Drivers of summer Arctic sea-ice extent at interannual time scale in CMIP6 large ensembles revealed by information flow

Drivers of summer Arctic sea-ice extent at interannual time scale in CMIP6 large ensembles revealed by information flow | Scientific Reports

Abstract

Arctic sea-ice extent has strongly decreased since the beginning of satellite observations in the late 1970s. While several drivers are known to be implicated, their respective contribution is not fully understood. Here, we apply the Liang-Kleeman information flow method to five different large ensembles from the Coupled Model Intercomparison Project Phase 6 (CMIP6) over the 1970-2060 period to investigate the extent to which fluctuations in winter sea-ice volume, air temperature and ocean heat transport drive changes in subsequent summer Arctic sea-ice extent. This allows us to go beyond classical correlation analyses. Results show that air temperature is the most important controlling factor of summer sea-ice extent at interannual time scale, and that winter sea-ice volume and Atlantic Ocean heat transport play a secondary role. If we replace air temperature by net shortwave and downward longwave radiations, we find that the sum of influences from both radiations is almost similar to the air temperature influence, with the longwave radiation being dominant in driving changes in summer sea-ice extent. Finally, we find that the influence of air temperature is more prominent during periods of large sea-ice reduction and that this temperature influence has overall increased since 1970.

Introduction

Recent changes in Arctic sea ice are one of the key indicators of the ongoing climate change 1. The annual mean Arctic sea-ice extent has linearly decreased by 2.2 million km\(^2\) (−17 \(\%\)) between 1979 and 2023, with the largest changes occurring in summer (−44 \(\%\)) compared to winter (−11 \(\%\)) based on satellite observations 2, 3, 4, 5. According to climate model projections, the Arctic Ocean could be ice free in summer before the middle of this century 6, 7, 8, 9, 10, 11, 12, although results depend on the greenhouse gas emission scenario 1 and on internal climate variability 13, 14, 15. In this context, understanding the causes of the recent Arctic sea-ice loss is highly important. Both anthropogenic global warming and internal climate variability have played a role in these changes 1, 16, 17, 18, 19, 20, but the relative contribution from atmospheric and ocean processes leading to these changes is far from being understood.

Arctic sea-ice variability has been shown to be primarily driven by advected air temperature based on observations, reanalyses and global climate model (GCM) simulations, especially in summer 21. In addition, summertime atmospheric circulation may have contributed as much as 60 \(\%\) to the September sea-ice extent decline between 1979 and 2014, through changes in low-level air temperature, integrated atmospheric water vapour and downward longwave radiation 22. While the Arctic Oscillation (AO) was suspected to drive summer sea-ice extent in earlier studies 23, sea-ice extent has continued to decrease regardless of the atmospheric mode 24. Previous causality analysis with the Liang-Kleeman information flow method showed that the AO does not influence Arctic sea-ice area based on the EC-Earth3 large ensemble 25. Atmospheric surface heat fluxes have also contributed to Arctic sea-ice changes, e.g. the enhanced absorbed shortwave radiation resulting from a reduced surface albedo leads to further sea-ice decline via the ice-albedo feedback 26, 27, 28. The previous winter sea-ice extent and volume are important in setting the course of the following summer sea-ice extent 24, 29. Furthermore, ocean heat transport to the Arctic, mainly via the Barents Sea Opening, Fram Strait and Bering Strait, has been shown to strongly impact Arctic sea ice 5, 30, 31, 32, 33, 34, 35, although this influence mainly occurs in winter 25, 36, 37, when the sea-ice pack is more extensive.

Previous studies mainly used correlation and regression analyses to infer causal influences, but correlation does not necessarily imply causation. A significant correlation simply means that there is a relationship, or synchronous behavior, between two variables without explicitly confirming a causal link between the two. Causal methods are useful in identifying cause-effect relationships and have started to be widely used in the context of Earth system sciences 38. Contrarily to correlation, they allow to remove spurious links, identify directional dependencies between variables as well as the presence of confounding variables, and can be used in a multivariate framework. One such causal method, directly derived from the propagation of information entropy between variables, is the Liang-Kleeman information flow 39, 40, 41. It provides a simple expression of the information flowing from one variable to the other using covariances between all pairs of variables as well as covariances between all variables and the time derivative of the target variable (see Methods). This causal method assumes linearity and can be used in the context of this study as the relationships between the variables used here are roughly linear (e.g. sea-ice extent vs. surface air temperature 7, 42 and sea-ice extent vs. ocean heat transport 43, 44), but we acknowledge that some nonlinear processes could appear and are not taken into account. Also, the method assumes stationarity and this is dealt with by removing the linear trend (see Methods). This method has recently been used in various climate studies 25, 45, 46, 47, 48, 49. The first study to apply the method to understand the causes of recent past and future Arctic sea ice 25 showed that surface air temperature, sea-surface temperature and ocean heat transport were the most important drivers. However, the latter study only investigated one large model ensemble (EC-Earth3), did not consider the preconditioning (previous winter sea-ice volume) as well as surface atmospheric heat fluxes, and did not separate periods of large sea-ice reduction from the rest. In our analysis, we use five different large model ensembles (Table 1, Methods) and compute the rate of information transfer to better understand the causes of recent and future summer Arctic sea-ice changes at interannual time scale, including the specific analysis of periods of large sea-ice reduction.

Results

Drivers of summer sea-ice extent

Our period of analysis is from 1970 to 2060. This period is chosen based on the constraints that (i) one of the large ensembles (EC-Earth3) was run only from 1970 and (ii) ice-free conditions (sea-ice extent below 1 million km\(^2\)) in summer (September) are reached for all models (except MPI-ESM1.2-LR) from 2060 onwards (Fig. 1 a). The ensemble mean summer sea-ice extent ranges from 6.9 to 9.1 million km\(^2\) in 1970 for the different models to values between 0.2 and 1.5 million km\(^2\) in 2060, with a complete disappearance of summer sea ice by the end of this century based on the Shared Socioeconomic Pathway 3-7.0 (SSP3-7.0; Fig. 50. A common feature is the large ensemble spread for all models considered, which shows the need for using large ensembles. For a more detailed visualization of the different members for each separate model, we redirect the interested reader to Supplementary Figs. S1-S5.

Time series of summer sea-ice extent and its drivers. Time series of the different variables for the five large ensembles using CMIP6 historical (1970-2014) and SSP3-7.0 (2015-2100) simulations. Solid colored curves represent ensemble means and shading shows the ensemble spread (between minimum and maximum). Black dashed lines represent observations / reanalyses. (a) Summer (September) Arctic sea-ice extent. (b) Winter (March) Arctic sea-ice extent. (c) Winter (March) Arctic sea-ice volume. (d) Annual mean Arctic 2m air temperature. (e) Annual mean Atlantic Ocean heat transport (OHT). (f) Annual mean Pacific OHT. (g) Annual mean net shortwave radiation (SWR). (h) Annual mean downward longwave radiation (LWR).

Associated with the strong reduction in summer sea-ice extent, the winter (March) sea-ice extent also decreases through the recent past and twenty-first century according to all model simulations, although at a much smaller rate than summer sea-ice extent, except for CanESM5, which displays a large negative trend (Fig. 1 b). Winter sea-ice volume also shows a strong decrease over the whole period, with ACCESS-ESM1.5 and MPI-ESM1.2-LR being relatively close to the PIOMAS reanalysis 51 over the observational period, EC-Earth3 and CanESM5 overestimating it, and CESM2 underestimating it (Fig. 1 c). The annual mean surface air temperature averaged over the Arctic regions (poleward of 70\(^\circ\)N) increases from \(\sim -15^\circ\)C (multi-model average) in 1970 to \(\sim -7^\circ\)C in 2060 (Fig. 52, while all other models underestimate it (Fig. 1 e). EC-Earth3 and CanESM5 display the largest increases in Atlantic Ocean heat transport, however with a more progressive increase for the former model and an acceleration followed by a deceleration for the latter model (Fig.

Based on these time series, it is tempting to conclude that the decrease in winter sea-ice extent and volume, the increase in surface air temperature and the increase in Atlantic and Pacific Ocean heat transports have been contributing to the reduction in summer sea-ice extent over the recent past and future periods. However, as already explained, correlation does not necessarily imply causation. In order to remove spurious dependencies based on correlations and identify true causal links, we compute the rate of information transfer from all potential drivers considered above (winter sea-ice volume, Arctic surface air temperature, and Atlantic and Pacific Ocean heat transports) to our target variable (summer sea-ice extent) based on the Liang-Kleeman information flow 41. We make this calculation over the whole period for each model member separately (after having removed the ensemble mean, which allows to remove the trend) and then compute the model ensemble mean, taking into account a 5 \(\%\) significance level (see Methods). Note that the data are not perfectly stationary after this detrending, but we prefer not to perform any additional data processing to introduce as few changes in the original data as possible.

Such a computation shows that surface air temperature is clearly the main driver of changes in summer Arctic sea-ice extent over the period 1970-2060, with all models displaying a statistically significant influence (Fig. 2 a). This result goes in hand with previous studies, which find that surface air temperature leads to strong changes in summer Arctic sea ice via direct ice melting or via the ice-albedo feedback 4, 18, 42, 53. Winter sea-ice volume appears to be the second main driver (a precursor, more precisely), although two models do not show a significant influence. A thinner ice pack at the end of the growth season increases the likelihood of reduced sea-ice extent during summer 29. Atlantic Ocean heat transport also plays a role in driving summer sea-ice extent, but only for two models. This is in agreement with previous studies showing that the Atlantification (i.e. the increasing influence of the warmer and saltier Atlantic water into the Arctic) is under way 30, 32. Pacific Ocean heat transport does not influence summer sea-ice extent for any of the models used here, although we note that the model ocean resolution is 40-50 km at 70\(^\circ\)N, while the width of the Bering Strait is 80 km. Note that meridional surface wind speed and atmospheric circulation (taken as 300 hPa geopotential height) do not have any influence on summer sea-ice extent for the models considered here (Supplementary Figs. S6-S7). An additional analysis with sea-surface temperature shows that it has an influence on summer sea-ice extent only for one model (Supplementary Fig. S8), and it mainly has an indirect effect via surface air temperature (not shown). The rates of information transfer coming from observations and reanalyses are relatively small and not significant (Fig. 2 a), even for air temperature, but the computation is based on a relatively short time period (1979-2018) with only one realization. As the method needs a sufficiently long time series, results from observations and reanalyses are just indicative and cannot be used in terms of model evaluation.

Drivers of summer sea-ice extent over 1970-2060. (a) Rate of information transfer (absolute value) from winter sea-ice volume (WSIV), 2m air temperature (T\(_{2m}\)), Atlantic Ocean heat transport (OHT\(_{Atl}\)) and Pacific OHT (OHT\(_{Pac}\)) to summer sea-ice extent over 1970-2060. (b) Corresponding correlation coefficients. Colored circles represent the ensemble means of the five large ensembles, with significant values at the 5 \(\%\) level highlighted by black contours (the number of members for each model is indicated in parentheses in the legend). The rates of information transfer and correlation coefficients are first computed for each different member, and then the ensemble mean is computed. Crosses show observations/reanalyses, with significant values highlighted by black circles.

It is particularly interesting to compare the rates of information transfer with the corresponding correlation coefficients between summer sea-ice extent and all other variables. In most cases (75\(\%\)), correlations are statistically significant (Fig. 2 b). Five significant correlations are not associated with a significant causal influence on summer sea-ice extent, i.e. from winter sea-ice volume for two models and from Pacific Ocean heat transport for three models. This means that if we had based our analysis only on correlations, we would have erroneously inferred an influence of Pacific Ocean heat transport on summer sea-ice extent. As such, the Liang-Kleeman information flow method allows us to remove spurious dependencies based on correlation analyses only. However, we acknowledge that this result is true for the summer period (an influence from the Pacific OHT could appear in winter, when the sea-ice cover is larger) and considering the main limitation of the method (linearity assumption). Despite the short time period, the observed correlation between surface air temperature and summer sea-ice extent is statistically significant; however, the causal analysis shows that there is no significant influence from surface air temperature to summer sea-ice extent in the observations. We stress again that this finding should be taken with care since the sample size in observations is severely limited by the length of the observational period.

The combination of rates of information transfer (Fig. 2 a) with correlation coefficients (Fig. 21, 22, 42. For two models (EC-Earth3 and CanESM5), an increase in Atlantic Ocean heat transport leads to a decrease in summer sea-ice extent, which also goes in the same direction as previous studies 33, even if this impact is reduced in summer compared to winter 25.

When replacing winter sea-ice volume by winter sea-ice extent, the latter has less influence on summer sea-ice extent for all models, and only EC-Earth3 shows a significant rate of information transfer (Supplementary Fig. S9). Additionally, the influence of surface air temperature becomes slightly larger (compared to the case in which sea-ice volume is included), which compensates for the decreased influence of winter sea-ice extent. The Atlantic and Pacific Ocean heat transport influences remain very similar between the case with winter sea-ice volume and the one with winter sea-ice extent. These results suggest that it is important to consider not only the areal extent of winter sea ice, but also winter sea-ice thickness (e.g. through sea-ice volume), as a precursor of summer sea-ice extent variations 54.

Atmospheric surface heat fluxes

Due to the prominent role of Arctic surface air temperature in driving changes in summer sea-ice extent and the tight connection between surface air temperature and atmospheric surface heat fluxes, we then replace annual mean surface air temperature by annual mean net shortwave and downward longwave radiations and repeat the causal analysis. Turbulent heat fluxes are not considered here because they are oriented towards the atmosphere for all models on an annual basis, suggesting that these fluxes respond rather than drive sea-ice variability, in agreement with previous studies 55, 56, 57. However, it might well be that during certain seasons, these fluxes are oriented towards the surface, which would imply a possible driving influence of the turbulent heat fluxes on sea-ice extent.

EC-Earth3, CanESM5 and ACCESS-ESM1.5 present radiation values that are in broad agreement with satellite observations over the recent period, while CESM2 and MPI-ESM1.2-LR underestimate the net shortwave radiation (Fig. 1 g) and overestimate the downward longwave radiation (Fig. 35, 58, 59, but this is the first time a causal method is used to make such an analysis.

We find that the downward longwave radiation is the most important driver of changes in summer sea-ice extent over 1970-2060, with all models displaying a significant impact (Fig. 3 a). The influence of downward longwave flux was also found in previous studies 22, 35, 55, 60, 61, 62. According to Burt et al. 60, a thinner sea-ice cover leads to larger surface air temperature, increased water vapor and enhanced cloud cover, which results in increased downward longwave radiation, ultimately leading to further sea-ice melting. The net shortwave radiation also has some influence, but only for two models (EC-Earth3 and CESM2; Fig. 3 a). Shortwave radiation is tightly linked to the ice-albedo feedback, which mainly operates in spring and summer 28: as the atmosphere warms, sea-ice extent decreases, leading to enhanced open-water area. As the ocean has a much lower albedo than sea ice, this results in an increased absorption of shortwave radiation, a warmer atmosphere and more sea-ice melting. The larger influence of downward longwave radiation compared to net shortwave radiation will be analyzed in more details in the next section, in which we look at the temporal evolution of the causal influences.

All other influences (winter sea-ice volume, Atlantic and Pacific Ocean heat transports) remain similar compared to the case where we consider surface air temperature, which provides confidence in the robustness of our results. It is particularly interesting to see that the sum of the rates of information transfer from both net shortwave and downward longwave radiations to summer sea-ice extent (Fig. 3 a) is approximately equal to the rate of information transfer from surface air temperature alone to sea-ice extent (Fig. 2 a). This suggests that the effect of surface air temperature is comparable to the combined influence of longwave and shortwave radiations. We will see in the next section that the sum of both radiation influences is relatively similar to the surface air temperature influence over the majority of the period and for most models.

Combining rates of information transfer (Fig. 3 a) with correlation coefficients (Fig.

Drivers of summer sea-ice extent over 1970-2060, including surface heat fluxes. (a) Rate of information transfer (absolute value) from winter sea-ice volume (WSIV), net (downward) shortwave radiation (NSWR), downward longwave radiation (DLWR), Atlantic Ocean heat transport (OHT\(_{Atl}\)) and Pacific OHT (OHT\(_{Pac}\)) to summer sea-ice extent over 1970-2060. (b) Corresponding correlation coefficients. Colored circles represent the ensemble means of the five large ensembles, with significant values at the 5\(\%\) level highlighted by black contours (the number of members for each model is indicated in parentheses in the legend). The rates of information transfer and correlation coefficients are first computed for each different member, and then the ensemble mean is computed.

Non-stationarity of causal influences

In the previous sections, we computed the rate of information transfer between variables over the whole 1970-2060 period for each different member, after which we computed the ensemble mean rate of information transfer. However, causal influences of the different potential drivers of summer Arctic sea-ice extent may change over time. That is why we conduct an additional analysis in which we compute the rate of information transfer across all members of the same model for each 10-year period (see Methods). This way, we are able to investigate the temporal evolution of the rate of information transfer from the different drivers to summer sea-ice extent.

We find that the effect of winter sea-ice volume generally decreases until 2060, except for ACCESS-ESM1.5 (Fig. 4 a), while the influence of surface air temperature increases over that time period for three models (CanESM5, MPI-ESM1.2-LR and CESM2; Fig.

Temporal evolution of drivers of summer sea-ice extent. Temporal evolution of the rate of information transfer (absolute value) from (a) winter sea-ice volume (SIV), (b) 2m air temperature, (c) Atlantic Ocean heat transport (OHT), and (d) Pacific OHT to summer sea-ice extent (SIE) for each period of 10 years over 1970–2060 (the starting year is indicated on the x-axis). Temporal evolution of the percentage of (e) years of sea-ice lows and (f) years of rapid sea-ice decline. The five large ensembles are represented by different colors, with error bars indicating the 95\(\%\) confidence level based on bootstrap resampling (the number of members for each model is indicated in parentheses in the legend). In panels (a) and (b), straight lines represent the linear regressions for the five different models; solid (dotted) lines are used when the slope is (not) statistically significant at the 10\(\%\) level.

The impact of Atlantic and Pacific Ocean heat transports remains relatively small over the whole period (Fig. 4 c,d), with the exception of the influence of Atlantic Ocean heat transport in 1970-1990 and 2010-2020 for CanESM5 (Fig. 1 e), and it could explain the increased influence over that period. EC-Earth3 also shows a significant influence of Atlantic Ocean heat transport in the beginning of the period, but with relatively small values of the rate of information transfer (Fig. 4 c). The effect of the four drivers (winter sea-ice volume, surface air temperature, Atlantic and Pacific Ocean heat transports) does not change substantially when looking at five-year periods instead of 10 years, but error bars become larger due to the lower number of years taken into account (Supplementary Fig. S10).

We then replace surface air temperature by net shortwave and downward longwave radiations and repeat the analysis for each 10-year period. The temporal evolution of the net shortwave radiation influence displays a general decrease (except for MPI-ESM1.2-LR; Fig. 5 a). This suggests that, as the sea-ice extent progressively decreases over the twenty-first century, the effect of the ice-albedo feedback is reduced. This could partly explain why the effect of the shortwave radiation is lower compared to the longwave radiation when computed over the whole 1970-2060 period (Fig. 3 a). The influence of the downward longwave radiation generally increases for three models (MPI-ESM1.2-LR, CanESM5 and CESM2), while the trend is close to 0 for ACCESS-ESM1.5 and slightly negative for EC-Earth3 (Fig. 5 b). This makes sense from a physical point of view, as the progressive reduction in sea-ice extent and thickness increases surface air temperature, water vapor and cloudiness, leading to enhanced downward longwave radiation and further melting of sea ice.

Temporal evolution of drivers of summer sea-ice extent, including surface heat fluxes. Temporal evolution of the rate of information transfer (absolute value) from (a) net shortwave radiation (NSWR), (b) downward longwave radiation (DLWR), (c) sum of both NSWR (dark colors) and DLWR (light colors), (d) 2m air temperature, and (e) difference between the sum of NSWR and DLWR and air temperature to summer sea-ice extent (SIE) for each period of 10 years over 1970–2060 (the starting year is indicated on the x-axis). The five large ensembles are represented by different colors, with error bars indicating the 95\(\%\) confidence level based on bootstrap resampling. In panels (a) and (b), straight lines represent the linear regressions for the five different models; solid (dotted) lines are used when the slope is (not) statistically significant at the 10 \(\%\) level.

Overall, for the majority of models and 10-year periods (82 \(\%\) of the case), the influence of downward longwave radiation is larger compared to the one of net shortwave radiation, especially toward the end of the period (Fig. 5 c). This suggests that, as the sea-ice extent and volume decrease over time, the effect of the ice-albedo feedback on summer sea-ice extent becomes weaker, while the effect of downward longwave radiation increases, potentially via a warmer atmosphere, enhanced humidity and increased cloudiness. A notable exception is the dominant influence of net shortwave radiation for CESM2 between 1980 and 2010. This goes in hand with the large reduction in summer sea-ice extent associated with this model (Fig. 1 a). A more detailed analysis looking at different seasons, and potentially different sectors, could be done to better understand the difference between shortwave and longwave radiation influences, and this will be the subject of future work.

We highlight the almost similarity between the summed influence of net shortwave and downward longwave radiations (Fig. 3 a) and the influence of surface air temperature (Fig. 2 a) in the previous section. We show that this similarity holds during most 10-year periods and for all models (compare Fig. 5 c with Fig.

Drivers of sea-ice lows

The recent decline in summer Arctic sea-ice extent has not been monotonic, with large interannual variations (Fig. 1 a). Over the observational period starting in 1979, two sea-ice lows (see Methods for exact definition), presenting a large drop in sea-ice extent compared to the previous years, have been recorded, i.e. 2007 and 2012 (Fig. 63, 64. The 2012 sea-ice low has been attributed to the combined impact of preconditioning and a strong storm 65. It is likely that other sea-ice lows will occur in the future. Furthermore, rapid sea-ice declines (see exact definition in the Methods), featuring at least four years with a strong sea-ice extent reduction, although not present in the observational time period, could happen in the future 33. These events can have profound influences on the global climate, ecosystems and societies, and identifying their potential drivers is thus important.

In the models studied, the percentage of sea-ice lows generally increases over time, although a peak is found around 2030-2050 for EC-Earth3 and around 2030-2040 for CanESM5 (Fig. 4 e). The temporal evolution of the percentage of rapid sea-ice decline years is less clear, with model-dependent variations (Fig.

Next, we compute the rate of information transfer over the whole period but only considering sea-ice lows or rapid sea-ice declines (Fig. 6). Starting with sea-ice lows, as the summer sea-ice extent from CESM2 strongly decreases in the 1990s and the 2000s (Fig. 1 a), the historical trend line of this model is more negative than other models and no sea-ice low is present in CESM2. Also, only 55 sea-ice lows are present in CanESM5 (Table 2), so results from this model need to be taken with caution. These considerations taken apart, we find that the influence of surface air temperature on summer sea-ice extent is larger when only considering sea-ice lows (\(\tau>\) 15 \(\%\); Fig. 6 a) compared to the whole period (\(\tau ~=\)9-15 \(\%\); Fig. 2 a).

Drivers of sea-ice lows and rapid sea-ice declines. (a) Rate of information transfer (absolute value) from winter sea-ice volume (WSIV), 2m air temperature (T\(_{2m}\)), Atlantic Ocean heat transport (OHT\(_{Atl}\)) and Pacific OHT (OHT\(_{Pac}\)) to summer sea-ice extent over 1970-2060, only considering sea-ice lows. (b) Same as (a), only considering years of rapid sea-ice decline. (c) Correlation coefficients corresponding to (a) (sea-ice lows). (d) Correlation coefficients corresponding to (b) (rapid sea-ice declines). Colored circles represent the five large ensembles, with significant values at the 5 \(\%\) level highlighted by black contours. The number of sea-ice lows (SIL) and years of rapid sea-ice decline (RSID) for each model is indicated in parentheses in the legend of panels (c) and (d), respectively.

Other influences (winter sea-ice volume, Atlantic and Pacific Ocean heat transports) remain small and not significant (Fig. 6 a), and are weaker compared to the whole period (Fig. 2 a). In a similar way as for the whole period, if we had only considered the correlation coefficient, we would have ended up with biased conclusions. In particular, the correlation between winter sea-ice volume and summer sea-ice extent is significant for all models, while no causal influence of winter sea-ice volume exists (Fig. 6 c). In addition, EC-Earth3 presents a significant correlation between ocean heat transport (both on the Atlantic and Pacific sides) and summer sea-ice extent, but no causal influence is detected.

When we only consider years of rapid sea-ice decline, the influence of surface air temperature is also larger (\(\tau>\) 15 \(\%\); Fig. 6 b) than the whole period. Again, the effect of other drivers is small and not significant, despite significant correlations (Fig. 2).

Conclusions

By using a relatively novel causal method, the Liang-Kleeman rate of information transfer, we find that surface air temperature is the largest driver of summer sea-ice extent over 1970-2060 according to five different CMIP6 large ensembles (Fig. 2 a). We also show that the previous winter sea-ice volume and the annual mean Atlantic Ocean heat transport have some influence for some models. When replacing the surface air temperature by downward atmospheric surface heat fluxes and repeating the computation, we find that the downward longwave radiation has the largest influence on summer sea-ice extent, with additional impact of the net shortwave radiation (Fig. 3 a). The sum of both downward longwave and net shortwave radiation influences is comparable to the influence of surface air temperature alone for each model; further analysis could be done in the future to better understand the connection between surface air temperature, atmospheric heat fluxes and summer sea-ice extent during different seasons. The temporal evolution of the rate of information transfer from each driver to summer sea-ice extent shows that the winter sea-ice volume influence decreases over time and the air temperature influence increases, in conjunction with an increase in the percentage of sea-ice lows (Fig. 4). In addition, the effect of downward longwave radiation generally increases, while the impact of net shortwave radiation decreases overall (Fig. 5). A final analysis of the causal method only considering sea-ice lows or years of rapid sea-ice decline reveals that the effect of surface air temperature becomes stronger and the other influences are weaker (Fig. 6) compared to the whole period.

The Liang-Kleeman information flow method allows to go beyond classical correlation analyses and to remove spurious dependencies based on correlations 66. Its advantages compared to other causal methods are its derivation from first principles of information entropy and its relative simplicity 40, 41. However, some limitations exist, the main one being the linearity assumption. For some highly nonlinear problems, this causal method may not be accurately computed. In a recent study, Pires et al. 67 developed a nonlinear version of the Liang-Kleeman information flow method and showed that indeed some nonlinear causal links correctly appear in theoretical models presenting strong nonlinearities, which is not the case when using the original linear formulation. Thus, testing this newly developed version on real world-case studies will be the subject of further investigation. In the case of this study, despite the relatively linear relationships between the target variable and the drivers used here, some nonlinearities could appear. The use of the nonlinear version of the causal method could add some insights, but this goes beyond the scope of the current analysis as the nonlinear version of the method is new and needs additional tests on simpler systems 68. Another limitation is that the method needs to be used with approximately stationary time series. We coped with this limitation by detrending the data (removing the ensemble mean; see Methods). However, we acknowledge that even after this detrending, the residuals are not perfectly stationary. Additionally, the method is less robust than causal network algorithms, such as the Peter and Clark momentary conditional independence (PCMCI) 69, when the number of variables taken into account is larger than 7-10 66. In our study, we use six variables maximum, so that we reduce the impact of this problem. Finally, the use of this causal method needs to be accompanied by a good physical understanding of the processes at play.

Our study has focused on Arctic summer sea-ice extent, as this variable has considerably changed over the past decades 4. A similar analysis could be conducted with Arctic winter sea-ice extent, as well as Antarctic sea ice. Some work using the same causal tool has already been carried out with Arctic winter sea-ice extent, but only using EC-Earth3. We showed that winter sea-ice extent is influenced by both the atmosphere (Arctic surface air temperature) and the ocean (total Arctic Ocean heat transport and sea-surface temperature) 25. Another recent study using the Liang-Kleeman information flow method showed the important influence of ocean heat transport on annual mean Barents Sea ice area 49. Thus, results depend on the time of the year (i.e. whether we focus on summer or winter sea ice) and on the region analyzed (total Arctic or a specific Arctic region). It would also be possible to investigate spatial variations of the rate of information transfer, as was done in a previous study 48. Additionally, the definition of rapid sea-ice declines could be extended to take longer periods (e.g. 10 years). Finally, a more detailed analysis of the energy budget could be done, especially looking at different seasons, to check whether the influence of longwave and shortwave radiations changes with the time of the year.

Methods

Climate models

We retrieve monthly mean model outputs from five different large ensembles using the forcing from the Coupled Model Intercomparison Project Phase 6 (CMIP6) 70. Our analysis period is from 1970 (due to the availability of EC-Earth3) to 2060 (summer sea-ice extent becomes close to zero around that year for the majority of models; Fig. 1 a). CMIP6 historical forcing is used from 1970 to 2014, and the Shared Socioeconomic Pathway 3-7.0 (SSP3-7.0) is used from 2015 to 2060. The latter scenario is chosen because it is the only scenario that was run by the CESM2 model. All five models have at least 30 members, which were run with the same external forcing but using different initializations that are detailed in the references mentioned in Table

Both EC-Earth3 and CanESM5 use the same ocean and sea-ice models, although the version of the former model is newer. Beside of that, all other models present different atmosphere and ocean models. The nominal atmospheric resolution varies between 0.7\(^\circ\) (EC-Earth3; \(\sim\) 30 km at 70\(^\circ\)N) and 2.8\(^\circ\) (CanESM5; \(\sim\) 110 km at 70\(^\circ\)N), while the nominal ocean resolution is 1\(^\circ\) for all models (40-50 km at 70\(^\circ\)N), except MPI-ESM1.2-LR (1.5\(^\circ\)). Thus, there is a relatively large variety of atmospheric resolutions, while the ocean resolution is relatively similar among models. More information about the different models can be found in the references that are provided in Table 1.

From these models, we retrieve sea-ice concentration, equivalent sea-ice thickness (sea-ice volume per area; except for CanESM5, which only provides actual sea-ice thickness, from which we derive equivalent sea-ice thickness), surface (2 m) air temperature, ocean potential temperature (all vertical levels), ocean zonal and meridional velocities (all levels), downward and upward shortwave radiations at the surface, downward longwave radiation at the surface, meridional surface wind speed, 300 hPa geopotential height and sea-surface temperature. We compute the net shortwave radiation as the difference between downward and upward shortwave radiations. Both net shortwave and downward longwave radiations are positive downward.

From these model outputs, Arctic sea-ice extent is computed as the areal sum of all ocean grid points north of 40\(^\circ\)N that have at least 15 \(\%\) sea-ice concentration. Arctic sea-ice volume is the product of equivalent sea-ice thickness and grid-cell area summed over the ocean region north of 40\(^\circ\)N. Summer sea-ice extent corresponds to September, while winter sea-ice extent and volume are taken in March. Arctic surface air temperature, atmospheric surface heat fluxes, 300 hPa geopotential height and sea-surface temperature are spatially averaged north of 70\(^\circ\)N. For atmospheric surface heat fluxes (shortwave and longwave radiations), we only compute the spatial average over ocean grid points. The Arctic meridional surface wind speed is taken as the average over a latitudinal band between 68\(^\circ\)N and 72\(^\circ\)N. Atlantic Ocean heat transport is the sum of ocean heat transport at the Barents Sea Opening, Fram Strait and Davis Strait, while Pacific Ocean heat transport corresponds to ocean heat transport at the Bering Strait. Ocean heat transport at each gate is computed via the product of monthly mean ocean temperature and velocity integrated across depth and the corresponding transects, neglecting sub-monthly anomalies. The location of the four gates (Barents Sea Opening, Fram Strait, Davis Strait, Bering Strait) is provided in Supplementary Fig. S11.

Reference products

In order to evaluate the model results, we use monthly mean data from both satellite observations and reanalyses as references products. For each variable, we tried to get the best available dataset, taking the length of the time period into account. For Arctic sea-ice extent, we retrieve the sea-ice index (OSI-420, version 2.2; computed from the 25 km resolution sea-ice concentration product) from the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) Ocean and Sea Ice Satellite Application Facility (OSI SAF) 2 from 1979 to 2023. We also use the Arctic sea-ice volume from the Pan-Arctic Ice-Ocean Modeling and Assimilation System (PIOMAS 51; 22 km resolution) from 1979 to 2023. PIOMAS provides reasonable agreement with satellite observations 83; 5\(^\circ\) grid) is also used for computing the reference Arctic near-surface temperature (spatial average north of 70\(^\circ\)N) from 1970 to 2023. We retrieve ocean potential temperature, zonal and meridional velocities from the European Centre for Medium-Range Weather Forecasts (ECMWF) Ocean Reanalysis System 5 (ORAS5 52; 0.25\(^\circ\) resolution) from 1979 to 2018. Ocean heat transport at the different Arctic gates is computed in a similar way as with model outputs. We also use net shortwave radiation and downward longwave radiations at the surface from the Clouds and the Earth’s Radiant Energy System (CERES 84; 1\(^\circ\) resolution) Edition 4.0 (Ed4) Energy Balanced and Filled (EBAF)-surface data product from 2001 to 2023.

Liang-Kleeman information flow

The rate of information transfer from variable \(x_j\) to variable \(x_i\), noted \(T_{j \rightarrow i}\), is computed in a multivariate framework via 41:

where C is the covariance matrix, d is the number of variables, \(\Delta _{jk}\) are the cofactors of C (\(\Delta _{jk} = (-1)^{j+k} M_{jk}\), where \(M_{jk}\) are the minors), \(C_{k,di}\) is the sample covariance between all \(x_k\) and the Euler forward difference approximation of d\(x_i\)/dt (annual derivatives are used for all variables in our study), \(C_{ij}\) is the sample covariance between \(x_i\) and \(x_j\), and \(C_{ii}\) is the sample variance of \(x_i\). To be able to compare causal influences between each other, we normalize the rate of information transfer as in Liang 41 and express it in percent:

where \(Z_i\) is the normalizer, computed as follows:

where the first term on the right-hand side represents the information flowing from all variables \(x_k\) to the target variable \(x_i\) (including the influence of \(x_i\) on itself), and the last term is the effect of noise (taking stochastic effects into account). When \(\tau _{j \rightarrow i}\) is significantly different from 0, \(x_j\) has an influence on \(x_i\), while if \(\tau _{j \rightarrow i}\) = 0 there is no influence. In our study, we only use the absolute value of \(\tau\), which indicates the strength of the causal influence. A value of \(\left| \tau _{j \rightarrow i}\right|\) = 100 \(\%\) would mean that \(x_j\) causes a maximal impact on \(x_i\). However, this is rarely the case, and usually this value is not much larger than \(\sim\) 30 \(\%\), except for the self-influence (i.e. \(\tau _{i \rightarrow i}\)), which often displays a value larger than \(\sim\) 40-50 \(\%\). Note that the normalization includes a noise term (Eq. ( 3)). Due to the presence of the self-influence and the noise term, we cannot simply infer that \(\left| \tau _{j \rightarrow i}\right|\) = 10 \(\%\) means that \(x_j\) influences \(x_i\) for 10 \(\%\). However, if \(\left| \tau _{j \rightarrow i}\right|\) = 10 \(\%\) and \(\left| \tau _{l \rightarrow i}\right|\) = 5 \(\%\) (where \(x_l\) is a third variable), \(x_j\) is twice more important than \(x_l\) in leading to changes in \(x_i\). Statistical significance of \(\tau _{j \rightarrow i}\) is computed via bootstrap resampling with replacement of all terms included in equations ( 1)-( 3), with 1000 bootstrap realizations, and using a significance level \(\alpha\) = 5 \(\%\). The rate of information transfer \(\tau\) is computed for each bootstrap realization, and the error in \(\tau\), which we refer to as \(\epsilon _{\tau }\), is calculated as the standard deviation across all \(\tau\) bootstrapped values. If the confidence interval \(\tau \pm 1.96 \, \epsilon _{\tau }\) does not contain the zero value, then \(\tau\) is significant at the 5 \(\%\) level; otherwise, it is not significant.

As a first analysis (sections ‘Drivers of summer sea-ice extent’ and ‘Atmospheric surface heat fluxes’), we compute the rate of information transfer \(|\tau |\) (absolute value) from drivers depicted in Fig. 1(winter [March] sea-ice volume, annual mean surface air temperature, annual mean Atlantic Ocean heat transport and annual mean Pacific Ocean heat transport) to our target variable (summer [September] sea-ice extent) for each model member separately. Taking annual means has the advantage to consider not only the previous summer, but also the previous winter and spring months. Note that we detrend all variables before computing \(|\tau |\) by removing the ensemble mean from each member. Due to the almost absence of summer sea ice after 2060, we compute \(|\tau |\) over the period 1970-2060, meaning that we have 91 data points for each member (1 point each year). After that, we compute the ensemble mean rate of information transfer for each different model and check the statistical significance by combining the p-values from the different members (which were previously computed via bootstrap resampling, see previous paragraph) via the Fisher’s method for multiple tests. This analysis is repeated by replacing winter sea-ice volume by winter sea-ice extent to check whether the latter has a larger or lower influence on summer sea-ice extent compared to the former. This analysis is also done by replacing surface air temperature by atmospheric surface heat fluxes (net shortwave and downward longwave radiations). Finally, supplementary analyses with meridional surface wind speed, 300 hPa geopotential height and sea-surface temperature have also been performed. To compute the rate of information transfer on observed and reanalysis products (excluding surface heat fluxes as the temporal coverage is too short), we use the 1979-2018 period. As only one realization is available for observations and reanalyses, we remove the linear trend before applying the causal method.

Second (section ‘Non-stationarity of causal influences’), we compute \(|\tau |\) for each range of 10 years separately across all members of the same model, meaning that we have between 300 and 500 data points for each 10-year range depending on the model. This allows to check the temporal evolution of the rate of information transfer between our drivers and the target variable. No detrending is performed in this case as the time duration is relatively short and includes all members. Statistical significance is computed in the same way as the boostrap method described above (1000 bootstrap realizations and \(\alpha\) = 5 \(\%\)) for each 10-year period. We repeat this analysis for 5-year periods (i.e. between 150 and 250 data points) to check the sensitivity to the time duration. Due to the availability of only one realization in observations and reanalyses, we do not compute the rate of information transfer for those.

Finally (section ‘Drivers of sea-ice lows’), we compute \(|\tau |\) from the same drivers as the first analysis only considering years with large sea-ice reduction. For characterizing such years, we either use sea-ice lows or rapid sea-ice declines. A sea-ice low is an event during which the September Arctic sea-ice extent is below the historical (1970-2014) trend line by more than three standard deviations of the modeled variability and is below the previous year by more than one standard deviation. A rapid sea-ice decline is a period of at least four years for which the trend in the five-year running mean September sea-ice extent is lower than -0.3 million km\(^2\)/year, as defined by Auclair and Tremblay 33. The number of sea-ice lows and years of rapid sea-ice decline per model over 1970-2060 is presented in Table 2. The reason we use two different definitions for years with large sea-ice reduction is because CESM2 does not present any sea-ice low and CanESM5 only has 55 sea-ice lows over all its members and for the period 1970-2060 on the one hand, and MPI-ESM1.2-LR and CanESM5 present a limited number of years of rapid sea-ice decline (29 and 53 years, respectively). Before computing the rate of information transfer, we remove the ensemble mean from each model member, exactly the same way as in the first analysis above. We also compute the temporal derivatives of the detrended data. Then, we compute the rate of information transfer over all sea-ice lows or years of rapid sea-ice decline (period 1970-2060) for each different model. Statistical significance is also computed via the boostrap method described above (1000 bootstrap realizations and \(\alpha\) = 5 \(\%\)).

Data Availability

All CMIP6 70 model outputs (except CESM2) used in this study (historical and SSP3-7.0 simulations) were retrieved from the Earth System Grid Federation (ESGF) nodes: https://esgf-index1.ceda.ac.uk/search/cmip6-ceda/. Table 1 provides the references of the model simulations used. CESM2 74 model outputs were retrieved from the National Center for Atmospheric Research (NCAR) Climate Data Gateway: https://www.earthsystemgrid.org/dataset/ucar.cgd.cesm2le.output.html.

The observed sea-ice extent from OSI SAF 2 can be accessed through the EUMETSAT repository: https://doi.org/10.15770/EUM_SAF_OSI_0022. The PIOMAS 51 sea-ice volume data can be accessed via the Polar Science Center of the University of Washington: http://psc.apl.uw.edu/research/projects/arctic-sea-ice-volume-anomaly. The HadCRUT5 84 near-surface temperature was retrieved from the Climatic Research Unit (University of East Anglia) and Met Office: https://crudata.uea.ac.uk/cru/data//temperature/. The ORAS5 52 ocean temperature and velocity data were accessed via the portal of the Center for Earth System Research and Sustainability (CEN) from the University of Hamburg: https://www.cen.uni-hamburg.de/icdc/data/ocean/easy-init-ocean/ecmwf-or…. The CERES 85 surface heat flux data were retrieved from the NASA CERES Data Products: https://ceres.larc.nasa.gov/data/.

The Python script to compute the Liang-Kleeman rate of information transfer is available on GitHub: https://github.com/Climdyn/Liang_Index_climdyn.

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Acknowledgements

This study is supported by the Belgian Science Policy Office (BELSPO) under the RESIST project (contract no. RT/23/RESIST). David Docquier is funded by BELSPO through the RESIST project. François Massonnet is a F.R.S.-FNRS Research Associate.

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Docquier, D., Massonnet, F., Ragone, F. et al. Drivers of summer Arctic sea-ice extent at interannual time scale in CMIP6 large ensembles revealed by information flow. Sci Rep 14, 24236 (2024). https://doi.org/10.1038/s41598-024-76056-y

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DOI: https://doi.org/10.1038/s41598-024-76056-y