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Fig. 17.2 Time series of net volume transport through Davis Strait in the 1/4° resolution version (blue) and in the 1/12° resolution version of NAOSIM (Fieg et al., manuscript in preparation). Northward transports are positive; axis labels are in Sv

2007). Considering the narrow channels that connect the Arctic Ocean with Baffin Bay, model resolution is an obvious candidate for the differences. Figure 17.2 shows volume transport time series of net volume transport through Davis Strait (which is identical to that through the Canadian Archipelago) in two versions of NAOSIM. In the lower resolution version (1/4° resolution in a rotated spherical grid) the volume transport almost vanishes whereas the higher resolution version (1/12°) has a more realistic southward transport of around 1 Sv. Results from the even lower resolution version of NAOSIM with 1° resolution suggest, however, that an exaggerated Channel width may at least help in getting a realistic net outflow of water though the Archipelago (Koberle and Gerdes 2007).

The resolution dependent representation of the Canadian Archipelago topography is a critical issue in modelling the Arctic freshwater balance. This is aggravated by the possible resolution dependence of the fresh water export distribution between the Archipelago and Fram Strait.

The magnitude of the liquid fresh water flux through the Canadian Archipelago is around 0.1 Sv or approximately 3,000 km3/year in the high-resolution NAOSIM version. This is of the same order of magnitude as the liquid Fram Strait export and about twice as large as the estimate of Aagard and Carmack (1989). Newer observational estimates put the total liquid fresh water transport through the Canadian Archipelago at around 3,000 km3/year (Prinsenberg and Hamilton 2004, 2005). These estimates rely on 3 years of mooring data in Lancaster Sound and assumptions about the additional flow through other channels, especially Nares Strait. The transport through the Canadian Archipelago is not solely determined by resolution. The passages in the model have to be well resolved. This might be achieved in coarse resolution models by overly wide channels through the Canadian Arctic. In a 1°-resolution model, Prange and Gerdes (2006) find an average southward fresh water transport of almost 1,400 km3/year while Koberle and Gerdes (2007) simulate a transport of more than 2,200 km3/year with different surface forcing and a somewhat different land-sea configuration. Another important factor is the representation of flow through Bering Strait. In a simple two-dimensional model, Proshutinsky et al. (2007) show that inflow through Bering Strait sets up a surface elevation pattern with highest amplitudes along the North American coast and indicating strong flows through the Canadian Archipelago and Fram Strait. Simulations with a comprehensive model (Karcher and Oberhuber 2002) that includes an artificial tracer for Pacific Water confirm this direct path from Bering Strait to the Canadian Archipelago. All these relatively coarse resolution models have a prescribed volume influx at Bering Strait while the higher resolution NAOSIM models have a closed boundary where only hydrographic properties are imposed.

Many Arctic Ocean models employ 'virtual salt fluxes' instead of fresh water fluxes to represent precipitation, melt water, and continental run-off. This is imposed by a rigid-lid condition that leads to volume conservation and cannot accommodate volume fluxes across the surface. In this case, a choice of reference salinity is necessary to convert fresh water fluxes into salt fluxes. Usually, a constant value or the local surface salinity is used. A constant value Sref with which the surface fresh water flux becomes FS = (-P + E - R)Sref, allows tracer conservation when the total surface fresh water fluxes (including evaporation) sum up to zero over the model surface. However, locally very large errors are possible. This includes the possible occurrence of negative salinities near strong fresh water sources like the Siberian river mouths during summer. Local surface salinity SSS, FS = (-P + E - R)SSS, avoids these errors but involves a spatially variable weighting of the fresh water fluxes which implies a deviation from the originally specified surface fresh water fluxes. Prange and Gerdes (2006) discuss these choices and their consequences for the Arctic Ocean fresh water balance. Depending on the chosen surface boundary condition, Fram Strait liquid fresh water transports differ by up to 1,000 km3/year. In the case of prescribed volume fluxes through the surface, the Arctic Ocean is becoming saltier while in case of 'virtual salt fluxes' with the local SSS for conversion from fresh water fluxes, the Arctic Ocean is getting fresher in Prange and Gerdes' calculation.

In equilibrium, the exchanges of volume and salt between the subpolar North Atlantic and the Arctic Ocean are strongly constrained by the mass and salt balances of the Arctic Ocean. On short time scales, inflow and outflow salinities do not change substantially and an increase in the run-off, precipitation minus evaporation, or Bering Strait inflow will result in increasing transports of both the Atlantic inflow and the outflow of Polar Water. Besides other processes, this exchange will eventually lead to a new equilibrium. Important questions are how long the adjustment processes will last (determined by the size of the involved fresh water reservoirs and the magnitude of the flux anomaly) and what changes in fresh water content in the Arctic Ocean will develop during the transition phase. Over decadal or longer time scales, the outflow with the EGC can be described by a simple formula derived from a 1.5-layer model of the Polar Water flow (Koberle and Gerdes 2007). The volume transport is proportional to the square of the upstream thickness of the Polar Water layer. An adjustment of the lateral fluxes thus likely involves changes in the thickness of the

Arctic halocline. In a model with prescribed fresh water input through precipitation, run-off and Bering Strait inflow (usually with prescribed salinity), the lateral fluxes will adjust accordingly to reach equilibrium. A bias in the prescribed fluxes will result in a bias in the lateral fluxes as well as in the Arctic hydrography. Even in a perfect model, the biases in fresh water fluxes prescribed as forcing will introduce biases in the distribution of salinity and the lateral fluxes in a model. The equilibrium response in the volume transports of in- and outflows to a change in run-off and precipitation is amplified by a factor Sref/AS where Sref is the salinity of the inflow or the outflow and AS is the salinity difference between inflow and outflow. Because of the large salinity contrast between inflow and outflow in the case of the Arctic, this factor is only O(10) for current conditions. However, the uncertainty in precipitation over the Arctic Ocean as expressed in the different integral numbers of fresh water flux from different data sets is almost 0.1 Sv. For the ocean area north of 65° N with the exception of the Nordic Seas and the Barents Sea south of 79° N and east of 50° E we calculate 5,600 km3/year in the Large and Yeager (2004) dataset, 2,900 km3/year in the ERA40 reanalysis data based Roske (2006) atlas, and 5,000 km3/year in the satellite-based NASA GPCP V1DD data set. An ocean model confronted with a precipitation data set that is perhaps 0.1 Sv off will react either with a bias in the exchanges between the Arctic and adjacent seas of around 1 Sv or a corresponding change in the outflow salinities, i.e. a massive bias in the Arctic Ocean hydrography.

Because of the above difficulties to satisfactorily combine prescribed fresh water fluxes, lateral exchange rates, and hydrograhy in the interior Arctic, many modellers have relied on additional artificial fresh water sources. Perhaps the most frequently used device is the restoring of modelled surface salinity to climatological values. Steele et al. (2001) discuss the effect of surface salinity restoring in different Arctic Ocean models. Koberle and Gerdes (2007) discuss the spatial and temporal distribution of the restoring flux in their model under NCAR/NCEP reanalysis forcing. Biases in the model that were compensated for include a lack of fresh water originating at the Siberian rivers and following the transpolar drift into the interior Arctic Ocean. Run-off in their model is around 1,000-2,000 km3/year less than more recent estimates (Shiklomanov et al. 2000). More important, however, was the failure of the model to disperse the fresh water away from the coasts. The insufficient communication between shallow shelf seas and the deep interior is a common problem in this class of ocean models. River water is accumulating near the river mouths, leading to unrealistically low salinities. This diminishes the efficiency of the fresh water flux that is transformed into a salt flux by multiplying with the local surface salinity. In other areas of the Arctic, the flux adjustment is typically less than 0.5 m/year in each direction. These values still are comparable to the annual mean precipitation in this area.

The flux adjustment partly compensates for a mismatch between the climato-logical surface salinities, based on observations mainly between 1950 and 1990, and the forcing period that extends to 2001. For instance, north of the strong fresh water input through the flux adjustment Koberle and Gerdes (2007) find an area where fresh water is extracted. This can be ascribed to the changed pathways of river water in times of the strongly positive North Atlantic Oscillation (NAO)

towards the end of the 20th century (Steele and Boyd 1998) that is not well represented in the climatological surface salinities. Similarly, the climatology might not reflect completely the supposed high ice export rates from the Arctic during positive NAO phases, thus featuring relatively low surface salinities in the sea ice formation regions and relatively high salinities in the melting regions of the EGC.

Restoring introduces a negative feedback that acts against surface salinity anomalies. With time-varying atmospheric forcing the restoring term represents a strongly varying component in the Arctic Ocean fresh water balance. To avoid the feedback that damps variability, surface fresh water fluxes are prescribed. A naive application of fresh water fluxes will lead to large biases in simulated hydrography and lateral exchanges as explained above. A flux-compensation can be introduced as described for instance in Koberle and Gerdes (2007). Basically, the restoring term is evaluated for an experiment run and averaged over a certain period. In a repetition of the run with otherwise identical forcing, this climatology of the restoring term is applied as a fixed salt flux to the surface box of the ocean model. This is an artificial fresh water flux that, however, compensates for biases in the forcing fields and deficiencies of the model. Since the flux is constant in time and there is no connection with the surface salinity, the former feedback is no longer present. This allows much larger variability in all components of the fresh water balance. As an example we show in Fig. 17.3 time series for Arctic fresh water content in a model run with restoring and a model run with flux adjustment.

While this procedure seems a feasible solution to the problem, potentially it has a grave drawback. Prescribing surface temperature through bulk formulae that tie the SST to fixed atmospheric temperatures and surface fresh water fluxes (mixed boundary conditions) is known to cause too high sensitivity in large-scale models of the oceanic circulation (Zhang et al. 1993; Rahmstorf and Willebrand 1995; Lohmann et al. 1996). Regional models are more constrained by lateral boundary conditions where large-scale transports are prescribed. In the example of Fig. 17.3, we see that the fresh water content is systematically higher in the flux-adjusted case but the value at the end of the integration is close to that of the restored case again. This indicates that no substantial shift in the circulation regime has occurred due to the change in the surface boundary conditions. We conclude that this model

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