The key switches for the Arctic Ocean are set out schematically in Fig.  and comprise wind anomalies both interior (WI) to the Arctic and exterior to it (WO), perturbations to the runoff (R), and ocean transports into the Arctic from outside (A and B). To illustrate our approach here we focus on perturbations to the wind field over the Beaufort Gyre and the Greenland Sea (GS), the heat flux through the Fram Strait, and river runoff. Many other perturbations could also be considered. Our choice of switches are motivated by the following considerations.

Wind forcing: wind is one of the most important forcing parameters driving variability of ice drift and ocean circulation (“wind blows, ice goes”, a rule of thumb well known since Arctic exploration in the 17th century) and responsible for mechanical changes in sea-ice concentration and thickness, freshwater content variability, and upwelling and downwelling processes, with implications for both oceanic geochemistry and ecosystem changes.

There are two major wind-driven circulation regimes over the Arctic Ocean, namely cyclonic and anticyclonic, which have decadal variability with significant differences in environmental parameters between these regimes (Proshutinsky and Johnson, 1997; Proshutinsky et al., 2002; Thompson and Wallace, 1998; Rigor et al., 2001; Proshutinsky et al., 2015). The Beaufort Gyre and Greenland Gyre regions are key circulation cells in the central Arctic Ocean and central Nordic seas and regulated by Beaufort and Icelandic High atmospheric systems, respectively. In our recommended experiments, anomalous wind direction and intensity in these regions have been chosen, as inspired by observational data (NCAR/NCEP reanalysis products).

River runoff: river runoff is the major source of freshwater for the Arctic Ocean. The FW is a key component in the Arctic hydrological cycle, affecting ocean, sea ice, and atmosphere. In the Arctic Ocean, the FW at the surface maintains a strong stratification that prevents release of significant deep-ocean heat to the sea ice and atmosphere (i.e., halocline catastrophe; Aagaard and Carmack, 1989; Toole et al., 2010).

Arctic FW exports can affect the climate of the North Atlantic by potentially disrupting deep convection in the North Atlantic, and it can affect the Atlantic Meridional Overturning Circulation (AMOC) if Arctic freshwater reaches convective sites in the Labrador Sea (Yang et al., 2016), for example. Thus, understanding the response to river runoff (especially as the climate warms and the hydrological cycle intensifies) is important for predicting future change. Numelinn et al. (2016) and Pemberton and Nilsson (2016), for example, have found that increased river runoff leads to a strengthening of the central Arctic Ocean stratification and a warming of the halocline and Atlantic Water layers. Further, excess freshwater accumulates in the Eurasian Basin, resulting in local sea-level rise and a reduction of water exchange between the Arctic Ocean and the North Pacific and North Atlantic Oceans. Thus, we expect that our recommended experiments, with different scenarios of runoff intensity and employing a set of models with different resolutions and parameterizations, will shed light on these behaviors.

Fram Strait salt and heat fluxes: one of the fundamental aspects of the Arctic Ocean is the circulation and transformation of Atlantic Water, which plays a critical role in Earth's climate system. Profound modification and conversion of these waters into North Atlantic Deep Water occur within the Arctic, making this region the “headwaters” of the global meridional overturning circulation. As far back as the early 1900s, Nansen concluded that the warm intermediate layer of the Arctic Ocean originated in the North Atlantic Ocean; oceanographers have since explored the intricate pathways, behavior, and impacts of Atlantic waters throughout the Arctic basin. While we have gained an understanding and appreciation of the importance of Atlantic Water, much remains to be learned. In our recommended experiments, the heat flux through the Fram Strait is perturbed, enabling us to test a set of hypotheses about the role Atlantic waters play in the Arctic. One of them is that heat release from the Atlantic water layer is responsible for sea-ice decline in the Arctic Ocean (e.g., Carmack et al., 2015). CRF experiments will also shed light on the pathways and intensity of Atlantic water and the interaction of boundary currents with the Arctic interior.

Ideal observables – the left-hand side of Eq. () – are integrated quantities (not, for example, the temperature at one point in space), which should be constrained by observations, indicative of underlying mechanisms and of climatic relevance. Two key attributes of useful “observables” are worth emphasizing: (a) those that make reference to existing theories or hypotheses about Arctic ocean dynamics (their CRFs can then inform our understanding) and (b) those for which CRFs can be constructed from observations, providing a quantitative measure for evaluation of model skill. With regard to the latter, given the difficulty of obtaining in situ observations, our focus is on large-scale integrated quantities. Some of the best available are satellite-derived, e.g., sea-ice concentration (and ice area and extent, derived from it) and ice drift from CryoSat, freshwater content inferred from CryoSat's sea-surface height fields and sea-surface temperatures in open water areas. Ocean fluxes through straits are perhaps best constrained by in situ observations, although they suffer from a lack of near-surface observations (i.e., Woodgate et al., 2015; Beszczynska-Möller et al., 2012), especially for the freshwater flux.

The following Arctic “observables or metrics” are a useful starting point, each one of which is constrained to some degree by observations:

freshwater and heat storage of the Beaufort Gyre;

The simulation is integrated on the Arctic cap of a cubed-sphere grid, permitting relatively even grid spacing throughout the domain and avoiding polar singularities (Adcroft et al., 2004). The Arctic face comprises 210×192 grid cells with a mean horizontal grid spacing of 36km. A linearised free surface is employed. There are 50 vertical levels ranging in thickness from 10m near the surface to approximately 450m at a maximum model depth of 6150m. Bathymetry is from the 2004 (W. Smith, unpublished) blend of the Smith and Sandwell (1997) and the General Bathymetric Charts of the Oceans (GEBCO) 1 arc-minute bathymetric grid. The nonlinear equation of state of Jackett and McDougall (1995) is used. Vertical mixing follows Large et al. (1994) with a background diffusivity of 5.4×10-7m2s-1. A seventh-order monotonicity-preserving advection scheme (Daru and Tenaud, 2004) is employed and there is no explicit horizontal diffusivity. A meso-scale eddy parameterization in the spirit of Gent and McWilliams (1990) is used with the eddy diffusivity set to K=50m2s-1. The ocean model is coupled to a sea-ice model described in Losch et al. (2010) and Heimbach et al. (2010).

The 36km resolution model was forced by the JRA-25 (6 h, 1∘) reanalysis for the period 1979–2013, using bulk formulae following Large and Pond (1981). Initial conditions for the ocean are from the WOCE Global Hydrographic Climatology (annual-mean, 1990–1998 from Gouretski and Koltermann, 2004). Open boundary conditions on S,T,u and v were employed using “normal-year” conditions averaged from 1992–2002 derived from an ECCO climatology (Nguyen, Menemenlis and Kwok, 2011). Decadal runs take a few hours on 80 cores.

Very similar 18 and 4km configurations of the same model exist and can be used in eddy permitting simulations for comparison with the coarse model run shown here.

Our model has a reasonable climatology, as briefly illustrated in Figs.  and . Figure a shows a plan view of the FWC (freshwater content; see Aagaard and Carmack, 1989)

Freshwater content is defined here (as reviewed in Haine et al., 2015) as the amount of zero-salinity water required to reach the observed salinity in a seawater sample starting from a reference salinity. It is computed as follows: FWC=∫DηSref-SSrefdz, where η is the free surface and we choose Sref=34.80 and D is its depth. This is the quantity mapped in Fig. a. Similarly, freshwater flux (FWF) is defined by multiplying the integrand of the above expression by velocity and integrating along the section.

Time series of FWC and heat content (HC) (top 400m) over the Beaufort Gyre (the horizontal region over which we integrate is delineated by the box in Fig. a) are shown in Fig. a and b. Figure a and b reveal that the freshwater and heat content are varying on decadal timescales, with an increased accumulation of FWC

To convert the FWC of the BG to meters of freshwater, divide by the surface area of the BG, here taken to be 1.24×106km2, the area of the box in Fig. a. Thus a FWC =20×103km3 corresponds to a depth of 20×103km31.24×106km2=16m of freshwater.

It is also clear from Fig.  that the model is drifting with a downward (upward) trend in FWC (HC). The model described here has undergone no data-assimilative procedure and so might be expected to exhibit such drifts as it adjusts to the initial conditions and forcing.

Figure c plots the annual cycle of sea-ice area from the 1980s onwards, showing a decline in the minimum (summer) ice area on the order of 106km2 in 30 years. The observed rate of sea-ice extent loss is much more dramatic than captured in our model: observations suggest that sea ice has declined by ∼0.5×106km2 per decade (annual mean) in the last few decades to below 8×106km2 (see, e.g., Fig. 1a of Proshutinsky et al., 2015), whereas the modeled annual-mean area is 11×106km2.

Figure b shows a vertical temperature section through our model, roughly coinciding with the Fram Strait (as indicated in Fig. a), and Fig. e–f plot time series of FWF (freshwater flux) and HF (heat flux) through the strait: positive indicates a flux into the Arctic, negative out of the Arctic. We observe a strong seasonal cycle and much interannual variability superimposed on longer-term trends and/or drifts. The magnitude of the mean value of FWF is somewhat smaller than the 2700±530km3yr-1 estimated from observations (see Table 1 and Fig. 4 of Haine et al., 2015). The HF through the Fram Strait varies by ∼10TW over the period of our simulation, roughly comparable with the CORE ocean models reported in Ilicak et al. (2016).

In Fig.  we plot time series of annual-mean anomalous heat flux through various Arctic straits shown in Fig. a. We observe, for example, that heat transport through the Barents Sea strait seems to be increasing and that through the Fram Strait is decreasing with a decadal trend. In contrast the transport through the Bering Strait and Baffin Bay vary primarily on interannual timescales, with less evidence of decadal trends. Comparison of the time series shown in Fig.  with those in Figs. 11 through 14 of Ilicak et al. (2016) shows broad similarities despite the fact that the latter study uses CORE forcing and a variety of models employing differing physical parameterizations, open boundary conditions, and grid resolutions.

It is clear from the above brief review of key circulation and sea-ice metrics (clearly many more are likely to be of interest) that they respond to the various external drivers in different ways with respect to amplitude and timescale. As we now go on to describe, we can expose and explore some of the underlying mechanisms by computing how the model responds to a step increase in the forcing.

Simplified forms of the surface pressure anomalies over the Beaufort Gyre and Greenland Sea have been constructed and are plotted in Fig. . The center for the BG pressure anomaly is located at 77∘ N, 149∘ W and the center for the GS anomaly is located at 71∘ N, 6∘ W, with a radius of influence on the order of 1000km. The magnitude of the anomaly is the same for all experiments. Our choice of BG and GS atmospheric centers of action were identified based on 1948–2015 6 hourly NCAR/NCEP data. These data were analyzed to identify key locations of centers of action and typical magnitudes north of the Arctic Circle. These centers can also be determined from Thompson and Wallace's (1998, 2001) studies of the Arctic Oscillation (AO, first mode of SLP EOF analysis which describes approximately 19 % of SLP variability in December–March).

In the series of experiments described here we assumed a central maximum/minimum of 4 hPa. Our perturbation of 4 hPa is small relative to seasonal changes, which can reach 20–30 hPa. However, a more reasonable measure is to compare with longer-term trends. During the 1948–2015 period, SLP over the Arctic changed by about 6 hPa suggesting that our chosen magnitude is not unrealistic. As can be seen by inspection of the right hand panels of Fig. , there is a noticeable perturbation to the long-term climatology of SLP when anomalies of this magnitude are assumed.

To compute surface winds from these pressure anomalies, the following relation is used (Proshutinsky and Johnson, 1997): Ws=0.7×cos⁡30-sin⁡30sin⁡30cos⁡30×Wg where Wg is geostrophic wind implied by the pressure anomaly, and Ws is the applied surface wind anomaly. The resulting anomalous winds are also plotted in Fig. .

We perturb the properties of water masses flowing through the Fram Strait. For simplicity we aligned the section with our model grid, extending from grid points centered at 80∘ N, 10∘ E (near Svalbard) to 80∘ N, 19∘ W (the Greenland coast), marking a line close to a true parallel (see Fig. a). Our objective is to perturb the temperature of water flowing across the section into the Arctic, but without a concomitant density change. This is accomplished by rapid restoration of temperature while simultaneously restoring salt to compensate. In the experiments described here, the restoring temperature was T+2K and restoring salinity was S+0.253psu

Compensating for salinity, δS=αβδT=0.253 psu, was computed using a δT=2 K assuming α=1×10-4 K-1 and β=7.9×10-4 psu-1, roughly corresponding to 5 K and 33 psu seawater, respectively.

For the anomalous river runoff experiment (RUN3x), the freshwater input from all rivers which drain into the ocean north of the Arctic Circle (66∘ N) was multiplied by a factor of 3. In our regional Arctic setup, no effort was made to balance this anomalous freshwater input with additional evaporation.

The framework we have set up can be used to help us understand how the FWC of the BG has varied over the past few decades. Comparing Figs. a, a, and a, we see that wind anomalies in the GS region and perturbations to runoff do not significantly affect FWCBG when compared to changes in the local wind field over the BG. Moreover, if the wind field over the BG oscillates on timescales shorter than the equilibration timescale of the FWC response function, then the FWC will not be in phase with variations in the wind but instead will lag it in time.

Figure b plots an index of the BG high (the AOO, the Arctic Ocean Oscillation Index, a measure of the wind-stress curl integrated over the BG) from 1948 up until 2015 – see Proshutinsky et al., 2015, and the legend therein for more details – which oscillates over a period of 11 years or so, as assumed in the analytical solutions shown in Fig. a. Also plotted is the FWC from observations from a short period in the 1970s and continued on from 2003. From the early 1990s up until the mid 2000s the anticyclonic driving (as measured by the AOO) over the BG markedly increased. In 2007, the Beaufort High reached a maximum because very strong anticyclonic winds dominated over the gyre throughout the year, decaying in later years. The observed FWC, however, lags the forcing and continues to build, not unlike the prediction obtained from our analytical forcing, plotted in Fig. a for comparison. One can see that the maximum FWC is observed approximately 3 years after maximum forcing. Of course this is only suggestive – given the short observational record it is impossible to quantitatively check the correctness of the predicted 90∘ lag (∼ 3 years) between forcing and the BG FWC response to it. Note, for example, that the short observational record in the mid-1970s appears to be in phase with the forcing. That said, it is very unlikely that the FWC can immediately come into equilibrium with the forcing and is much more likely to exhibit a lagged response to the wind, as hinted at in the longer observational record starting in 2003 (shown in Fig. b).

What is the physics behind the FWC response function setting the timescale γ-1? At least three important mechanisms come to mind. Firstly the wind-stress curl pumps water down from the surface, inflating the freshwater layer. But this occurs in the presence of ice whose ability to communicate the wind stress to the fluid column beneath depends on the nature of the ice pack – a difficult process to model. Perhaps sea-ice dynamics are fast relative to γ-1, whereas slower sea-ice thermodynamical processes play more of a role in the CRF timescale. Secondly, baroclinic instability of the BG may be an important mechanism that spreads the FW away laterally, allowing an equilibrium to be achieved (Manucharyan and Spall, 2016; Manucharyan et al., 2016). The timescale and equilibrium level at which this is achieved depends on the eddy field which is imperfectly modeled and/or parameterized. Thirdly, the availability of freshwater sources and timescales associated with its modification by mixing near continental shelves may come in to play. Thus there is uncertainty in γ and FWC^BG, which controls the detailed response.