applying those analyses separately over the three periods, we aim to document the internal variability in the absence of any external forcing during the pre-industrial period. By comparing the pre-industrial results with those for the historical and future periods, we estimate the evolution of the SIT and SIV internal variability under anthropogenic forcing.
The results from the wavelet analysis are presented in Fig.
The temporal variability of the Arctic SIV anomaly over the pre-industrial period is depicted in Fig.
Over the historical period, the Arctic SIV temporal variability shows a first peak centred on 5 years and two others centred on 10 and 16 years, all with
Wavelet analysis applied to the Arctic sea ice volume anomaly over the pre-industrial (200 years preceding the historical integration)
The main characteristics of the temporal variability of the Arctic SIV under pre-industrial conditions seem to persist under anthropogenic forcing. The two major temporal peaks of variability centred on 8 and 16 years, found in the pre-industrial run, are also present during the historical period. For the first half of the 21st century, the future projections are also dominated by the two main peaks but centred at 5 and 10 years in the integrated spectrum, and with relatively weaker power compared to the pre-industrial and historical runs. Furthermore, the SIV variability seems to be non-stationary since the power is not always above the
The wavelet analyses applied to the other 30 ensemble members of the historical and future simulations bring robustness to our results since, overall, each member shows a similar pattern of temporal variability. To promote such a multi-member comparison among the different spectra, we have first normalised all spectra (and the significance curve) by their respective maximum value so that the power ranges from 0 to 1. This step is required to make the spectrum from each member have the same weight in the averaging. As shown in Fig.
The spatial variability of the Arctic SIT anomaly is depicted by the major modes of variability in Fig.
Modes of Arctic SIT spatial variability. From the left to the right, each row shows the first three EOFs of Arctic SIT over the pre-industrial (200 years preceding the historical integration)
The first mode of SIT is stable over time and stays the dominant mode of spatial variability in all three periods.
There are some disparities in percentage explained and in magnitude, which could be explained by the different lengths of the periods.
As the first mode, the second mode of SIT spatial variability is persistent in the historical period. For the future climate period, the second mode of SIT variability is no longer persistent. It presents a dipole of variability as the first mode, but the Pacific part of the dipole is larger and no longer located in the East Siberian Sea.
The third modes of the three periods (Fig.
After 2050, the SIT spatial variability is impacted by the sudden decrease in SIT. EOFs computed over the 2050–2100 period (not shown) exhibit the same pattern of the dipole as the first mode for the 2005–2050 period, but the area of high variability is not the same. The Atlantic part of the dipole is shifted toward the north coast of Greenland, and the Pacific part of the dipole is also reduced near the coast.
Arctic sea ice mean circulation during low
By computing the temporal oscillation between phases of a certain mode of variability, we are able to characterise this mode by low and high indices.
In order to find the physical drivers of the SIT modes of variability, we investigate the differences in dynamic and thermodynamic features (sea ice velocity, atmospheric surface temperature) between both phases of the modes.
Figure
Furthermore, applying wavelet analysis to the associated time series of the first spatial mode of variability indicates that the main periodicity of this mode is centred on 8 years and spans from 5 to 10 years (not shown). This result is suggestive of a link between the first mode of temporal variability of the wavelet analysis and the first mode of spatial variability, and so to the Arctic Oscillation.
We also used the associated time series of the second mode of SIT spatial variability to characterise it by low and high indices.
The same analysis over the sea ice velocity is performed for the second mode. For both indices, the sea ice velocity fields are similar. We concluded that the second mode is not dynamically driven.
Following Olonscheck et al. (2019) results, which demonstrate that the internal variability of Arctic sea ice area and concentration are primarily caused by atmospheric temperature fluctuations,
we investigated the differences in mean surface air temperature anomaly over the pre-industrial period between the low and high indices for both the first and second modes of SIT variability. Two widely different states of surface air temperature are found between indices for both modes (the surface air temperature anomaly for the second mode is depicted in Fig.
In this work, we have analysed the internal variability of the Arctic SIT both spatially and temporally with the CESM1-CAM5-BGC-LE dataset. We conducted wavelet analysis of the pan-Arctic SIV anomaly and EOF decomposition of the gridded SIT anomaly, both over a 200-year control run conducted under pre-industrial conditions. Then, to assess the persistence of the SIT anomaly internal variability under anthropogenic forcing, we performed the same analyses with 30 ensemble members over the historical and future periods.
The temporal analysis of the SIV anomaly internal variability shows two peaks of significant variability. One centred on 8 years, spanning from 5 to 10 years, and another one centred on 16 years, spanning from 10 to 20 years. These two peaks of temporal variability are present in both the pre-industrial and historical periods, as well as in the first half of the 21st century. After that, a sudden loss of variability due to ice-free summer events is found. Furthermore, despite a dominant periodicity over the three periods, the SIV anomaly has been observed to be non-stationary. Indeed, the dominant periodicity of the SIV variability can be centred on either 8 or 16 years, depending on the timescale and period. Wavelet analyses over the 30 ensemble members for the post-industrial period have shown the same behaviour of temporal variability within members, except that the peaks are not always centred in 8 and 16 years but somewhere between 5–10 and 15–26 years, depending on the member.
The spatial analysis of the SIT anomaly internal variability has been applied to the 30 ensemble members and reveals two important modes of variability. The first one is a mode with opposite signs centred in the East Siberian Sea and in the Fram Strait area, accounting for 22 % of the variability in the pre-industrial period. This first mode is a dynamical one, related to the Arctic Oscillation, and persists over all pre-industrial, historical and future periods. Furthermore, this first mode of spatial variability has a temporal variability of 8 years (spanning from 5 to 10 years), corresponding to the first peak of variability found in the temporal analysis. The second mode exhibits a large pole of variation centred on the East Siberian Sea going through the Arctic Basin. It represents 14 % of the variability in the pre-industrial period.
The loss of sea ice in summer starting in 2050 and the strong decrease in SIV in winter during the second half of the 21st century (from 15 to
This analysis of the Arctic SIT and SIV variability bears some limits. Indeed, our results for the temporal and spatial patterns of variability are based on only one model, and despite the use of 30 ensemble members and a reasonable validation against observations, the model is not perfect. Furthermore, the spatial modes of SIT variability are robust for all the 30 ensemble members, but the temporal analysis shows some dissimilarities between members. Other studies with other model outputs are therefore needed to confirm our conclusion.
Finally, in the context of recent climate changes, predicting sea ice has never been so important. However, to validate and improve our predictions, observational data are crucial. In this sense, our variability analysis of internal SIV and SIT variability might help the development of an optimal sampling strategy, taking into account the selection of well-placed sampling locations for monitoring the SIT and, therefore, the pan-Arctic SIV that are not as well documented as the sea ice extent and area (Ponsoni et al., 2020).
The wavelet analysis is performed with the Waipy module on Python (
Data can be downloaded from the following source:
GVA, LP, FM, TF and VL designed the science plan. GVA conducted the data processing, produced the figures, analysed the results and wrote the manuscript based on the insights from all co-authors.
The authors declare that they have no conflict of interest.
François Massonnet and Leandro Ponsoni are a F.R.S.-FNRS research associate and a post-doctoral researcher, respectively. Guillian Van Achter is funded by the PARAMOUR project which is supported by the Excellence Of Science programme (EOS), also founded by FNRS. We thank the two referees for their very helpful comments on an earlier version of this paper.
The work presented in this paper has received funding from the European Commission, H2020 Research Infrastructures (APPLICATE project – Advanced prediction in Polar regions and beyond, grant no. 727862 and PRIMAVERA project – PRocess-based climatesIMulation: AdVances in high-resolution modelling and Europeanclimate Risk Assessment, grant no. 641727).
This paper was edited by Michel Tsamados and reviewed by two anonymous referees.