As in most other scientific disciplines, we have two major sources of information to examine the loss of Arctic sea ice in the real world: observational estimates and models. As both these sources of information have certain limitations, the most robust insights into the ongoing and future evolution of Arctic sea ice are obtained from combining observations and models, ideally minimizing the impact of the limitations of either [3].

Observations

Observational records of Arctic sea ice are the best possible estimate of the real evolution of the sea-ice cover. However, all existing observational records of Arctic sea ice have three distinct limitations, which imply that these observational records alone do not allow one to fully understand the drivers of the current ice changes or to fully characterize the future evolution of the sea-ice cover.

The first limitation is related to internal variability: Because the climate system is chaotic, any given set of external boundary conditions allows for an infinite number of possible climate trajectories. However, only one of these trajectories is actually realized and can be observed. This implies that observations can never capture the richness of possible trajectories that the climate system could have taken in recent decades. Hence, in the same way in which a single observation of the throwing of a dice only allows for a very limited understanding of the range of possible outcomes, a record of a climate observable often only allows for limited insights into the relative impact of external forcing or internal variability on the time evolution of that observable. In particular, all reliable observational records of sea ice only capture the behaviour of Arctic sea ice during a period of a rapidly changing background climate. Because of these rapid changes, even a 30-year long record is not long enough to provide a meaningful “average climate condition” that would sufficiently minimize the impact of internal variability [4, 5]. Their relatively short duration is hence a major drawback of all reliable records of sea-ice evolution.

The second limitation derives from observational uncertainty. In particular, all satellite records are based on indirect methods to obtain the underlying sea-ice property that one is ultimately interested in. Therefore, all major observational products are only an approximation of the true state of the sea-ice cover at any given time [6, 7].

The third limitation derives from the fact that we can only observe a very limited subset of climate variables that matter for the evolution of sea ice. For example, we have only limited observations of the major atmospheric heat fluxes that determine the surface energy balance of the ice cover, and no Arctic-wide observations of the oceanic heat flux underneath the ice.

If one keeps these limitations in mind, observational records can give us information about the sea-ice cover that offer a wealth of valuable insights into the past and also into the future evolution of Arctic sea ice. Indeed, we would argue that the most robust quantitative estimates of the future evolution of the ice cover are based on linear relationships between temperature or cumulative CO 2 emissions and sea-ice coverage identified in models and observations, where the slope of the linear relationship is taken directly from the observational record.

The studies that we summarize here are primarily based on the 40-year long record of gridded Arctic sea-ice concentration as obtained from passive-microwave satellite observations. This record started in the late 1970s, and is based on a series of successive multi-frequency passive microwave sensors that allow scientists to observe the polar regions year-round regardless of polar night or cloud cover [8, 9]. The stark differences in emissivity between open water and ice allow for a binary classification of ice vs. no ice present. In reality, due to the coarse resolution, satellite pixels often contain a mixture of ice, open water, leads, etc., allowing for characterization of the fractional area of sea ice per satellite pixel. This is typically done through setting tie-points for open water and ice, and interpolating between these extremes to determine the sea-ice concentration. While current algorithms to convert the satellite observation to sea-ice cover are relatively robust during winter, once melt begins the sensitivity of the microwave emissivity to liquid water at the sea-ice surface can result in large underestimation of the true sea ice fraction within a satellite pixel [7]. Further, near the ice edge and within coastal regions, the large satellite footprint can result in false ice concentrations or underestimation of the actual ice edge location [10].

The studies that we discuss here primarily use the sea-ice area or the sea-ice extent derived from such satellite-retrievals of gridded sea-ice concentration. Arctic sea-ice area is usually calculated by multiplying sea-ice concentration with grid-cell area and adding up over all Northern-hemispheric grid cells. Arctic sea-ice extent is usually calculated by adding up the grid-cell area of all grid cells with at least 15% sea-ice coverage. In the following, we will use the term “sea-ice coverage” for any statement that is true for both sea-ice area and for sea-ice extent.

Models

Any climate model has limitations that must be kept in mind when employing it to understand the evolution of the sea-ice cover in the real world.

First, climate models cannot capture all processes that govern the evolution of our climate system, and hence usually represent the real evolution of an observable less realistically than a given observational record. This is particularly true for sea ice, where climate-model simulations have been found to have substantial biases compared to the observed evolution of the ice cover. Among others, the models usually have a too low sensitivity of the simulated ice loss to simulated warming [3, 11,12,13] and to simulated CO 2 emissions [14], they often have a too low or too high mean sea-ice area [15], they often have an erroneous distribution of ice thickness [16, 17], and they can have substantial biases in the albedo evolution throughout summer [18, 19]. These biases must be kept in mind when assessing the robustness of model-based studies on the future trajectory of Arctic sea ice.

Second, the relationship of a model to the real world is often very difficult to estimate [5], which makes it difficult to infer robust quantitative statements from model simulations. In particular, internal variability renders a perfect agreement of a model simulation with reality impossible, such that a disagreement between a model simulation and the real world does not allow one to directly obtain insights on the quality of a particular model simulation [5, 20]. Any model evaluation must hence take internal variability into account [15]. On the other hand, an agreement of a specific model simulation with some observed record does not necessarily indicate a reasonable description of the underlying processes in the numerical code of the model, but might instead just indicate a reasonable tuning of the model to match the observational record [5, 21] or be caused by compensating errors. For example, [22] suggest that models participating in the fifth phase of the Coupled Model Intercomparison Project (CMIP5 [23]) better reproduce the observed loss of Arctic sea ice compared to the models participating in CMIP3, because in CMIP5, the prescribed external forcing from volcanic eruptions is too strong. Furthermore, agreement of a model with the past evolution of an observable is not necessarily an indication for reliable projections of the future evolution of that observable [3, 5].

On the plus side, however, models overcome many of the mentioned limitations of observational records: models can be run several times and over long periods to capture the range of possible internal variability, they provide full three-dimensional fields of all major climate variables at nearly any desired temporal resolution, and they are internally consistent. In addition, they reflect possible future changes in the physical processes that drive the evolution of the sea-ice cover. Such future changes can obviously not be observed, which is why model simulations contribute important insights into the future evolution of the ice cover that can not be inferred from the observational record.

Most recent studies that employ climate-model simulations to explore the ongoing and future evolution of Arctic sea ice are based on the coordinated set of simulations from about 40 different climate models that participated in CMIP5. In addition, some recent studies are based on large ensembles of simulations with individual models. Such single-model large ensembles have been used for sea-ice-related studies for the Community Earth System Model (CESM [24]), the Canadian Earth System Model (Can-ESM [25]), and the Max Planck Institute Earth System Model (MPI-ESM). These large ensembles allow for robust insights into the impact of internal variability in individual models.