Abstract

The large decrease in Arctic sea ice in recent years has triggered a strong interest in Arctic sea ice predictions on seasonal-to-decadal time scales. Hence, it is important to understand physical processes that provide enhanced predictability beyond persistence of sea ice anomalies. This study analyzes the natural variability of Arctic sea ice from an energy budget perspective, using 15 climate models from phase 5 of CMIP (CMIP5), and compares these results to reanalysis data. The authors quantify the persistence of sea ice anomalies and the cross correlation with the surface and top-of-atmosphere energy budget components. The Arctic energy balance components primarily indicate the important role of the seasonal ice–albedo feedback, through which sea ice anomalies in the melt season reemerge in the growth season. This is a robust anomaly reemergence mechanism among all 15 climate models. The role of the ocean lies mainly in storing heat content anomalies in spring and releasing them in autumn. Ocean heat flux variations play only a minor role. Confirming a previous (observational) study, the authors demonstrate that there is no direct atmospheric response of clouds to spring sea ice anomalies, but a delayed response is evident in autumn. Hence, there is no cloud–ice feedback in late spring and summer, but there is a cloud–ice feedback in autumn, which strengthens the ice–albedo feedback. Anomalies in insolation are positively correlated with sea ice variability. This is primarily a result of reduced multiple reflection of insolation due to an albedo decrease. This effect counteracts the ice-albedo effect up to 50%. ERA-Interim and Ocean Reanalysis System 4 (ORAS4) confirm the main findings from the climate models.

1. Introduction

The Arctic sea ice has shown a rapid decrease over the last few decades. An ice-free Arctic summer is already likely within the first half of this century (Overland and Wang 2013). With the sea ice in the Arctic region retreating, the economic activities in the region are expanding and diversifying. More shipping lanes are becoming ice free, and natural resources will become better accessible (Stephenson et al. 2013). These increasing economic activities offer opportunities, but also threats, to the region. To be able to reduce the stakes at play and improve the operational planning for offshore activities in the Arctic region, improvements on forecasts of Arctic sea ice on seasonal-to-multiyear scales are needed.

Arctic sea ice forecasts for seasonal-to-annual time scales are often based on statistical methods (e.g., Lindsay et al. 2008; Kapsch et al. 2013). With the fast-changing Arctic climate, however, the historical records on which the statistical relations are based are not necessarily valid for the current climate state. Another method currently employed is the use of initialized simulations with fully coupled (atmosphere and ocean) climate models (e.g., Sigmond et al. 2013; Chevallier et al. 2013; Wang et al. 2013). However, correct initializations are still hampered by a lack of robust sea ice–thickness observations and by model error (Holtslag et al. 2013). These simulations show increased forecast skill compared to anomaly persistence models (Sigmond et al. 2013). It is noteworthy, however, that even though the dynamical model forecast skill is higher than the relative simple anomaly persistence model, an important source of the dynamical forecast skill on seasonal-to-annual time scales originates from persistence of anomalies (Sigmond et al. 2013). It is therefore important to understand the physical mechanisms behind these processes.

Multiple studies (e.g., Bitz et al. 2005; Holland et al. 2011; Blanchard-Wrigglesworth et al. 2011, hereafter BW11; Chevallier and Salas-Mélia 2012) have investigated the inherent predictability of Arctic sea ice. These studies show a typical decorrelation time scale of 2–5 months, with higher persistence during summer and winter and lower persistence in between. Furthermore, a reemergence of sea ice anomalies is often observed in the ice-growth season that originates from the ice-melt season. The original anomaly in spring yields a (persistent) sea surface temperature (SST) anomaly because of reduced or enhanced cumulative heating, which again results in a sea ice anomaly in the growth season (BW11; Day et al. 2014, hereafter DA14). Another mechanism that offers predictability is the maintenance of the sea ice edge in winter because of the convergence of heat transported by ocean currents (Bitz et al. 2005). The analysis of Bitz et al. (2005) suggests that absorption of shortwave radiation mainly determines the rate of ice melting in the marginal ice zone but that the ice edge is primarily determined by the strength and region of ocean heat flux convergence.

All these processes can lead to enhanced predictability on seasonal-to-annual time scales and can bridge the gap between short-term predictability originating from correct initialization and longer term predictability originating from external forcing (BW11; van Oldenborgh et al. 2012). In this study, we aim for a better understanding of the mechanisms that offer predictability on seasonal-to-annual time scales. Therefore, we perform a process-based evaluation of the Arctic sea ice characteristics by looking at the monthly-to-annual Arctic variability from an energy balance perspective. Herein we study lead–lag relations between the different components of the energy balance and the Arctic sea ice properties, both locally and averaged over the Arctic region, and identify the physical processes that provide the inherent predictability found in Arctic sea ice. In this way, we also test the robustness of the findings of BW11 and DA14 by extending their analysis with a CMIP5 multimodel analysis.

2. Data and methods

Our analysis is based on a multimodel ensemble of atmosphere–ocean general circulation models (AOGCMs) and Earth system models (ESMs; see Table 1), which are all part of phase 5 of the Coupled Model Intercomparison Project (CMIP5) dataset (Taylor et al. 2012). The selection criteria were data availability, in particular ocean data for constructing the energy balance. From this dataset we selected the control simulations, which have fixed atmospheric constituents equal to the values from the preindustrial era (1850). The control simulations allow us to focus on the role of natural variability in Arctic sea ice, as it lacks a long-term trend in the data because of changing external forcing. It must be noted here that the Arctic sea ice in the preindustrial simulations might not be representative for the current sea ice conditions. The thinning of the Arctic sea ice over the last decades (Serreze et al. 2007) has led to an increase of relatively thin first-year ice, which is much more susceptible to (chaotic) weather forcings, resulting in reduced persistence and thus predictability (Holland et al. 2011). Therefore, we will also perform part of the analysis with representative concentration pathway 4.5 (RCP4.5) climate simulations, in which the radiative forcing increases with 4.5 W m−2 in 2100 (relative to preindustrial forcing), to see if some of the findings presented here are also valid in the lower sea ice area (SIA) regimes.

Table 1.

List of selected CMIP5 climate models. The models denoted with an asterisk are not included in the calculations of the cloud radiative forcing because clear-sky radiation components were not available. (Expansions of model name acronyms are available at http://www.ametsoc.org/PubsAcronymList.)

List of selected CMIP5 climate models. The models denoted with an asterisk are not included in the calculations of the cloud radiative forcing because clear-sky radiation components were not available. (Expansions of model name acronyms are available at http://www.ametsoc.org/PubsAcronymList.)
List of selected CMIP5 climate models. The models denoted with an asterisk are not included in the calculations of the cloud radiative forcing because clear-sky radiation components were not available. (Expansions of model name acronyms are available at http://www.ametsoc.org/PubsAcronymList.)

From the CMIP5 monthly dataset we select only the Arctic region, here defined as north of 65°N, and 200 years of simulation time for each model. This latitude does not cover the complete Arctic region, but it allows us to more accurately close the energy balance over a region. Figure 1 illustrates the different components of the energy balance that are computed. We focus on both atmospheric and oceanic components. The atmospheric energy balance can be formulated by

 
formula

where FTOA represents the net radiation at the top of the atmosphere (TOA), F65N–A is the moist static energy (MSE) flux across 65°N from the surface to the TOA, FSURFACE is the sum of net radiation and turbulent fluxes at the surface, and dMSE/dt is the change in moist static energy content over time. The latter is calculated by

 
formula

where g is the gravitational acceleration, psfc is the surface pressure, cp is the specific heat for air at constant pressure, T is the temperature in kelvin, L is the latent heat of evaporation, q is the specific humidity, and Φs is the surface geopotential. By subtracting the values of two subsequent months and dividing by the time step (1 month) we determine the change of MSE over time. The energy flux at 65°N is assumed to be the residual of the other terms in Eq. (1).

Fig. 1.

Conceptual view of Arctic energy balance components. The H indicates the sensible heat flux and the term LυE is the latent heat flux (refer to the text for the definition of the remaining terms/variables).

Fig. 1.

Conceptual view of Arctic energy balance components. The H indicates the sensible heat flux and the term LυE is the latent heat flux (refer to the text for the definition of the remaining terms/variables).

The oceanic energy balance can be approximated in a similar way:

 
formula

where F65N–O is the meridional ocean heat flux at 65°N, FSURFACE is the heat flux into the ocean from the surface, and dQ/dt is the change in ocean heat content (OHC) over time, which is calculated by

 
formula

where ρ is the density, cp the specific heat of water, T the temperature of the ocean in kelvin, and zseabed and zsfc are respectively the height of the seabed and of the ocean surface. Again, F65N–O is the residual of the other terms in Eq. (3). We analyze the relation of the different components of the atmospheric and ocean energy balance with the (lagged) Arctic sea ice, both locally and averaged over the Arctic region.

The anomalies for the statistical calculations are computed by 1) removing a linear trend to correct for any model drift, 2) removing the average seasonal cycle, and 3) subtracting an 11-yr running mean. This last step allows for a better evaluation of the seasonal-to-annual predictability, as otherwise the signal is dominated by low-frequency climate variability, as demonstrated by DA14. Note that the latter is not the focus of this analysis. The linear trend and 11-yr running mean were computed and subtracted for the 12 months individually, to avoid introducing an artificial seasonal signal when the anomalies are not evenly distributed over the season.

Model results will be compared to observational and reanalysis products. For Arctic sea ice observations we use the Bootstrap sea ice concentrations from NSIDC (Comiso 2000). The reanalysis products are ERA-Interim (Dee et al. 2011) and Ocean Reanalysis System 4 (ORAS4; Balmaseda et al. 2013). These reanalysis products should be used carefully in data-sparse regions such as the Arctic. Lindsay et al. (2014) evaluated seven different reanalysis products that cover the Arctic, and ERA-Interim was one of the three reanalysis products that stood out as being more consistent with observations. Zygmuntowska et al. (2012) did however find a strong dry bias in summer. From ORAS4 we do not use the first two decades, as these have large uncertainties (Balmaseda et al. 2013). For the comparison we use all five ensemble members of ORAS4 but present only the ensemble mean. For ERA-Interim, ORAS4, and NSIDC Arctic sea ice observations we use the years 1979–2013.

The (lagged) relations are quantified by calculating the correlation coefficient between different physical quantities. The multimodel mean is computed by combining the individual correlation scores through Fisher’s z transformation. The associated p values are combined using Fisher’s combined probability test. For the model results and the observations, significance levels of 99% and 95%, respectively, were chosen. Note that, because of the large amount of data (i.e., a large sample size), correlation scores of lower than 0.1 are already significant. The average decorrelation time scale per month, here defined as the e-folding time scale of SIA, was calculated by fitting an exponential decaying function to the first months where the correlation coefficient is higher than 1/e. The climate models, NSIDC observations, and reanalyses from ERA-Interim and ORAS4 all undergo the same filtering procedure.

The total Arctic sea ice can be quantified by the total extent, area, and volume. Extent is defined as the sum of gridcell areas with more than 15% sea ice coverage, and area as the sum of the sea ice–covered part of the grid cells. In this research we will focus on the sea ice area instead of the sea ice extent, as the area is a more relevant variable from an energetic and end-user viewpoint. Additionally, BW11 and DA14 found comparable results in lead–lag relations between sea ice area and extent. Sea ice volume is also an important variable, as shown by Chevallier and Salas-Mélia (2012), but mainly as a predictor for sea ice area anomalies.

A first analysis revealed that the Arctic integrated F65N–A, dMSE/dt, and the turbulent surface fluxes showed no clear relation with sea ice variability. Therefore, we have excluded these results from section 3.

3. Results

In this section we present the lagged correlation of sea ice and the cross correlation between energy balance components and lagged sea ice.

a. Persistence

First we will follow the analysis of BW11 and determine the lagged correlation of sea ice to investigate the decorrelation time scale and possible reemergence of anomalies in sea ice. Figure 2a shows the multimodel mean lagged correlation of sea ice. From this figure we can identify some distinct patterns, which we will go through one by one. First, a typical decorrelation time scale of 2–5 months is evident (indicated in Fig. 2a by a 1), with the higher values in late winter and late summer and lower values in spring and autumn. Second, a reemergence limb is visible (indicated by a 2) during autumn, which is related to SST anomalies originating from SIA anomalies in the melt season and its prolonged/shortened shortwave cumulative heating (i.e., a sea ice–albedo effect). Hence, we can identify pairs of months in the reemergence of anomalies coupled through the location of the sea ice edge (May and December, June and November, etc.) (BW11). Furthermore, a relative weak winter-to-winter (January–March) reemergence is visible (indicated by a 3). Bitz el al. (2005) relate this winter-to-winter reemergence to regions of ocean heat flux convergence anomalies, which determine the winter sea ice edge. Because of the relatively long time scales of these processes, this offers a winter-to-winter predictability. From this figure, however, it is difficult to isolate the winter-to-winter reemergence from the sea ice–albedo effect. Last, a weak growth-to-melt reemergence is found (indicated by a 4), although this is mainly visible as enhanced persistence. BW11 relate this reemergence to sea ice–thickness anomalies, which originate from a later (or earlier) freeze up resulting in less time for the ice to grow thicker. The thinner ice will become ice free earlier, which results in a reemergence of the original SIA anomaly. Note that the enhanced persistence in winter and summer is mostly due to these reemergence mechanisms.

Fig. 2.

(a) Lagged correlation of total SIA for multimodel mean, (b) simple exponential decay persistence model, (c) the standard deviation between the lagged correlation of different climate models, and (d) the lagged correlation of total SIA from observations (NSIDC). The black dots indicate significant values on the 99% level for multimodel mean in (a) and 95% level for ERA-Interim in (d). See text for the definition of the numbers in (a).

Fig. 2.

(a) Lagged correlation of total SIA for multimodel mean, (b) simple exponential decay persistence model, (c) the standard deviation between the lagged correlation of different climate models, and (d) the lagged correlation of total SIA from observations (NSIDC). The black dots indicate significant values on the 99% level for multimodel mean in (a) and 95% level for ERA-Interim in (d). See text for the definition of the numbers in (a).

To illustrate that there is added information beyond simple persistence of anomalies, Fig. 2b shows a simple persistence model (exponential decay) based on the decorrelation time scales found in Fig. 2a. Especially at longer time scales there is added information, mainly because of the reemergence mechanisms.

The lagged correlation patterns found in Fig. 2a are comparable to those found by BW11 and DA14. Note, however, that the low-frequency climate variability is removed by subtracting an 11-yr running mean, which makes a direct comparison between their figures and Fig. 2a difficult. BW11 and DA14 also found a stronger winter-to-winter and summer-to-summer reemergence of SIA anomalies, which is largely absent in Fig. 2a. The first is, as already described, said to be related to ocean heat flux convergence and the latter to sea ice–thickness anomalies, which determine to some extent the summer sea ice minimum anomalies (BW11). Because these processes are related to climate processes on longer time scales, these reemergence processes are partly removed by subtracting the 11-yr running mean. Indeed, if we do not remove an 11-yr running mean, these reemergence mechanisms are also present in the lagged correlation plots (not shown).

Even though in this analysis we use 15 different climate models, the correlation patterns are comparable to the results from BW11 and DA14. This illustrates that the patterns found are quite robust across the different climate models. This is further illustrated in Fig. 2c, which shows the standard deviation of the correlation scores between the different models. The areas (months) where the persistence and reemergence patterns are visible show a relative low standard deviation, indicating little spread between the models. An exception herein is the winter enhanced persistence.

When we compare the lagged correlation found in the multimodel mean to the observations (Fig. 2d) of total Arctic sea ice we notice distinct differences. There is a more distinct winter-to-winter reemergence, but the melt-to-freeze reemergence is partly lacking. Also, the melt-to-growth reemergence is absent. It must be noted that the observations cover only the satellite era (1979–2013) and show a strong trend toward less and thinner sea ice. A fair comparison between observations and CMIP5 preindustrial simulations is therefore difficult. However, the proposed mechanism behind the persistence and reemergence of sea ice anomalies should still be active in the current Arctic climate. Note that the decorrelation time scales are much smaller (~2–3 months) except in the summer months. Also, the enhanced persistence in winter is largely absent. This is, as Fig. 2c shows, also not agreed on in all models. This may indicate that some models overestimate predictability in winter months. The results agree with what BW11 found in their comparison with observations.

b. Atmospheric energy balance and sea ice variability

Next, we study the relation between components of the Arctic energy budget and the total SIA. Figure 3 shows the cross correlation between the surface net radiation (SNR) and top-of-atmosphere net radiation (TOANR) and the total SIA, with lags ranging from −4 (sea ice leads) to +12 months (sea ice lags). The first row shows the correlation between January SNR and lagged SIA, the second row for February, and so forth. The zero lags are marked by black squares. This figure therefore allows us to study SIA anomalies before and after net radiation anomalies for every individual month. To simplify further explanations, we describe relationships with respect to negative sea ice anomalies only. If we look at Figs. 3a and 3b, SNR and TOANR of May–August (on the vertical axis) show a relative strong negative correlation with SIA, where in the months October–March (vertical axis) there is mainly a positive correlation. The negative correlation indicates that a positive anomaly in SNR (i.e., more net radiation toward the surface) relates to less sea ice. The positive correlation in the autumn months can be explained by the fact that the extra heat absorbed by the ocean in spring and summer, because of less sea ice, has to be released to the atmosphere before sea ice can grow again. Hence, less sea ice in spring and summer relates to a more positive net radiation in spring and summer but a more negative net radiation in autumn. A distinct feature in Figs. 3a and 3b is that the negative correlations are mainly found at positive lags; that is, positive net radiation anomalies lead to less sea ice. The highest positive correlations, however, are mainly found at negative lag; that is, less sea ice leads to negative net radiation anomalies. The TOANR in November and December must be noted as an exception, with relatively large positive correlation at lag zero and lag one. The negative correlation in summer can be seen as a positive feedback on sea ice anomalies, which can enhance the persistence of sea ice anomalies. Further, in the negative correlation found in summer, we can clearly identify the pairs of months in the sea ice edge locations (May and December, June and November, etc.), as described in the previous section. When comparing both figures (Figs. 3a,b) with ERA-Interim (Figs. 3c,d), we find many similarities. Again, however, the ERA-Interim data are much noisier because of their shorter time span (1979–2013), making it more difficult to distinguish noise from signal. The main features found in Figs. 3a and 3b are also visible in ERA-Interim (Figs. 3c,d). A distinct difference, however, is the relative strong negative correlation for April and May SNR.

Fig. 3.

Cross-correlation plots of total SIA (horizontal) and (a) SNR (vertical) and (b) TOA net radiation. (c),(d) As in (a),(b), but for ERA-Interim. Zero lags are indicated by black squares. Also, where sea ice anomalies lead and lag relative to the radiation anomaly are illustrated in (a). The black dots indicate significant values on the 99% level for multimodel mean and 95% level for ERA-Interim.

Fig. 3.

Cross-correlation plots of total SIA (horizontal) and (a) SNR (vertical) and (b) TOA net radiation. (c),(d) As in (a),(b), but for ERA-Interim. Zero lags are indicated by black squares. Also, where sea ice anomalies lead and lag relative to the radiation anomaly are illustrated in (a). The black dots indicate significant values on the 99% level for multimodel mean and 95% level for ERA-Interim.

To identify the role of the individual components of SNR and TOANR, and to be able to explain some features found in Fig. 3, we have calculated the lead–lag relations between the individual radiation components and the total SIA. Figure 4 shows the individual radiation components of the SNR. The radiation components are defined positive downward. A positive radiation anomaly is thus either more radiation downward or less radiation upward. The radiation components are labeled S or L for shortwave and longwave radiation, respectively, and ↑ or ↓ to indicate the upwelling or downwelling component. A first look at the multimodel mean and ERA-Interim reveals that all radiation components match reasonably well, both in sign of correlation and in amplitude, which gives reasonable confidence in the multimodel mean. A striking feature in Figs. 4a–d is the relative high correlation found in early spring for all four plots, which is not seen in the net radiation plots in Figs. 3a,b. The strongest correlations are found in S↑ and L↑. The negative correlation of S↑ can be easily explained, as this is directly related to the amount of solar radiation absorbed by the Arctic region, thus heavily dependent on surface albedo. More radiation absorbed in the ocean (i.e., a positive anomaly of S↑) relates to less sea ice. Interestingly, when comparing Fig. 2a with Fig. 4a, we find that the S↑ anomaly of April and May is an even better predictor for September total SIA than sea ice itself (the correlation coefficient is 0.15 higher). We will discuss this in more detail in the next section. Note, however, that this is not evident in ERA-Interim.

Fig. 4.

As in Fig. 3, but for surface radiation components (a) S↑, (b) S↓, (c) L↑, and (d) L↓. (e)–(h) As in (a)–(d), but for ERA-Interim.

Fig. 4.

As in Fig. 3, but for surface radiation components (a) S↑, (b) S↓, (c) L↑, and (d) L↓. (e)–(h) As in (a)–(d), but for ERA-Interim.

The L↑ (Fig. 4c) shows strong resemblance to S↑ in correlation strength, albeit with positive values. This may seem counterintuitive, as less energy away from the surface would result in a warmer surface, and thus less sea ice, which would yield a negative correlation. However, L↑ anomalies originate from surface temperature anomalies, linked through the Stefan–Boltzmann relation. The L↑ therefore acts to restore surface temperature anomalies to their equilibrium state and is therefore of opposite sign to the radiation components that force a surface temperature anomaly.

The role of L↓ (Fig. 4d) is different, as this is mainly related to the amount and height of clouds and humidity, which emit longwave radiation back to the surface. The negative correlation found in Fig. 4 can be explained by more L↓, and thus a positive anomaly, resulting in a negative SIA anomaly. The fact that L↓ shows relative high correlation, especially in autumn, suggests that clouds and humidity play an important role in SIA variability. This relation will be explained in more detail in the discussion. The role of S↓ is more difficult to understand. Figure 4b shows positive correlations between downward shortwave radiationand sea ice anomalies. This indicates that with less shortwave radiation reaching the surface there is also less sea ice, which may seem counterintuitive. These results therefore again point to a possible influence of clouds. It is striking, however, that the variables most influenced by clouds (L↓ and S↓) show no clear relation with SIA in July.

Shortwave radiation is largely absent in Arctic winter; hence, longwave radiation is dominant over shortwave radiation in winter months, which explains the positive correlations found in the winter months in Fig. 3. The fact that L↑ anomalies mainly follow after SIA anomalies also explains the positive correlation in Figs. 3a,b at negative lags.

Another distinct pattern found in all plots in Fig. 4 is the difference between radiation anomalies in December–May and those in June–October. In general, the former are not preceded by SIA anomalies and the latter are. In March–May, the radiation anomalies precede sea ice anomalies and thus act as a forcing. From June onward, the sea ice anomalies originating in June seem to persist and possibly strengthen the sea ice and radiation anomaly in the subsequent months through the sea ice–albedo effect.

The TOANR components (Fig. 5) show similar patterns, albeit less strong and with no clear relation between early spring radiation and total SIA. Also, the S↑ has no relation with total SIA anomalies from October onward, which is in contrast to the surface S↑. This also explains the relatively strong positive correlation found in Fig. 3b in the autumn months, as when the influence of S↑ is absent, TOANR is dependent only on L↑. We can identify the same differences between the multimodel mean and ERA-Interim as with Fig. 4.

Fig. 5.

As in Fig. 3, but for TOA radiation components: (a) S↑ and (b) S↓. (c),(d) As in (a),(b), but for ERA-Interim.

Fig. 5.

As in Fig. 3, but for TOA radiation components: (a) S↑ and (b) S↓. (c),(d) As in (a),(b), but for ERA-Interim.

Because correlation indicates only how much two variables can covary, but nothing about the amplitude of both signals, we also performed the above analysis by calculating the regression coefficients (not shown). This helps us to identify the relative importance of the different energy balance components. The results indicate that the amplitudes of the radiation anomalies correlated with sea ice anomalies are in the same order of magnitude (not shown), with S↑ and L↑ slightly higher.

c. Ocean energy balance and sea ice variability

Next, we study the components of the ocean energy balance in relation to sea ice variability. Figure 6 shows the components of the ocean energy balance in relation to SIA anomalies. The ocean surface heat flux (OSHF), defined as positive down, is the heat flux at the top of the water column. Hence, over open ocean it is strongly related to the surface net radiation and also yields comparable results except for the months April and May. The negative correlation in summer months is explained by more radiation into the ocean, relating to negative total SIA anomalies. As also described in section 3b, the extra heat in the ocean has to be released back to the atmosphere before ice can grow again. Thus, less sea ice relates to a more positive OSHF in late spring and summer but to a more negative OSHF in autumn, hence the positive correlation in autumn months at negative lags. The change in ocean heat content (dQdt) gives almost the same results as the OSHF, which indicates that with an 11-yr running mean removed, most of the variability in dQdt is related to variability in OSHF. The correlation between the OSHF and dQdt anomalies vary from 0.6 to 0.8 between the models (not shown), which further strengthens this idea. There is some impact of ocean heat transport in summer in the models (both in forcing and in response), but from ORAS4 no clear relation is found. These findings support the idea that, with low-frequency climate variability removed, the main function of the ocean in relation to SIA variability is to store SST anomalies forced by OSHF anomalies. ORAS4 yields generally the same results, except for the summer months in OSHF where the negative correlation is not as strong as in the multimodel mean.

Fig. 6.

As in Fig. 3, but for (a) OSHF, (b) dQdt, and (c) the 65°N meridional ocean heat flux. (d)–(f) As in (a)–(c), but for ORAS4.

Fig. 6.

As in Fig. 3, but for (a) OSHF, (b) dQdt, and (c) the 65°N meridional ocean heat flux. (d)–(f) As in (a)–(c), but for ORAS4.

d. Local surface radiation anomalies

To identify which regions in the Arctic sea ice cover are related to the spring and summer correlation found in Fig. 4a, we have plotted the local S↑ anomaly of April (Fig. 7a) and July (Fig. 7b), correlated with the total SIA anomaly of the subsequent eight months. The regions that show higher correlation for the April S↑ are the Bering Sea and the Barents Sea, where the latter also shows relative strong correlation up to lag 3 and a weak reemergence in lag 7. For the July S↑ anomaly the main region consists of the Beaufort, Chukchi, East Siberian, Laptev, and Kara Seas. For both Figs. 7a and 7b, the regions with relative high correlation are situated close to the sea ice edges, except for typical sea ice export regions (e.g., the Fram export region). The other radiation components show similar spatial patterns (not shown), indicating that the anomalies for S↑, S↓, L↑, and L↓ are all spatially related. It must be noted here that the multimodel mean correlation is quite small, mostly between 0.2 and 0.3. The correlation for the individual models is often higher (~0.4–0.5). The lower multimodel mean is caused by differences in location of the sea ice edge, which therefore also changes the regions where the higher correlations are found. The multimodel mean thus results in a lower correlation and spread over a larger area.

Fig. 7.

Correlation between the local surface S↑ of (a) April and (b) July and total SIA for lags 0–7. The black contours indicate the model mean sea ice edge.

Fig. 7.

Correlation between the local surface S↑ of (a) April and (b) July and total SIA for lags 0–7. The black contours indicate the model mean sea ice edge.

Figure 7 can also help us to understand why spring S↑ is a better predictor for September sea ice area than spring sea ice itself (as seen in Figs. 3 and 4). This can be explained by the fact that an SIA anomaly in spring provides information only in the region of the sea ice edge, while the sea ice edge in September is farther to the north. The spring Arctic integrated upwelling solar radiation does contain information about conditions farther north through surface albedo anomalies. The albedo of sea ice slowly decreases in spring because of melting of snow and ice and the formation of melt ponds. A change in surface albedo in spring therefore provides information on the rate of melting at the region of the sea ice edge in September, as also suggested by Schröder et al. (2014), who show that spring melt-pond fraction could be a good predictor for September sea ice.

4. Discussion

The results above support the important role of the sea ice–albedo effect, which is manifested in SST anomalies originating from prolonged, or shortened, cumulative heating by shortwave radiation as a result of SIA anomalies. This is especially evident in OSHF, OHC, and S↑ anomalies. The atmospheric radiation components, however, also point to an important role for clouds in explaining SIA anomalies, notably the correlation between L↓ and SIA and the positive correlation between S↓ and SIA. The role of clouds on Arctic sea ice variability has been investigated before both in observational studies (e.g., Francis et al. 2005; Kay and Gettelman 2009) and in modeling studies (e.g., Gorodetskaya and Tremblay 2008). These studies emphasize the complicated relationship between clouds and Arctic sea ice, showing that the cloud radiative forcing (CRF) is strongly dependent on the insolation, surface albedo, and type of clouds, which in turn vary strongly during the season. Here we elaborate further on the role of clouds in the context of this study.

To understand and quantify the relation between the radiation components, clouds, and sea ice variability we determine how radiation and cloud anomalies evolve prior to and after the occurrence of sea ice anomalies. We do this by first selecting the locations and times of sea ice anomalies for all models. Herein we distinguish between positive and negative sea ice anomalies. We will consider only negative sea ice anomalies to simplify the explanation. We calculate the radiation and cloud anomalies at the location of these negative sea ice anomalies in the range of 12 months prior to and 12 months after their occurrence. The radiation and cloud anomalies are computed relative to sea ice conditions. In this way the anomaly represents the difference between sea ice and open water conditions. The radiation and cloud anomalies are then averaged over the different grid points, years, and models to get the average anomaly, prior to and after a sea ice anomaly, for the different months. The results are presented in Fig. 8. We also performed the above analysis for positive sea ice anomalies. These values are generally similar but of opposite sign. Note that, in contrast to Figs. 36, here the radiation anomalies are lagged and not the sea ice anomalies.

Fig. 8.

Multimodel (a)–(d),(f)–(j) mean radiation and (e) cloud fraction anomalies at the location of negative sea ice anomalies and 12 months prior to and 12 months after their occurrence.

Fig. 8.

Multimodel (a)–(d),(f)–(j) mean radiation and (e) cloud fraction anomalies at the location of negative sea ice anomalies and 12 months prior to and 12 months after their occurrence.

From Fig. 8a we can see that a negative sea ice anomaly in spring relates, on average, to an SNR anomaly of approximately 25 W m−2 at zero lag (indicated by a 1 in Fig. 8a). In late autumn and winter the SNR anomaly at zero lag is very small compared to in spring and summer (indicated by a 2). However, we do find a positive SNR anomaly of approximately 12–18 W m−2 prior to the sea ice anomalies in late autumn–winter (indicated by a 3). This nicely illustrates the reemergence of an anomaly in autumn from an original anomaly in spring, as illustrated before in Fig. 2a. This figure shows the pairs of months (May and December, June and November, etc.) that share the location of the sea ice edge. These pairs of months can also be seen in the shortwave (Figs. 8g,h) and longwave (Figs. 8b,c) radiation components. The individual radiation components also reveal that the increase in SNR of approximately 25 W m−2 in late spring–summer is mainly related to a positive anomaly of S↑ (i.e., less upwelling solar radiation), which is directly related to the decreasing surface albedo. Interestingly, however, the S↓ decreases by approximately 20 W m−2, which partly compensates for the reduced S↑. Less S↓ could be caused by a higher cloud fraction related to enhanced evaporation from open water, but as Fig. 8e shows, June–August show no cloud response to a sea ice anomaly (indicated by a 4 in Fig. 8e). The decrease in S↓ is then most likely related to the multiple-reflection component of S↓, which reduces as the surface albedo becomes smaller. We can estimate the reduction of S↓ resulting from a surface albedo change. For a nonabsorbing cloud, S↓ is given by S↓ = F0(1 − r)(1 − αr)−1 (e.g., Shine 1984; DeWeaver et al. 2008), where F0 is the solar downwelling radiation above the cloud, r the cloud reflectivity, and α the surface albedo. Following DeWeaver et al. (2008) we assume an Arctic cloud reflectance of 0.7. Values associated with the decrease in S↓ are a decrease in albedo from ~0.5 to ~0.25, an F0 of approximately 320 W m−2, and a cloud fraction of approximately 0.7 (not shown), which yields a decrease of approximately 22 W m−2. This indicates that the decrease of S↓ can indeed be caused by the decrease of the multiple-reflection component of S↓.

Figure 8f shows the anomaly of OSHF resulting from less sea ice. It increases approximately 60 W m−2, which is more than twice the response of SNR. This can be explained by the fact that the extra solar radiation is directly absorbed by the ocean, while if there were ice, a large portion of this energy would be absorbed by the sea ice and only a small portion of that would reach the water column.

Even though there is no direct cloud response to sea ice anomalies from June to August, we do find a delayed response (indicated by a 5 in Fig. 8e). Such a delayed response can also be found in the turbulent fluxes (Figs. 8d,i) and the longwave radiation components (Figs. 8b,g). These results correspond to findings from Kay and Gettelman (2009), who found a seasonal dependence on cloud response to sea ice decline in an observation study in the 2006–08 period. They found no clear cloud response in summer on sea ice anomalies, while in early fall more clouds did form. They related the lack of response in summer to a weaker ocean–atmosphere coupling because of stronger atmospheric stability and weaker air–sea temperature gradients. In early fall, however, the lower static stability and stronger air–sea temperature gradients result in stronger turbulent fluxes, which are in turn further strengthened by the SST anomaly. The larger turbulent fluxes increase the moisture in the air and hence yield a higher cloud fraction, which in turn enhances L↓. Our analysis supports this finding and shows that this is an integral part of the seasonal sea ice–albedo feedback in the climate models used for this analysis.

It is now also interesting to see how this delayed cloud response influences the seasonal sea ice–albedo feedback—that is, a cloud–ice feedback. Kay and Gettelman (2009) already concluded that cloud changes resulting from sea ice anomalies play only a minor role in regulating the sea ice–albedo feedback in spring but that they may contribute to a cloud–ice feedback during early fall. They could not quantify the magnitude or sign of this feedback. Our analysis does provide this opportunity. Figure 8e shows the anomaly in surface CRF for negative sea ice anomalies. This is calculated by summing the longwave radiative forcing (LWCLOUD − LWCLEAR-SKY) and the shortwave radiative forcing (SWCLOUD − SWCLEAR-SKY), where LW and SW are the net longwave and net shortwave radiation at the surface. A positive CRF thus means more clouds warm the surface. During spring and summer, around lag zero, the CRF decreases by approximately 25 W m−2. This is primarily related to the decrease in the multiple-reflection component of S↓, hence an indirect radiative effect. This is, as described above, caused by the decrease in surface albedo. The cloud response in fall, as a result of an SIA anomaly in spring, does result in a larger CRF of approximately 6 W m−2. This increase in CRF is not due to a change in multiple reflection as it is also visible in the longwave cloud radiative forcing (not shown). If we compare this response to the original net radiation anomaly in spring (~25 W m−2; i.e., the direct sea ice–albedo effect), we find that the delayed response contributes about 20% to the seasonal sea ice–albedo feedback. It must be noted here that this is true only if the sea ice anomaly indeed reemerges, as it does in about 25%–50% of the times, depending on the month (see Fig. 2a).

To understand why an increase in cloud fraction results in a positive CRF anomaly, we have calculated the multimodel mean surface CRF climatology (Fig. 9). From this figure we can deduce both a strong seasonal (i.e., solar zenith angle) and albedo dependence. CRF is positive if the warming effect of enhanced L↓ is larger than the cooling effect of less S↓. During Arctic winter the enhanced L↓ dominates because S↓ is largely absent; hence clouds have a net warming effect. During Arctic summer S↓ becomes larger; hence the cooling effect of less S↓ also becomes larger. It depends on the surface albedo and the strength of S↓ (i.e., the net solar radiation) whether the cooling effect of less S↓ becomes stronger than the warming effect of more L↓. For the largest part of the year, the CRF is positive over the sea ice (indicated by the white line). Only during June and July are there regions on the Arctic sea ice with a negative CRF. Because there is no cloud response in spring, there is also no cloud–ice feedback in spring. When there is indeed a cloud response in late summer and autumn, the CRF becomes positive because of the absence of solar radiation. The increase in clouds in autumn thus yields a more positive CRF. The cloud response to the seasonal sea ice–albedo effect therefore strengthens the feedback mechanism.

Fig. 9.

Multimodel mean climatology of cloud radiative forcing. The white contour indicates the multimodel mean sea ice edge and the blue contour the 0 W m−2 CRF isoline.

Fig. 9.

Multimodel mean climatology of cloud radiative forcing. The white contour indicates the multimodel mean sea ice edge and the blue contour the 0 W m−2 CRF isoline.

From Figs. 8 and 9 we can find two possible explanations for the positive correlation between S↓ and Arctic sea ice, found previously in Fig. 4b. The first is a positive CRF, where, as described above, an increase in S↓ is compensated by a stronger decrease in L↓. The second explanation is the decrease of the multiple-reflection component of S↓ due to an albedo decrease. Our analysis shows that, on average, the latter effect is stronger than the former. It should be noted, however, that S↓ can also be negatively correlated with sea ice variability. As indicated in Fig. 9, the CRF is not always positive; hence an S↓ anomaly can also enhance sea ice retreat. This is clearly demonstrated by Kay et al. (2008) in the 2005 and 2007 sea ice melt seasons.

We have also performed the analysis presented in Figs. 8 and 9 with ERA-Interim and ORAS4. These results (not shown) also show the delayed cloud response on sea ice anomalies and the decrease of S↓ because of a decrease of the multiple-reflection component. The overall picture of CRF for the multimodel mean and ERA-Interim match reasonably well, although the amplitude of the seasonal cycle is smaller in ERA-Interim.

Recent work by Kapsch et al. (2013, 2014) also investigated the role of spring atmospheric forcing on sea ice variability. They showed a clear connection between anomalies in spring L↓ and S↓ and September sea ice anomalies in a large part of the Arctic Ocean. Our results (Figs. 8d,h) also show a small L↓ anomaly in April and May (Fig. 8d) and an S↓ anomaly from May onward. Our results therefore confirm their findings, but it must be noted that the signal is relatively small.

In this analysis we have used the preindustrial (control) CMIP5 climate simulations. Because the simulations lack a long-term trend, it allows us to focus on the role of natural variability in the Arctic sea ice. The question must be asked, however, whether the findings presented above are also valid for the future climate. To test this we have performed part of the analysis presented above using the RCP4.5 scenario simulations (2005–2100). Figure 10 shows the lagged autocorrelation of SIA and the cross correlation of SNR and the individual components of SNR with (lagged) sea ice, presented in the same manner as in Fig. 4. The RCP4.5 multimodel mean shows strong overall resemblance to the control multimodel mean. There are some slight differences in the specific values of the correlation, but the main patterns are very similar, indicating that the analysis presented above also seems valid for future sea ice regimes. This can be expected, as the physical mechanisms for the enhanced persistence and reemergence of anomalies should still be working in a thinner, and of smaller extent, sea ice regime. O. Andry et al. (2014, unpublished manuscript) even show that the sea ice–albedo feedback will strengthen only when the amplitude of the seasonal cycle increases, as projected in future sea ice regimes.

Fig. 10.

As in Figs. 2a, 3a, and 4, but now for RCP4.5 scenario, lagged correlation of (a) total sea ice area and cross correlation between (lagged) sea ice and (b) L↑, (c) L↓, (d) SNR, (e) S↑, and (f) S↓.

Fig. 10.

As in Figs. 2a, 3a, and 4, but now for RCP4.5 scenario, lagged correlation of (a) total sea ice area and cross correlation between (lagged) sea ice and (b) L↑, (c) L↓, (d) SNR, (e) S↑, and (f) S↓.

5. Conclusions

We performed an analysis on the natural variability of Arctic sea ice from an energy balance perspective. In this analysis we aimed to explain the physical mechanisms that provide predictability of Arctic sea ice on seasonal-to-annual time scales. For this we used a selection of state-of-the-art CMIP5 climate models. In the first part of the analysis we computed the lagged correlation of total Arctic sea ice and cross correlation between radiation components and (lagged) total arctic sea ice. In the second part we analyzed the radiation anomalies on locations prior to and after sea ice anomalies. We compared our results with reanalysis data, namely ERA-Interim and ORAS4.

In the lagged correlation plots we found 1) typical decorrelation time scales ranging from 2 to 5 months, 2) a reemergence of anomalies in autumn related to the seasonal sea ice–albedo effect, 3) a winter-to-winter memory most likely related to ocean heat convergence anomalies (Bitz et al. 2005), and 4) a weak autumn–spring reemergence related to ocean thickness anomalies (BW11). These findings correspond to BW11 and DA14, which shows that these persistence and reemergence mechanisms are robust mechanisms in current climate models.

Net radiation, both at the surface and at the top of atmosphere, are negatively correlated with sea ice in summer and weakly positively correlated in winter. The negative correlation in summer is mostly determined by upward shortwave radiation, which is directly related to the surface albedo. Hence, more radiation upward relates to more sea ice. The negative correlation during winter is mostly determined by upward longwave radiation, which acts to restore temperature anomalies to their equilibrium state. Hence, a positive sea ice anomaly is related to less upward longwave radiation, which results in a positive correlation.

The individual radiation components also provide interesting insights. Spring upward shortwave radiation is a better predictor for September sea ice area than spring sea ice itself. This can be explained by the fact that a sea ice anomaly in spring provides information only in the region of the sea ice edge, while the sea ice edge in September is farther north. The upwelling solar radiation also provides information about the albedo where the sea ice edge will be in September. The albedo of sea ice slowly decreases in spring because of melting of snow and ice. A change in surface albedo in spring therefore provides information on the rate of melting at the region of the sea ice edge in September, as also suggested by Schröder et al. (2014), who show that spring melt-pond fraction is a very good predictor for September sea ice. The downward shortwave radiation component is, counterintuitively, positively correlated with sea ice area. Hence, more radiation downward yields a positive sea ice area. This has previously been attributed to the generally positive cloud radiative forcing over the Arctic (Francis et al. 2005). Our analysis reveals, however, that this is primarily due to a decrease (increase) of multiple reflection of shortwave radiation resulting from a decreasing (increasing) surface albedo. Our results therefore suggest that under cloudy conditions, the direct effect of the sea ice–albedo feedback (i.e., the enhanced absorbed solar radiation at the surface) is compensated up to 50% by reduced multiple reflection of downwelling solar radiation.

By analyzing radiation anomalies at locations of sea ice anomalies, we found a delayed atmospheric response on spring sea ice anomalies. This delayed response is previously documented in an observational study by Kay and Gettelman (2009) over the 2006–08 period. They related this lack of response in summer to a weaker ocean–atmosphere coupling due to a stronger atmospheric stability and weaker air–sea temperature gradients. In early fall, the lower static stability and stronger air–sea temperature gradients result in stronger turbulent fluxes, which are further increased by the SST anomaly. The enhanced turbulent fluxes result in a higher cloud fraction, which in turn enhances downwelling longwave radiation and slows the ice growth. Our analysis reveals not only that this mechanism is present in the 2006–08 period but also that it is an integral part of the seasonal sea ice–albedo feedback in the selected climate models and ERA-Interim. Because of the delayed response, the cloud radiative effect on the seasonal sea ice–albedo effect results in a net warming.

Acknowledgments

We are grateful for useful advice and suggestions from Hylke de Vries, Richard Bintanja, and Bert Holtslag. Furthermore, we thank three anonymous reviewers for their constructive comments that helped to improve the manuscript. This research is part of the Wageningen UR strategic research and development program TripleP@Sea. We acknowledge the World Climate Research Programme’s Working Group on Coupled Modelling, which is responsible for CMIP, and we thank the climate modeling groups (listed in Table 1 of this paper) for producing and making available their model output.

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