Arctic sea ice plays an important role in modulating the global climate system by influencing the atmospheric and oceanic circulation in polar regions. Moreover, it has a strong impact also on the global economic system through changes in marine and natural resources development. The sea ice extent over the Arctic region has undergone an extraordinary decline during the last decades that can be linked to climate change (Allison et al., 2009; Kay et al., 2011; Notz and Marotzke, 2012; Stroeve and Notz, 2018). The trends in the Arctic sea ice extent are negative for all months, with the largest trend recorded at the end of the melt season in September (Serreze et al., 2007), with an average decline of 12.9 % per decade relative to the long-term mean of 1981–2010 September average (Cavalieri and Parkinson, 2012; Comiso et al., 2017). These negative trends, with their environmental and economic implications as well as its impacts on human society, have led to a rising demand for accurate sea ice predictions at monthly, seasonal and up to decadal timescales, which in turn will be able to address the growing demands from different stakeholders and the scientific community (Meier et al., 2014). As such, an accurate sea ice prediction plays a crucial role for ecosystems, coastal communities, planning for new shipping ports, oil and gas exploration and marine transportation. The 10 lowest September sea ice extents all occurred in the past 10 years, and climate projections indicate that the Arctic Ocean could be ice free (sea ice less than 1×106 km2 for at least 5 consecutive years) in September in the second half of the 21st century (IPCC, 2013). As a result, the ship traffic and Arctic resources extraction have already increased (Pizzolato et al., 2014). For example, the exploitation of shipping via the Northwest Passage or Northeast Passage could reduce the navigational distance between Europe and Asia by ∼40 % compared to the route via the Suez Canal (Schøyen and Bråthen, 2011). The reduction in distance compared to the Suez and/or Panama Canal routes could result in large cost savings due to reduced fuel consumption and an increase in the number of ships (Lassere, 2015). Melia et al. (2016) have shown that by mid-century, the frequency of navigable period will double and the routes across the central Arctic will become available. For example, for a high-emission scenario, they have shown that by the late 21st century trans-Arctic shipping might become commonplace, with the shipping season ranging from 4 to 8 months. Overall, the summertime use of these routes by different vessels (i.e., cargo ship and tanks) has increased (Eguíluz et al., 2016); thus, the need for a proper forecast for the Arctic sea ice conditions has become imperative. Currently, forecasting the open water route through the Arctic basin is accurate within 200 km when the predictions are initialized in July (Melia et al., 2016). As such, early knowledge on the potential opening of the maritime Arctic routes could allow a better management for the shipping companies to optimize (in terms of time and costs) shipping routes between the Atlantic and the Pacific Oceans (Hassol, 2004; Smith and Stephenson, 2013). However, the opening of the Northeast and Northwest passages does not guarantee ice-free transects along the passages at all times and can always include the possibility of drifting ice flows, which pose high risks and potential environmental danger for conventional ships when they are damaged in case of accidents. Pizzolato et al. (2016) have shown that, despite the persistence of low sea ice conditions since 2007, very few shipping activities have been recorded within the northern route of the Northwest Passage. This might be attributed to the multiyear ice concentrations in the Canadian Arctic waters, which strongly influences the shipping activity. Hence, a proper forecast does not imply a danger-free transect as long as the Arctic Ocean is ice covered with thick multiyear ice for its larger parts over the significant times of the year.

Although the evolution of Arctic sea ice physical properties has been extensively studied, the prediction of detrended Arctic sea ice extent, with lead times of 3 months and longer, has not been very promising (Lindsay et al., 2008; Blanchard-Wrigglesworth et al., 2011). From a forecasting point of view, the evolution of autumn Arctic sea ice is closely associated with initial conditions in the previous winter and spring. Different studies have emphasized that some parameters contribute significantly to the improvement of the seasonal sea ice forecast skill at different time lags (Holland and Stroeve, 2011; Lindsay et al., 2008). For example, sea surface temperature and sea ice concentration in spring are highly relevant predictors for the minimum Arctic sea ice extent (Drobot et al., 2006). Some studies suggested that accurate sea ice thickness could increase the forecast skill 2 months ahead (Day et al., 2014; Dirkson et al., 2017). Also, the spring melt pond fraction has been employed to improve the forecast skill of the Arctic minimum sea ice extent (Schröder et al., 2014).

Currently, there are different approaches used to make sea ice forecasts: ice–ocean–atmosphere coupled models, statistical models, best-guess models and mixed models (Stroeve et al., 2014; Hamilton and Stroeve, 2016). From a statistical point of view, Drobot et al. (2006) showed that 46 % of the pan-Arctic minimum sea ice extent would be predictable as early as February based on monthly sea ice concentration, surface albedo, downwelling longwave radiation and surface skin temperature. Lindsay et al. (2008) have shown that their statistical model based on a wide range of predictors (e.g., atmospheric circulation indices, sea ice extent and sea ice concentration, ocean temperature at different levels) exhibited a greater skill in predicting the September sea ice extent (SSIE) than those by Drobot et al. (2006). The forecasts based on the state-of-the-art coupled atmosphere–ocean sea ice models (Chevallier et al., 2013; Sigmond et al., 2013) do not show better results when compared with the statistical models (Kapsch et al., 2014; Schröder et al., 2014; Zhan and Davies, 2017). These caveats indicate that our understanding regarding the controlling factors of Arctic sea ice may still be insufficient. Overall, skillful forecasts extend only 2 to 5 months ahead, for the summer months (Stroeve et al., 2015; Schröder et al., 2014), regardless of the type of the model used for the forecast (dynamical or statistical). The results and error margins based on these different approaches have highlighted how difficult it is to make skillful prediction for the SSIE. This is particular true for the years with extreme low September sea ice concentrations (e.g., 2012 or 2007), with both the dynamical and the statistical models showing similar limitations (Stroeve et al., 2014, 2015; Schröder et al., 2014; Hamilton and Stroeve, 2016). Stroeve et al. (2014) have shown that seasonal predictions of the SSIE are most accurate in years when the sea ice extent is near the long-term trend, but skillful sea ice extent prediction appears challenging in years when the weather plays a larger role (Hamilton and Stroeve, 2016).

In order to improve the monthly/seasonal prediction skill of the sea ice extent, one possibility would be to identify stable predictors (the correlation coefficient between the predictor and the predictand does not change in time) and to develop a statistical forecast model based on these predictors. Following this idea, here we analyze the oceanic and atmospheric conditions associated with the SSIE in order to identify potential predictors based on a simple statistical methodology and place them in a longer temporal context. Our statistical model takes into account different atmospheric and oceanic variables following the approach in Ionita et al. (2008, 2014, 2018) and Ionita (2017). These parameters are sea level pressure (SLP), air temperature (TT), precipitable water content (PWC), surface zonal wind (USURF), surface meridional wind (VSURF), the ocean heat content integrated over the first 700 m (OHC), sea surface temperature (SST) and water temperature integrated over the first 100 m (OT100), and they are used in order to calculate an estimate of SSIE. The paper is structured as follows: the data and methods used in this study are presented in Sect. 2, while the main results of our analysis are shown in Sect. 3. The discussion and concluding remarks are presented in Sects. 4 and 5.

The results of this study demonstrate that statistically based models are able to predict SSIE with high skill, if the accurate drivers and their regional localizations (herein stable regions) are identified via various statistical techniques. In this paper, our analysis was focused on a single month (September), but the same methodology has been be successfully applied also for other months/seasons and also for the Antarctic region (Ionita et al., 2018).

Our results highlight the potential for skillful prediction of SSIE, both at pan-Arctic level as well as for ESS, based on large-scale drivers from stable regions. The ocean drivers (OHC, TT100 and SST) from the identified stable regions are strongly related to the Atlantic inflow or to the SST variability over regions strongly influenced by decadal modes of variability (e.g., Pacific Decadal Oscillation – PDO – in the central and north Pacific) to multidecadal modes of variability (e.g., Atlantic Multidecadal Oscillation – AMO – in the Atlantic Ocean region). The Atlantic inflow, AMO and PDO play a significant role in driving the Arctic sea ice variability (Polyakov et al., 2017; Miles et al., 2014; Ionita et al., 2016; Screen and Francis, 2016). For example, the North Atlantic might act as a source for the OHC anomaly identified over the Kara Sea, Laptev Sea and ESS (Figs. 1 and 5), thus contributing to the skill of our forecast. The OHC anomalies form the North Atlantic flow into the Arctic basin, via advection, and affect the sea ice distribution (Polyakov et al., 2017; Ono et al., 2018). In a recent study, Yu et al. (2017) have shown that the leading mode of variability of global sea ice concentration is positively correlated with the AMO and negatively correlated with the PDO. Furthermore, two-thirds of the total global sea ice trend can be explained by a combination of these two modes of variability. Superimposed on the interannual variability, the temperature and salinity of the Atlantic inflows to the Arctic Ocean show also pronounced decadal to multidecadal variability (Zhang, 2015). This aligns with the concept of different previous studies, which suggest that the decreasing trend in the Arctic sea ice is partially driven by AMO (Park and Latif, 2008; Lindsay et al., 2005; Ding et al., 2014; Yu et al., 2017). Moreover, starting at the beginning of 1990s, the AMO switched to a positive phase, at the same time when the Arctic sea ice extent started its abrupt decline. Thus, in this study, we have tested previous years' AMO index as a potential driver of the Arctic sea ice extent.

The stability maps based on the predictors related to the atmospheric variables (Figs. 1–3) show significant and stable correlations with regions restricted to the Arctic basin, indicating a very regional connection between the September sea ice variability and large-scale atmospheric circulation. The state of the Arctic SSIE depends both on the state of the ice in spring and on the atmospheric condition during summer (Ding et al., 2017). In this respect, the precipitable water content and air temperature in spring and early summer were found to show significant predictive skill for the SSIE both at pan-Arctic as well as regional levels. This is also in agreement with previous studies (Kapsch et al., 2013, 2014) which have shown a significantly increased cloudiness and humidity over the Arctic region in spring, thus accelerating the sea ice retreat in the upcoming summer, via enhanced longwave radiation.

Overall, such a methodology can be valuable also for the modeling community. If the coupled models, used for forecasting purposes, face problems to simulate the ocean and/or the climate background over the areas that play a significant role in driving the SSIE variability (stable regions), one expects a relatively small forecast skill. The opposite case is also valid: a good representation of the key regions that drive SSIE could imply a good forecast skill. For example, Parkinson et al. (2006) determined that many climate models tend to simulate more winter sea ice in the Barents Sea compared to observations. One hypothesis for this overestimation is that the models underestimate the heat content in the Atlantic basin (which has proven to be one of the main contributors for a skillful prediction for SSIE in our model). By using a simple and computationally inexpensive statistical approach, one can anticipate more than 80 % of SSIE up to 4 months in advance, based on the antecedent atmospheric and oceanic conditions over stable regions. Moreover, our statistical model is able to properly reproduce the years with extreme low/high sea ice extent, both at pan-Arctic level as well as at regional scale (e.g., 2007 and 2012 – low SSIE, and 1996 – high SSIE; see Figs. 4 and 8). The predictability of these extreme years poses big challenges for the sea ice prediction community (Hamilton and Stroeve, 2016).

For example, one of the most unpredictable years was 2012. Most of the models (statistical and dynamical) were unable to properly forecast the extremely low value of the sea ice extent in September 2012 (Stroeve et al., 2014). Overall, the statistical predictions came closer to the unexpected low sea ice extent in September 2012 than the dynamical-based predictions. In this respect, our statistical model was able to capture the overall decline in the SSIE and we forecasted the lowest sea ice extent since the observational period (Fig. 4). Nevertheless, in terms of amplitude, our forecast has underestimated the observed values (Fig. 4). One of the reasons for this underestimation could come from the fact that in August 2012 a strong storm prevailed over the Arctic basin, which triggered extreme sea ice melt by bringing heat and moisture from the south towards the central Arctic (Parkinson and Comiso, 2013). Another potential trigger of the extreme sea ice melt in 2012 might be a combination of extremely thin sea ice pack and increased upward ocean heat transport, which created conditions that made the sea ice particularly vulnerable to storms (Zhang et al., 2013). The storm in August 2012 allowed a large amount of oceanic heat to be mixed up to the surface, thus enhancing the sea ice melt. Because the atmosphere is mostly unpredictable beyond 1 or 2 weeks, we were not able to accurately predict, in terms of amplitude, the sea ice conditions that developed because of the Arctic storm in August 2012.

Another challenge for the sea ice community was the predictability of SSIE in 2013. Sea ice extent in September 2013 was characterized by a revival compared to the low values recorded in September 2012 (SSIE in 2013 was 1.69 million km2 above the record minimum extent in September 2012). Most of the models, involved in the Sea Ice Prediction Network (SIPN), have underestimated the September 2013 sea ice extent, despite the fact that this was not an extreme low sea ice year like 2012. The observed September 2013 sea ice extent lied outside the intervals given with 13 out of 16 predictions, but the modeling methods performed better than the statistical ones (Stroeve et al., 2014). For September 2013, our statistical model performed almost perfectly, giving one of the best predictions (in terms of amplitude) over the validation period. The revival of the sea ice extent in 2013 was due to a combination of different factors: a colder summer over the Arctic basin, compared to 2012, and no storms prevailing throughout the summer months; less winter clouds in January–February 2013, which resulted in more strongly negative surface radiation budget (Liu and Key, 2014); later melt onset, intermittent freezing events and an earlier fall freeze-up (Wang et al., 2016), among others. Summer 2013 was characterized by an unusual low pressure system over much of the Arctic Ocean, which acted as a limiting factor for the heat transport from the south. Both the SLP and air temperature over the Arctic basin were part of our final predictors for the sea ice extent in 2013 (Figs. 2 and 3). As such, the accurate predictions based on our statistical model for 2013 may arise from the fact that no extreme weather events were occurring throughout the summer months over the Arctic region. In addition, we had persistent negative temperature anomalies and a long-lasting low pressure system prevailing in June and July over the Arctic basin, variables which were used in our forecast model. A high/low skill in the predictability of extreme September sea ice can be the result of extreme spring preconditioning (e.g., very low ice thickness) and/or the results of extremely anomalous summer weather systems, independent of the spring preconditioning. In observation, not all extremes are the results of the same forcing, thus implying that different extreme events will have a different level of predictability.

In this study, we have developed a statistical method based on different oceanic and atmospheric variables to estimate the monthly signal and variability of the Arctic sea ice extent. Based on stepwise multiregression analysis, optimal predictors are identified in terms of stability maps to forecast SSIE on a pan-Arctic or regional scale. We have demonstrated that our well-established statistical approach can be used as a promising tool to improve the skill of sea ice extent prediction. In the future, the same methodology will be applied to test the potential predictability, up to 2 years ahead, by taking into account variables with long-term memory (e.g., heat content and water temperature integrated over different depths) for the whole Arctic. For other regions prone to extreme decrease in the sea ice extent (e.g., Chukchi Sea, Beaufort Sea, Barents Sea), as well as for Antarctica, the method will also be adopted. Finally, since the concept can be used as an early warning system for September sea ice extent, both at pan-Arctic level as well as regionally, the potential environmental and economic benefits can be very high.