3.1 Trends in ice advance and retreat date in observations and models Over 1980–2015, the ice-free season duration has increased by 9.8±12.1 days decade−1, with nearly equal contributions of earlier ice retreat ( - 4.8 ± 7.7 days decade−1) and later ice advance (4.9±5.8 days decade−1, median based on satellite observation, updated figures; see Table S1). Variability is high however. Significant trends in both d r and d a at the 95 % confidence level are found over a relatively small fraction (22 %) of the seasonal ice zone (Fig. 3), independently of the details of the computation (Table S1). The patterns of changes are regionally contrasted, and Chukchi Sea is the most notable exception to the rule, where later ice advance clearly dominates changes in the ice-free season (Serreze et al., 2016, Fig. 3). Download Trends simulated by the mean of selected CMIP5 models are comparable with observations, in terms of ice retreat date ( - 4.4 ± 3.5 days decade−1), ice advance date (5.9±3.3 days decade−1) and ice-free season duration (10.3±6.3 days decade−1, Fig. 3). Individual models show larger errors (Fig. S4 to compare with Fig. 3), to be related notably with mean state issues or the spread in the strength of strong oceanic currents, in the North Atlantic and the North Pacific. One common location where trends are underestimated is the North Atlantic region, in particular the Barents Sea, which arguably reflects a weak meridional oceanic heat supply (Serreze et al., 2016). One should be reminded that as reality is a single realisation of internal climate variability (Notz, 2015), a model–observation comparison of this kind is intrinsically limited. This could be of particular relevance in the Barents Sea, which is subject to internally generated decadal-scale variations driven by ocean heat transport anomalies (Yeager et al., 2015).

3.2 Earlier sea ice retreat implies later ice advance In terms of mean state and contemporary trends, models seem realistic enough for an analysis of changes at pan-Arctic scales but might be less meaningful at regional scales. We first study the contemporary link between earlier retreat and ice advance by looking at the sign of R a∕r values in contemporary observations and models. Because R a / r long is a ratio of significant trends, and because all models have regional differences as to where trends are significant, we base our analysis on individual models. Based on observations (Fig. 4), we find positive values of R a / r long in more than 99 % of grid points in the studied zone, provided that computations are restricted where trends on ice retreat and advance dates are significant at a 95 % level (N=5257). In a warming climate, positive R a / r long values mean concomitant and significant trends towards earlier retreat and later advance, whereas missing values reflect either that the trends are not significant or that the point is out of the seasonal ice zone. R a / r short (Fig. 6) is generally smaller (0.21±0.27) than R a / r long (0.71±0.42, 95 % confidence level), and also positive in most pixels (87 % of 23 475 pixels). Download CMIP5 models are consistent with the robust link between earlier ice retreat and later advance dates found in observations (Stammerjohn et al., 2012; Stroeve et al., 2016). More generally, we find a robust link between earlier retreat and later advance in all cases: both R a∕r values are virtually always positive for short- and long-term computations, from observations and models (Figs. 4, 5) over the three analysed periods (1980–2015 for observations and models, 2015–2050 and 2050–2085 for models only) and regardless of internal variability (Figs. S5 and S6). This finding expands previous findings from satellite observations using detrended time series (Stammerjohn et al., 2012; Serreze et al., 2016; Stern and Laidre, 2016), in particular the clear linear correlation found between detrended ice retreat and ice advance dates (Stroeve et al., 2016). Following these authors, we attribute the strong earlier retreat and later ice advance relationship as a manifestation of the ice–albedo feedback: earlier ice retreat leads to an extra absorption of heat by the upper ocean. This heat must be released back to the atmosphere before the ice can start freezing again, leading to later ice advance. Such a mechanism, also supported by satellite SST analysis in the ice-free season (Steele et al., 2008; Steele and Dickinson, 2016), explains the sign of the changes in ice advance date. However, it does not explain the relatively larger magnitude of the trends in ice advance date compared with trends in ice retreat date, studied in the next section. Download

3.3 Increasingly late ice advance dominates future changes in open-water season We now focus on the respective contribution of changes in retreat and ice advance dates to the increasingly long open-water season by analysing the magnitude of R a / r long . Contemporary values of R a / r long match between model and observations but not spatially (Fig. 4). Over 1980–2015 the simulated R a / r long (CMIP5 mean) is slightly higher (1.1±0.7) than the observational value (0.7±0.4). Since none of the models position the sea ice edge correctly everywhere, it is not surprising that the spatial distribution and the modal R a / r long differ among models and between models and observations. The fact that, by definition, satellite data only sample one realisation of internal variability could contribute to the discrepancy as well. In support of these two arguments, the forced-atmosphere ISPL-CM simulation better simulates the spatial distribution of R a / r long (see Fig. S7), which underlines the role of mean state errors. As far as future changes are concerned, all models show a qualitatively similar evolution (Figs. 1 and S5). Projected changes in ice retreat and ice advance dates start by approximately 2000 and continue at a nearly constant pace from 2040 until 2200. By 2040, the trend in ice advance date typically becomes larger than the trend in ice retreat date, as indicated by the corresponding mean R a / r long = 1.8 ± 0.4 over 2000–2200 (Table 1). To further understand these contrasting trends between ice retreat and ice advance dates, we mapped R a / r long , over 2015–2050 and 2050–2085. We find that, in the course of the 21st century, trends in retreat and ice advance date become significant over increasingly wide regions. The overall R a / r long value increases, as illustrated in Fig. 4. This behaviour is found independent of the considered model and of the internal variability (Figs. S5 and S6). This finding expands the recent analyses of the CESM Large Ensemble project (Barnhart et al., 2016) and of Alaskan Arctic sea ice in CMIP5 models, finding faster ice coverage decrease in autumn than in spring (Wang and Overland, 2015). Both studies propose that the extra heat uptake in the surface ocean due to an increased open-water season as a potential explanation. As suggested earlier, this indeed explains why R a / r long would be positive but does not explain the amplified delay in ice advance date, that is, why R a / r long would be >1. We are now addressing this question.

3.4 A thermodynamic mechanism for an amplified delay in ice advance date The reason why R a / r long becomes >1 by 2040 is related to the asymmetric response of ice–ocean thermodynamics to warming: the upper ocean absorbs solar radiation about twice as efficiently as it can release heat right before ice advance. That summer feedback processes dominate is enabled by a relatively weak winter feedback (between later ice advance and earlier retreat the next year). To come to this statement, we would need diagnostics unavailable in CMIP5, in particular a daily description of the surface energy budget. This is why we used a 1-D thermodynamic model of sea ice growth and melt in relation with the upper-ocean energy budget (Semtner, 1976) to study the idealised thermodynamic response of seasonal ice to a radiative forcing perturbation. Without any particular tuning, the 1-D model simulations feature an evolution that is similar to the long-term behaviour of CMIP5 models (Fig. 1b), with trends in ice advance date (8.2 days decade−1) of larger absolute magnitude than trends in retreat date (−4.7 days decade−1), giving a corresponding value of R a / r long = 1.9 . All figures fall within the CMIP5 envelope (Table 1). As explained above, the seasonal relationships between ice advance and retreat dates are underpinned by atmosphere–ice–ocean feedbacks. The non-radiative feedback framework of Goosse et al. (2018; see Appendix A for details) clarifies the study of these relationships. Changes in dates of ice retreat (Δd r ) and advance (Δd a ) in response to a radiative forcing perturbation are split into reference and feedback response terms: (1) Δ d r = Δ d r ref - λ w Δ d a , Δ d a = Δ d a ref - λ s Δ d r . The sign convention for the feedback terms is such that the link between earlier retreat (Δd r <0) and later advance (Δd a >0) gives positive feedback factors. The feedback response refers to the change in d r (resp. d a ) that can solely be attributed to the change in d a (resp. d r ). It is expressed using a feedback factor λ w (resp. λ s ) related to winter (resp. summer) feedback processes. The reference response Δ d r ref (resp. Δ d a ref ) is that of a virtual system in which the feedback would be absent. Expressions for the reference and feedback response terms, as well as for feedback factors, stem from physical analysis, detailed in Appendix A. According to this analysis, feedbacks between the dates of retreat and advance dominate the thermodynamic response of ice seasonality (Fig. 5): the reference response to the applied perturbation of 0.1 W m−2 yr−1 is −0.2 day yr−1 of earlier retreat and 0.1 d yr−1 of later advance. Ice growth and melt processes generate a relatively weak winter amplifying feedback of ice advance date onto ice retreat date: a shorter growth season implies thinner ice, which subsequently melts away faster. The winter feedback factor is (see Appendix A for derivation) (2) λ w = 1 2 ⋅ d r - d h d h - d a , where d h is the date of maximum ice thickness, and is solely a function of the ice growth and melt seasonal parameters. λ w has a rather stable value of 0.31±0.04 over the 127 years of simulated seasonal ice. This value of λ w indicates a feedback response in ice retreat date of about one-third of the change towards later ice advance the previous autumn. λ w is <1 for two reasons. First the melt season is shorter than the growth season (Perovich et al., 2003); hence changes in ice advance date translate into weaker changes in ice retreat date. Second, the ice growth rate is larger for thin than for thick ice (Maykut, 1986); hence the maximum winter ice thickness does not decrease due to later advance as much as if the growth rate was constant. Energetics of the summer ice-free ocean generate a summer amplifying feedback of ice retreat date onto ice advance date, much stronger than the winter feedback. The summer feedback factor is (see Appendix A for derivation) (3) λ s = - Q + Q - , where 〈Q + 〉 and 〈Q − 〉 are the average net positive (negative) atmosphere-to-ocean heat fluxes during the ice-free period. The 1-D model diagnostics give an average value of 1.63±0.18 for λ s , meaning that earlier retreat implies a feedback delay in ice advance of ∼1.6 times the initial change in ice retreat date. Physically, the strength of the summer feedback is in direct relation with the ice-free upper-ocean energy budget and the evolution of SST. 〈Q + 〉 mostly corresponds to net solar flux, typically 150 W m−2, and is typically larger than 〈Q − 〉, which corresponds to the net non-solar, mostly long-wave heat flux, at freezing temperatures, typically 75–150 W m−2 (see Appendix B). Hence, after ice retreat, the SST rapidly increases due to solar absorption into the mixed layer and then decreases much slower until freezing, due to non-solar ocean-to-atmosphere fluxes (Fig. 7a), an evolution that is similar to a recent satellite-based analysis (Steele and Dickinson, 2016). In other words, the energy excess associated with later retreat, stored into the surface ocean, takes extra time to be released before ice advance. Download Download In practise, keeping only the dominant term, R a / r long (the seasonality of the system) reduces to the summer feedback factor: (4) R a / r long ≈ λ s . R a / r long appears to vary little among CMIP5 models and even with the 1-D model. Why this could be the case is because the winter and summer feedback factors are controlled by very basic physical processes of the Arctic ice–ocean–climate system and therefore feature relatively low uncertainty levels. Celestial mechanics, ubiquitous clouds and near-freezing temperatures provide strong constraints on the surface radiation balance and hence on the summer feedback factor, that all models likely capture. All models also include the growth and melt season asymmetry and the growth–thickness relationship (see Massonnet et al., 2018) at the source of the relatively weak winter feedback. In IPSL-CM5A-LR, the sole model for which we could retrieve daily SST (Fig. 7b), the evolution of the summer SST in seasonally ice-free regions features a rapid initial increase followed by slow decrease, an indication that the mechanism we propose is sensible.