The Arctic is warming 2 to 3 times faster than the global average. Arctic sea ice cover is very sensitive to this warming and has reached historic minima in late summer in recent years (e.g., 2007 and 2012). Considering that the Arctic Ocean is mainly ice covered and that the albedo of sea ice is very high compared to that of open water, any change in sea ice cover will have a strong impact on the climate response through the radiative surface albedo feedback. Since sea ice area is projected to shrink considerably, this feedback will likely vary considerably in time. Feedbacks are usually evaluated as being constant in time, even though feedbacks and climate sensitivity depend on the climate state. Here the authors assess and quantify these temporal changes in the strength of the surface albedo feedback in response to global warming. Analyses unequivocally demonstrate that the strength of the surface albedo feedback exhibits considerable temporal variations. Specifically, the strength of the surface albedo feedback in the Arctic, evaluated for simulations of the future climate (CMIP5 RCP8.5) using a kernel method, shows a distinct peak around the year 2100. This maximum is found to be linked to increased seasonality in sea ice cover when sea ice recedes, in which sea ice retreat during spring turns out to be the dominant factor affecting the strength of the annual surface albedo feedback in the Arctic. Hence, changes in sea ice seasonality and the associated fluctuations in surface albedo feedback strength will exert a time-varying effect on Arctic amplification during the projected warming over the next century.
Many studies, based on analyses of both models and observation, have shown that the warming in the Arctic region occurs 2 to 3 times faster than the global mean (Holland and Bitz 2003; Serreze and Francis 2006; Serreze and Barry 2011), a phenomenon that is commonly referred to as Arctic amplification (AA). This warming is accompanied by a strong decrease in summer Arctic sea ice extent and thickness, the former reaching historic low values in recent years (Comiso et al. 2008; Stroeve et al. 2012). Most recent projections for the coming century indicate that sea ice cover in the Arctic could shrink to sea ice–free conditions (<1 × 106 km2) during summer within 30–40 years from now (Wang and Overland 2009; Boé et al. 2009). These projections also show that sea ice extent will strongly reduce year-round during the next century. Recent satellite observations revealed that the 2015 maximum extent in Arctic sea ice was reached as early as 25 February. This is one of the earliest sea ice extent maximums ever recorded and also one with the smallest extent (Viñas 2015). It is clear that Arctic climate changes are ongoing, and they will continue to be a major and wide-ranging issue in the years and decades to follow, with possibly even irreversible consequences if tipping points are passed (Winton 2006a; Lenton et al. 2008).
Rapid Arctic warming will likely have wide-ranging (hemispherical scale) effects. Several studies have assessed the possible influence of AA and sea ice retreat on the midlatitude climate, such as an increasing occurrence of extreme events associated with changes in the jet stream, storm tracks, and planetary waves (Francis and Vavrus 2012; Liu et al. 2012; Screen and Simmonds 2013; Francis and Vavrus 2015). Even though the mechanisms involved in Arctic/midlatitude linkages are part of an ongoing debate (Cohen et al. 2014; Barnes 2013; Screen and Simmonds 2013), the likeliness of these teleconnections is generally supported. Hence, strong ongoing and projected climate changes in the Arctic will likely have widespread impacts on climate and weather in the midlatitudes.
Feedback analyses are useful to quantify the contributions of individual climate mechanisms associated with changes in temperature, surface albedo, water vapor, and clouds to the climatic system response to changes in external forcing and climate sensitivity (Bony et al. 2006). Radiative feedbacks can enhance, sustain, or damp forced changes in the climate state. Feedbacks analyses are commonly used in Arctic climate research to quantify the contributions of the various relevant feedbacks to AA. A well-known climate mechanism associated with AA is the surface albedo feedback, which is strongly linked to Arctic sea ice extent and thus to surface temperature (Hall 2004; Screen and Simmonds 2010).
Pithan and Mauritsen (2014) recently showed that the temperature (Planck) feedback by itself can explain AA to a certain extent. Graversen et al. (2014) performed feedback analyses using the CCSM4 and demonstrated that the lapse rate and surface albedo feedbacks explain 15% and 40% of AA, respectively. In contrast, Winton (2006b) found that the surface albedo feedback is smaller than the longwave radiative feedback in the Arctic. Bintanja et al. (2011) showed that a strengthening of the wintertime temperature inversion diminishes the surface longwave radiation to space, which favors warming. In summary, the relative strengths of the various Arctic feedbacks appear to depend, to a certain extent, on the models and forcings that are used to assess them. All these studies define a climate feedback as the contribution of an individual mechanism to the overall change in the radiative budget of Earth and thereby evaluate the feedbacks as being constant in time. However, it is widely known that climate feedbacks and climate sensitivity do vary in time, as they depend on the climate state. In this study, we address this time-varying behavior of climate feedbacks, and in particular of the surface albedo feedback, and use this information to shed light on the climate mechanisms behind this feedback. In the Arctic, the sea ice cover and surface temperature are undergoing rapid changes and are projected to keep changing radically. By definition, the surface albedo feedback and the lapse rate feedback are depending on the change in surface albedo (driven by changes in sea ice) and surface temperature, respectively (Soden and Held 2006). Hence, the evolution of the governing Arctic feedbacks and their contribution to climate sensitivity will likely vary considerably with ongoing future warming, which, incidentally, may be another reason why previous estimates of feedback strengths diverged.
In this paper we will focus on the characteristics of the surface albedo feedback. In particular, we will investigate the transient (i.e., time varying) behavior of this feedback in the Arctic. The temporal variability of global climate sensitivity has been addressed previously (Senior and Mitchell 2000; Williams et al. 2008) and has also been applied in relation to feedback changes on very long (paleo) time scales (Von der Heydt et al. 2014). However, assessing and quantifying time-varying feedbacks on near-future climate projections such as those provided by phase 5 of the Coupled Model Intercomparison Project (CMIP5; Taylor et al. 2012) is, to the authors’ knowledge, a novel approach that likely provides valuable insights into the physical processes that contribute to Arctic climate change. As such, this constitutes an advantage over assuming and applying time-averaged climate feedbacks.
2. Data and methods
a. Models and data
In the present study we use multimodel data from CMIP5 (Collins et al. 2013; Taylor et al. 2012) under the RCP8.5 emissions scenario (Moss et al. 2010). Various analyses (e.g., Reichler and Kim 2008) have shown that the multimodel approach often leads to more accurate results (the multimodel mean being more accurate than any of the individual models). Moreover, the use of a multitude of models (which inherently include different parameterizations and methods) provides a (rough) intermodel measure of the uncertainty associated with the best-estimate result. The RCP8.5 scenario prescribes strong emissions to reach a radiative forcing that has increased by 8.5 W m−2 at the end of the twenty-first century (2100), relative to preindustrial conditions. Most models from the CMIP5 initiative provide only 100 years of monthly data for the RCP8.5 scenario. Because the transient feedback computation requires comparison of climate states that should be sufficiently different, we only use models that provide 300 years of monthly data (i.e., BCC_CSM1.1, CCSM4, CNRM-CM5, CSIRO Mk3.6.0, IPSL-CM5A-LR, MPI-ESM-LR, GISS-E2-R, and GISS-E2-H; expansions of all model names are available online at http://www.ametsoc.org/PubsAcronymList). In these simulations the RCP8.5 emissions scenario is applied until 2100, after which the models are run for 200 additional years, with decreasing emissions leading to a stabilization in radiative forcing at 12 W m−2 (Van Vuuren et al. 2011). The feedback analyses are performed using the output of six CMIP5 models under RCP8.5 forcing, since we exclude both GISS models from the analyses based on inaccurate sea ice physics and a consequent unrealistic sea ice retreat, as explained in more detail in appendix C. It is also worth noting that two of the six remaining models (IPSL-CM5A-LR and MPI-ESM-LR) are very similar (i.e., they only differ in resolution) to two of the five “best” models in terms of Arctic sea ice changes as determined by Collins et al. (2013) and hence give quite similar results in terms of sea ice retreat.
Additionally, we analyzed the ERA-CLIM ERA-20CM reanalysis dataset (Hersbach et al. 2015) in terms of Arctic feedbacks to provide some observationally based validation. This is an ensemble reanalysis of the twentieth century, which prescribes SSTs and sea ice cover from HadISST2 realizations (Titchner and Rayner 2014).
In this study we focus on the radiative surface albedo feedback. We define the surface albedo feedback in terms of the change in surface albedo and not in terms of the changing surface conditions (e.g., sea ice or snow cover), as is sometimes done in Arctic climate studies. Moreover, we employ here the global temperature change and not the local Arctic temperature change to evaluate the surface albedo feedback. Feedback analyses have long been used in climate science to characterize and understand the response of the climate system to an external radiative forcing (e.g., Hansen et al. 1984). The climate system responds to an external radiative forcing by changing its global mean surface temperature ΔTs. This change can be related to ΔR, the radiative imbalance (net shortwave radiation minus outgoing longwave radiation) at the top of the atmosphere (TOA) (Bony et al. 2006; Shell et al. 2008). The relation between radiative imbalance of the climatic system and surface temperature can be written as follows:
where λ is the feedback parameter that characterizes the climate response to the forcing. In first order (i.e., neglecting interactions among individual feedbacks) the feedback parameter can be defined as
where X is a vector representing an ensemble of climate variables (xi) affecting R.
1) Evaluating feedback strengths: The kernel method
In this study we use the kernel method (Soden et al. 2008; Soden and Held 2006). A kernel characterizes the response of the climate system to a small perturbation in an individual climate variable xi. Each kernel [Ker(xi)] is obtained by perturbing the variable xi and measuring the net TOA radiative flux response using a radiative transfer algorithm. This method has several advantages. According to Soden et al. (2008), differences between radiative transfer schemes used to compute the kernels have a relatively minor effect on the spread of climate feedbacks. This means that the kernels are relatively insensitive to the model used to compute them, which allows one to intercompare models (see appendix B). Another advantage is that once the radiative kernels are computed they can be run offline at relatively low computational cost. The total feedback parameter can effectively be separated into individual contributions associated with relevant climate variables. Similar to earlier studies, we distinguish feedbacks associated with clouds C, albedo a, water vapor wv, and temperature T:
The temperature feedback can be further subdivided into the Planck feedback and the lapse rate feedback λT = λLR + λPlanck. Apart from the albedo feedback, all feedbacks are composed of a longwave and a shortwave component.
Using the kernel method, the feedback parameter associated with an individual climate variable is defined as the product of two terms: 1) the net radiative change at TOA in response to a change in a climate variable (=the kernel) and 2) the actual change in a climate variable as a response to a change in surface atmospheric temperature. The individual feedback associated with a climate variable xi then is
where Ker(xi) is the radiative kernel associated with the climate variable xi, Δxi is the difference in xi between two climate states, and, likewise, ΔTglo represents the difference in global mean near-surface atmospheric temperature between the two states. In this study, feedbacks are defined using change in global mean surface atmospheric temperature, similar to other studies using the kernel method. We could also have used Arctic average temperature, but we chose the global temperature to be able to relate changes in surface albedo to global climate changes and, more generally, to be able to compare to other global feedbacks. The kernel applied in this study was derived using the atmospheric general circulation model ECHAM6. The ECHAM6 atmospheric configuration is similar to the CMIP5 MPI-ESM-LR used in this study. Its atmospheric module is coupled to a 50-m mixed layer ocean model and was run to steady state with a preindustrial CO2 concentration of 284.7 ppmv. It was necessary to use this state to compute the various kernels (since kernels for most other climates states are not available), and we use the surface albedo kernel (which is thus based on preindustrial greenhouse gases, sea ice, and cloud conditions) throughout all analyses, acknowledging the uncertainty introduced by this inconsistency. A more detailed description of the ECHAM6 kernel is provided by Block and Mauritsen (2013). The all-sky surface albedo kernel represents the radiative response at TOA to a change of 1% in surface albedo.
2) Adaptation of the kernel method to compute time-varying feedbacks
In this study, our aim is to compute temporal variations in the strength of climate feedbacks. This is achieved by adapting the kernel method in order to provide time series of radiative feedbacks for the 295-yr model output data. We apply the kernel method on windows of 50 yr. The Δ used in Eq. (4) are computed as the difference of the average of the last 20 yr minus the average of the first 20 yr of these time windows. We then shift the time window by 10 yr, and so on (Fig. 1). By doing so, we obtain a value of the feedback every 10 yr. It should be noted that the time window used to compute the feedback potentially has a significant effect on the strength of the feedback. As a matter of fact, there are many uncertainties associated with this method, and the values of the strength of the feedback should therefore be considered qualitatively rather than quantitatively. A more detailed discussion and a test of the robustness of our approach to various values of the time windows are presented in appendix A.
It should also be noted that radiative kernels were computed from an atmospheric model coupled to a thermodynamic mixed layer ocean model (Block and Mauritsen 2013), meaning that the influence of deep ocean heat uptake is not taken into account. Considering the equilibrium assumption in evaluating feedbacks (Soden et al. 2008), one may question the applicability of our method to evaluate the transient behavior of feedbacks from fully coupled (i.e., ocean–atmosphere) climate model simulations (CMIP5). Several studies have shown a significant difference between equilibrium climate sensitivity and transient (effective) climate sensitivity (e.g., Winton et al. 2010; Williams et al. 2008). Since we focus on the Arctic, where changes seem to be driven largely by fast atmospheric and top of the ocean (sea ice) mechanisms, we here assume that the impact of the deep ocean on Arctic feedbacks is small.
In this section we will evaluate time-dependent variations of the surface albedo feedback in the Arctic. In addition to the surface albedo feedback, we will show time series of the surface albedo itself as well as incoming shortwave radiation and sea ice cover. Sea ice cover is the main factor affecting the surface albedo because the studied region (north of 70°N) consists mostly of Arctic Ocean. We first investigate time series of annual means and then address the changing seasonality of sea ice, surface albedo, and the albedo feedback.
a. Time-dependent behavior of the surface albedo feedback
Under the strong emissions scenario RCP8.5, all time series of annually averaged sea ice area (Fig. 2) in the Arctic (north of 70°N) show an approximate linear decrease except for the CSIRO Mk3.6.0 model. In the CSIRO Mk3.6.0 model, annual mean Arctic sea ice area is much higher than in the other models (especially in summer and autumn), which may affect the projected decrease since initial sea ice state can modify (local) climate and sea ice trends (van der Linden et al. 2014). Too much sea ice apparently slows down the melt rate so that the downward trend in the CSIRO Mk3.6.0 model in the first part of the simulation is much smaller than in the other models. Among the six models, the annual Arctic sea ice area ranges between 8 × 106 km2 and 10 × 106 km2 in 2006 and reaches sea ice–free conditions (<1 × 106 km2) between 2130 and 2180.
The surface albedo determines how much of the downwelling shortwave radiation reaching the surface is reflected back to the atmosphere. It is defined as the ratio of upwelling shortwave radiation and downwelling shortwave radiation at the surface. To first order, the Arctic Ocean either has a high surface albedo when covered by sea ice or a low albedo when the surface consists of open ocean. Open ocean can have an albedo as low as 0.1, whereas sea ice can have a maximum albedo of 0.9 if covered by sea ice and fresh snow (Perovich 2003). For the models considered here, the polar average of the annual mean albedo in the Arctic (north of 70°N) starts at a value between 0.5 and 0.65 in the early years of the simulation and declines toward values between 0.15 and 0.25 in the year 2250 (Fig. 3). Two of the six models exhibit a sudden drop in Arctic annual average albedo. This “event” occurs around the year 2120 for MPI-ESM-LR and the year 2150 for CSIRO Mk3.6.0. The four other models exhibit a fairly monotonic decrease in Arctic annual mean albedo. Using these values and applying the kernel method as described in section 2b(2), we evaluate the time-varying annual mean surface albedo feedback strength (Fig. 4). For all models the resulting time series show an increasing surface albedo feedback in the first 100 years or so, followed by a decrease in surface albedo feedback over the remainder of the period (from about 2150 until 2300). There is a clear and well-defined maximum in surface albedo strength between 2100 and 2150 in four models (Fig. 4). In the BCC_CSM1.1 the maximum in feedback strength is less pronounced, whereas the CNRM-CM5 does not exhibit a discernable peak but a more or less gradual decrease. Hence, five out of six models considered here exhibit a clear and well-defined maximum in surface albedo feedback strength around the year 2100, albeit of varying magnitude. Hence, even though the models may vary in their representation of sea ice processes, they largely exhibit a similar sea ice retreat and warming that is associated (at least partly) with a fairly robust time dependency of the surface albedo feedback. This suggests that, apparently, the exact parameterizations inherent in the sea ice and surface albedo formulations in these models presumably only play a secondary role with respect to the uncertainty of the Arctic response. We should also point out that the peak in surface albedo feedback strength is likely underestimated owing to the relatively long time window applied to evaluate the feedback, at least compared to the time scale of the climate changes at the time of the peak (Fig. 3); generally, the time scales associated with sea ice area and thickness decline vary with ongoing Arctic warming. Ideally one would like to relate the time windows to the time scales of the changes, but for various reasons we chose to apply a constant time window in evaluating the feedback, as explained in more detail in appendix A. Interestingly, the surface albedo feedback strength at the end of the simulation is consistently lower than in the beginning for all six models, which concurs with the notion that, generally, the strength of the feedback depends on the amount of snow and ice: less sea ice means a weaker albedo feedback. The physical mechanisms related to the peak in surface albedo feedback will be addressed in the next section.
The evaluation of the time-dependent feedbacks involves various sources of uncertainty. These include interannual variability of the climate variables (in this case, temperature and surface albedo), the kernel that is used to compute the feedbacks, and the choice of the windows (length and separation). To infer whether the temporal variations in the surface albedo feedback as shown in Fig. 4 are significant, we show in Fig. 5 the variability and kernel-related uncertainty estimates per model. Clearly, the uncertainty associated with interannual climate variability (which in the Arctic is comparatively large) dominates; the uncertainty due to kernel choice is small. Notwithstanding the considerable total uncertainty (for which we have assumed that uncertainties are independent), we can conclude that the peak in surface albedo feedback is significant in all models that exhibit a maximum. The uncertainties associated with window length are discussed in appendix A.
Evaluating feedbacks that vary in time clearly differs from the usual approach to analyze feedbacks. The “classic” approach would be to implicitly assume that the strength of a feedback is constant over a period of time (typically between the present-day and sometime in the future, say 2100) or to consider the “average” feedback strength over that period. Since our analyses (Fig. 4) demonstrate that the surface albedo feedback strength exhibits temporal variations of considerable amplitude, both assumptions clearly oversimplify matters, meaning that important physical processes involved in the climate response may have been overlooked.
b. Seasonality of sea ice and its impact on the albedo feedback
Climate feedbacks govern the ongoing and future evolution of Arctic warming. For that reason, it is important to address temporal changes in feedback strength as well as the physical processes associated with these fluctuations. As shown in the previous section, models project a peak in the surface albedo feedback strength near the end of the twenty-first century, which will amplify radiative forcing. This maximum cannot solely be related to the change in surface albedo (Fig. 3) since it also occurs in models that do not show the rapid decline in annual mean surface albedo. In the Arctic, surface albedo exhibits a strong seasonal cycle that is largely governed by the waxing and waning of sea ice cover (Hall and Qu 2006). Reductions in sea ice area will likely be associated with changes in the seasonality in sea ice cover (such that the various seasons exhibit differing reductions). Temporal variations in sea ice seasonality, defined here as the difference between maximum and minimum sea ice area (March and September, respectively) are shown in Fig. 6. Incidentally, this quantity can also be interpreted as the amount of seasonal sea ice, defined as the sea ice that forms and melts within the same year, as opposed to the multiyear sea ice.
We infer that, for all six models, the amplitude of the seasonality of sea ice area increases in the first years of the simulations and reaches a maximum around the year 2050 (except for the CSIRO model) because the decrease in summer sea ice is larger than in winter. This maximum is subsequently sustained for some time (up to 100 yr for IPSL-CM5A-LR). After roughly the year 2150, most models exhibit a decrease of the March minus September sea ice area, which can be attributed mainly to the summer ice having completely vanished so that the reduction in winter sea ice governs the seasonal cycle, which then reduces in magnitude. Hence, unlike the annual mean sea ice area, the seasonality of sea ice exhibits a clear maximum, after which it decreases. The maximum in sea ice seasonality seems to coincide with the peak in the surface albedo feedback (Fig. 4), which suggest that the seasonality of sea ice plays a role in the temporally changing surface albedo feedback.
The surface albedo, governed by the presence of sea ice, only has an impact on the surface radiative balance when there is incoming shortwave radiation to be reflected. In the Arctic region, this is the case from March to September (Fig. 7, middle). Hence, the albedo feedback can only be effective in spring (April–June) and/or summer (July–September). The seasonal cycle in sea ice area (Fig. 7, bottom) shows that Arctic mean sea ice extent is at its lowest in August and September, so the surface albedo during the summer months (July – September) is already quite low, and the possibility for it to decrease further through reductions in sea ice extent is limited; hence, changes in summer sea ice hardly affect variations in the surface albedo feedback. Both incoming shortwave radiation and sea ice coverage exhibit a strong seasonal cycle and peak during early and late spring; as a result, the reflected shortwave radiation peaks in spring (and exhibits minimum values in autumn) (Fig. 7, top). Therefore, conditions during the spring months contribute most to the annual mean surface albedo feedback. A rapid reduction in the sea ice extent during spring thus causes a comparatively strong decrease in surface albedo and therefore an increase in the surface albedo feedback. A reduced albedo in spring allows more shortwave radiation to heat the ocean surface, thereby enhancing the amount of energy stored in the system. This energy is subsequently released in winter, which is the main cause for the amplified winter warming (Bintanja and van der Linden 2013).
Differing temporal changes between seasons are thus key in terms of the surface albedo feedback. Figure 8 shows temporal changes in the seasonal cycles of albedo, downwelling shortwave radiation, and sea ice cover in the Arctic for the MPI-ESM-LR. This model is taken as an example; the evolution of seasonal cycles in other models is quite similar. Figure 8 clearly shows that the seasonal cycle of these quantities is not constant in time: generally, changes in shape and in amplitude occur. The seasonal cycle in downwelling shortwave radiation at the surface mainly exhibits a lower maximum over time, which may be attributed to multiple reflections of shortwave radiation between the initially high-reflective surface and the clouds aloft becoming progressively less important (Krikken and Hazeleger 2015). The seasonal cycle in Arctic surface albedo initially shows an increase in amplitude since the minimum is decreasing while its maximum remains high. Following the sea ice cover minimum, the minimum in albedo in summer is reached earlier because of strong summer melt. Interestingly, Arctic sea ice minimum is reached in August/September in the beginning of the simulation but shifts to July around the year 2100. Clearly, the spring and summer rates of melting and sea ice retreat are not similar (Fig. 9). During spring months, sea ice area is initially decreasing slowly in all models. Approaching the year 2150, most spring sea ice vanishes within two or three decades (Fig. 9a). As a result, the amplitude of the peak in surface albedo feedback is much larger in the spring months (April–June) than in other seasons (Figs. 9c,d), which corresponds to a drop in sea ice coverage in the spring months and thus to a strong decline in spring surface albedo. The annual surface albedo feedback is governed by the strong sea ice retreat in spring. When spring sea ice has mostly vanished, the surface albedo feedback is reduced to a small number, since considerable surface albedo variations no longer occur.
The timing of the maximum feedback clearly differs between models. Are these differences consistent with the intermodel differences in retreat of sea ice? To find out, we defined one model (CCSM4) as the reference model and determined the cross correlation in the spring sea ice time series of the five other models with that of CCSM4. From this we evaluated the temporal shift in the sea ice time series required to maximize the cross correlation. We applied this shift to the corresponding surface albedo feedback time series (Fig. 4) and determined the cross correlation with the CCSM4 feedback time series. The resulting correlations are 0.93, 0.51, 0.96, 0.82, and 0.95 for MPI-ESM-LR, CNRM-CM5, BCC_CSM1.1, IPSL-CM5A-LR, and CSIRO Mk3.6.0, respectively. This confirms that, generally, temporal variations in spring sea ice and surface albedo feedback are firmly linked and that this link is consistent among the climate models considered here.
c. The relation between seasonal sea ice area and thickness
For a deeper understanding of the processes driving temporal variations in the surface albedo feedback, we need to determine the causes of the abrupt decrease in spring sea ice area around year 2150 (Fig. 9a). Times series of spring sea ice volume in the Arctic exhibit an approximately linear decrease (Fig. 10). This suggests that, in the years leading up to 2150, sea ice melting in spring has little effect on sea ice extent (Fig. 9a). To further shed light on the relation between Arctic sea ice extent and sea ice thickness, we show in Fig. 11 a scatterplot of sea ice area versus thickness for spring. This shows that, initially, when mean sea ice thickness is greater than 1 m, sea ice reduction is dominated by a decrease in sea ice thickness so that sea ice area remains relatively constant. Then, when the Arctic average sea ice thickness falls below about 0.5 m, sea ice decline becomes dominated by (rapid) reductions in sea ice area. Apparently there exists a certain threshold in sea ice thickness for which Arctic sea ice reduction shifts from being dominated by thinning to being dominated by areal shrinking. Figure 11 suggests that this threshold corresponds to an Arctic average spring sea ice thickness of around 0.5 m. The presence of this threshold may be related to the way melt energy is being “supplied” to the sea ice slab. In any case, from this we can conclude that sea ice melting mechanisms during spring play a crucial role in determining temporal variations in Arctic surface albedo feedback. It should be noted that the magnitude of sea ice melt in spring is also related to the sea ice growth in winter (which is due largely to longwave cooling of the surface). Hence, sea ice formation and thickening in autumn and winter is a crucial element in the seasonal cycle of sea ice, as this projects to the potential melt in the subsequent warm season by modulating the abovementioned thickness threshold. Bathiany et al. (2016), for instance, showed that the asymmetry between sea ice freezing (in autumn/winter) and melt (in spring/summer) characteristics will lead to an abrupt decline in spring sea ice when winters become too mild for a thin layer of seasonal sea ice to form.
d. Geographical distribution of the surface albedo feedback
The kernel method also allows us to determine the feedback strengths per model grid point so that we can assess the spatial pattern of the annual mean surface albedo feedback. This is particularly useful for studying the associated physical mechanisms. Not very surprisingly, the spatial distribution in surface albedo feedback varies considerably among models, even though they do share some characteristic features. As an example, Fig. 12 shows spatial structures in surface albedo feedback in the Arctic at various times as simulated by the CCSM4. Clearly, the patterns during the early and later years of the simulation differ strongly. Initially, the surface albedo feedback is strongest near the margins of the Arctic sea ice, where most of the melt and hence the strongest reduction in surface area occurs, partly because of the northward transport of relatively mild Atlantic Ocean water (Schauer et al. 2004). When the surface albedo feedback peaks, around the year 2150 for most models, its strength reaches maximum values over the entire central Arctic, associated with spring sea ice thickness having reached the approximate threshold of 0.5 m, which causes a large-scale collapse in spring sea ice area. Toward the end of the simulation, when ice-free conditions are reached, the surface albedo feedback apparently peaks near the coasts, north of Canada, Russia, and Greenland. In the CCSM4 simulation, some residual sea ice remains in these regions as late as 2200. These sea ice remnants are not found in all models and may be a model bias.
e. Validation of feedback strengths using ERA-CLIM reanalysis data
Our analyses thus far are based solely on model projections, which raises the question of how accurate the results are compared to the real world. To address this question, we applied the time-varying feedback method to observation-driven reanalysis data of the twentieth century, specifically ERA-20CM (Hersbach et al. 2015), to investigate if the magnitude of the surface albedo feedback evaluated from the CMIP5 models is consistent with reality (as defined here by the reanalyses). The results are depicted in Figs. 4 and 13.
First, the strength of the surface albedo feedback at the end of the twentieth century is indeed consistent with those calculated from the CMIP5 models (historical + RCP8.5 forcing), as shown in Fig. 4, even though the CMIP5 models exhibit intermodel differences that are larger than the spread in the 10 reanalyses members. Second, the seasonal behavior of the feedback seems to support the seasonality hypothesis put forward in this paper (Fig. 13). Specifically, in the past few decades, spring [April–June (AMJ)] sea ice hardly declines, and therefore the surface albedo feedback in spring is relatively small. During summer [July–September (JAS)], however, sea ice area retreat is far more substantial, leading to a strong decrease in Arctic mean summertime surface albedo over the past few decades and, consequently, a relatively high surface albedo feedback. Hence, the fast-retreat mechanism that we have identified for spring in the twenty-second century seems to be largely equivalent to the summer events in recent decades. The “observed” warming signal over the past few decades is not as strong as future warming in the RCP8.5 projections, however, meaning for instance that using time windows shorter than 50 yr may lead to spurious feedback strengths because of the internal variability of surface albedo and global temperature (see appendix A).
4. Discussion and conclusions
To quantify the temporal behavior of the Arctic feedbacks, including the associated uncertainties, we applied the kernel method using shifting time windows for 295 yr of output (2006–2300) of six state-of-the-art global (CMIP5) climate models under the RCP8.5 warming scenario. In this paper, we focus on temporal variations in the surface albedo feedback, which we interpret in terms of the governing physical mechanisms. In particular, we find that the annual mean surface albedo feedback exhibits a distinct and significant maximum around the year 2100 (even though uncertainties are considerable). This is related to sea ice decline, since changes in the average surface albedo in the Arctic (70°–90°N) are governed by fluctuations in sea ice cover. More specifically, we have shown that the surface albedo feedback is mostly effective during the spring months (April–June) owing to the seasonal cycle of both incoming shortwave radiation at the surface (maximum in June) and sea ice extent (peaking in March). We also have shown that the seasonal cycle in Arctic sea ice changes with time. Hence, the sea ice minimum will be reached progressively earlier in the year when climate warms and sea ice recedes. In the climate model simulations, the spring (April–June) sea ice extent initially exhibits only a minor decrease; most of the mass loss occurs through sea ice thinning (i.e., melting from below). Around the year 2150, average Arctic sea ice thickness reduces below a threshold of about 0.5 m, spring sea ice extent reduces sharply, and winters become too mild to allow the formation of even a thin layer of seasonal ice (Bathiany et al. 2016). Consequently, most of the Arctic sea ice in spring melts away within the next few decades. Hence, when melt starts to affect spring sea ice extent, the incoming shortwave that is reflected declines sharply, increasing the amount of energy stored in the climate system, and the surface albedo feedback peaks. The behavior of Arctic sea ice during spring is thus crucial to understand the temporal behavior of the annual and Arctic mean surface albedo feedback.
Our results also clearly demonstrate that evaluating/assuming a temporally averaged value of the feedback(s), as is usually done, constitutes an oversimplification of the actual processes involved. For instance, the central role of spring sea ice retreat would be very difficult to determine from a temporally averaged albedo feedback, which may possibly lead to an incorrect interpretation of the transient climate response. Time-varying feedbacks provide a more accurate description of the climate response to an external forcing and the associated climate processes. Finally, this paper focuses on the surface albedo feedback in the Arctic in the coming three centuries. This technique can obviously be applied to other (polar) feedbacks as well and to other regions or other time periods. We expect the methodology to evaluate temporally varying feedbacks, when applied to other settings, to expand our knowledge on climate feedbacks and sensitivity as well as the associated climate mechanisms.
This work is part of the research program Netherlands Polar Program (ALW-NPP) with project number 866.13.011, which is (partly) financed by the Netherlands Organization for Scientific Research (NWO). We acknowledge the World Climate Research Programme’s Working Group on Coupled Modeling, which is responsible for CMIP, and we thank all climate modeling groups for producing and making available their model output. For CMIP the U.S. Department of Energy’s Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led the development of software infrastructure in partnership with the Global Organization for Earth System Science Portals.
Limitations and Sensitivity to How the Time-Varying Kernels Are Used to Evaluate the Surface Albedo Feedback
We have performed sensitivity calculations to test the robustness of our method to evaluate temporally varying climate feedbacks. Figure A1 shows that the length of the time window applied to average the climate state (the blue periods in Fig. 1) hardly affects the temporal evolution of the Arctic surface albedo feedback. Figure A2 depicts the dependence of the results to the length of the period over which the albedo feedback is computed (the red periods, denoted by ΔX in Fig. 1). The latter mostly affects the amplitude of the maximum but not the general shape and trend of the feedback time series. It also affects the associated uncertainty (because of interannual variability and choice of kernel) in the sense that feedbacks evaluated using a short window length exhibit the largest uncertainties. The choice of the “optimal” values of both quantities (20 and 50 yr, as used throughout this study) is somewhat arbitrary. However, in general we believe that both periods should not be set too short (as this would generate unnecessary “weather” noise in the feedback signal that is unrelated to actual climate feedbacks at work) but also not too long (which would increase the chance that interesting and relevant time-dependent signals are averaged out). With these optimal values, at least, the interannual noise unrelated to albedo changes is eliminated. We acknowledge that in periods of fast climate changes the time windows should optimally be shorter to allow the method to capture the rapid changes in feedback strength. However, even then the method would be susceptible to weather noise, causing spurious fluctuations in feedback strength that are unrelated to actual changes in feedback strength and a larger uncertainty (Fig. A2). Hence, decreasing the time window in case of faster changes in relevant variables would deteriorate the accuracy of the results. Moreover, doing the analyses with nonconstant time windows would yield results that are more difficult to interpret (since the magnitude to some extent depends on window characteristics, as per Fig. A2). The ambiguity in the choice of time windows adds to the uncertainty in the computed feedback values, as shown in Fig. A2. However, this study focuses on the temporal variations in the surface albedo feedback (and the associated climate mechanisms) rather than on the precise value of the feedback itself. Generally, the actual strength of feedbacks depends to a certain extent on the method chosen to evaluate it.
When analyzing the ERA-CLIM data (section 3e), the time-varying method yields spurious signals as a result of internal variability in the data when using windows significantly smaller than 50 yr (Fig. A3). Hence, on time scales smaller than 50 yr, the Arctic surface albedo may, generically speaking, increase (decrease) while global temperatures increase (decrease), meaning that, on these shorter time scales, changes in the surface albedo are caused by “random” internal fluctuations of the Arctic climate system.
Finally, the time-varying feedback method using kernels has some further caveats. One of the major limitations is related to the fact that the kernels are computed for preindustrial conditions. Therefore, our results implicitly assume that the radiative response to a change in surface albedo is linear. Also, the kernels disregard the effects of deep ocean heat uptake. These limitations preclude a precise quantification of the feedbacks but allow for a qualitative interpretation of underlying physical mechanisms.
Comparison of Kernels
To assess the reliability of the kernel method we have determined the time-varying surface albedo feedback in the Arctic (north of 70°N) for the MPI-ESM-LR using three different sets of kernels: 1) GFDL (Soden et al. 2008), 2) NCAR (Shell et al. 2008), and 3) MPI (Block and Mauritsen 2013). The latter one was used throughout this study. Figure B1 shows that the choice of kernels has no appreciable effect on the shape of the time series and only moderately affects the strength of the feedback. The relative insensitivity of the resulting feedback is in itself an interesting and surprising result given the (many) differences between models in terms of, for example, sea ice parameterizations. Apparently, analyzing a large-scale quantity, such as a feedback strength “averages out” smaller-scale differences (between kernels) related to, for example, sea ice dynamics. Also, it is likely that the main physics (the link between sea ice and surface albedo changes to changes in radiative fluxes) that govern the surface albedo feedback are captured sufficiently well by the different kernels. This is corroborated by the finding that the zonal-mean kernels in the Northern Hemisphere do not diverge more than 10% from each other (Soden et al. 2008).
Deviation of the GISS Models
Obviously, there is no a priori reason to exclude diverging models from the analyses. However, both GISS models exhibit a strong, counterintuitive, and decisive deviation in their climate change characteristics, especially in the Arctic (Fig. C1). Specifically, winter and spring sea ice area remains high throughout the simulation up to 2300, long after the sea ice in the other models have collapsed year-round (Fig. C2). As an explanation, Schmidt et al. (2014) point to a problem in the seasonal cycle of sea ice caused by excessive heat diffusion in the sea ice module of the GISS models. This problem could explain the weak temporal variation of the sea ice seasonal cycle as well as the difficulty to effectively reduce winter sea ice under positive climate forcing. The GISS models indeed exhibit unrealistic persistence of sea ice after 2150, which seems to confirm that the heat diffusion issue in sea ice in the GISS models is indeed a major problem. Finally, it is worth noting that two of the other models used here (IPSL-CM5A-LR and MPI-ESM-LR) are very similar (they only differ in resolution) to two of the five “best” models in terms of historical Arctic sea ice changes, as shown by Collins et al. (2013). Hence, we believe that the six “regular” models fairly accurately represent Arctic changes (even though these models also exhibit intermodel differences), whereas the GISS models do not, owing to a known problem in the sea ice physics, as argued above. On the basis of these considerations, we chose to exclude the diverging two GISS models from the analyses.