Coarse-resolution models, such as those used in climate studies, often do not properly represent transports through narrow channels. We consider the climatically important transports of volume, heat, and freshwater through Fram Strait. A coarse grid (nominally 1°) global ocean model is seen to underrepresent exchanges. We test effects of eddy stress (Neptune) parameterization, finding strengthened volume exchanges both to and from the Arctic and increased mean northward heat transport while limiting southward freshwater export. Results are closer to observed transports and to results from fine-resolution models. This study finds that the effects of the eddy stress on temporal variations of transports are small.
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 The West Spitsbergen Current (WSC) and the ice-infested East Greenland Current (EGC) are the two major currents in Fram Strait. However, the complex topography in the region makes the current system complicated. The WSC splits into at least three branches. One branch follows the shelf edge and enters the Arctic Ocean north of Svalbard. This branch crosses the Yermak Plateau which limits its depth to approximately 600 m. A second branch flows northward along the northwestern slope of the Yermak Plateau. A third branch recirculates immediately in Fram Strait between 78°N and 80°N. Schlichtholz and Houssais  and Schauer et al. [2008, hereinafter S08] give a comprehensive description of the current system in the strait.
1.1. Volume, Heat, and Freshwater Transports
 There have been efforts to estimate the volume, heat and freshwater transports of the EGC and WSC based on observations and numerical modeling studies. Differences in the mooring periods and the assumptions used can lead to different estimates.
Polyakov  lists the volume transports from both the observational and modeling studies. Here we expand the study period with updated results from the observational and modeling studies shown in Tables 1 and 2, respectively. Early estimates of the transports of the two flows are all less than 10 Sv (1 Sv = 106 m3 s−1) for EGC and WSC, Aagaard and Greisman  got 7 Sv for both EGC and WSC. Recent observational data tend to give stronger transports, such as 14 Sv of EGC and 12 Sv of WSC by S08. Coarser numerical models are seen to predict less inflow than observed while fine-resolution models obtain stronger flows. Sensitivity of transports in Fram Strait to inflow boundary conditions in the Nordic Seas also poses a difficulty for regional models [Mellor and Häkkinen, 1994]. Furthermore differences in the numerical models themselves could also lead to differences in the transports. Maslowski et al. , Lique et al. , and Fieg et al.  reported more than 8 Sv of EGC and more than 6 Sv of WSC from their modeling studies. Fieg et al.  obtained 12 Sv of EGC and 10 Sv of WSC in their 9 km resolution model, which are close to observed transports by S08.
Table 1. Observed Volume Transports (Sv) of EGC and WSC Through Fram Strait
 Estimates of the heat and freshwater transports have been made based on both observational data and model results. Aagaard and Greisman  reported heat transport of 16.3 TW (1 TW = 1012 W) by WSC in their observational study. S08 estimated a range of heat transport by WSC between ∼25 TW to ∼45 TW for the period from 1997 to 2006. Maslowski et al.  reported heat transport of 47 TW through Fram Strait in their modeling study. Nguyen et al.  obtained an average heat transport of 28 TW through Fram Strait for the 1992–2008 period from their regional model.
Gerdes and Schauer  report that their Atlantic-Arctic model with a resolution of 1° by 1° gives the lower core temperatures and salinities than the observed and they speculate that one reason for this discrepancy between model and observations is the coarse horizontal resolution of the model. Thus, the ability of numerical models to get a realistic amount of warm and salty water into the Arctic and cold fresh water out through Fram Strait is important for climate studies but difficult for modelers.
1.2. Eddy Effects: Entropic Forcing?
 Fine-resolution models produce stronger currents in and out of Fram Strait. Comparing results on 27 km and 9 km grids, Fieg et al.  observe that the finer grid exhibits eddying activity and stronger tendency toward more barotropic flow along contours of constant f/D, f is the Coriolis and D is the total depth. Fieg et al.  speculate that this is “the effect of eddy rectification… described by Holloway .” Further support is seen from the Estimating the Circulation and Climate of the Ocean, Phase II (ECCO2) model [Menemenlis et al., 2005] where Holloway et al.  use runs with (nominal) grid resolution of 18 km, 9 km and 4 km grids to show that runs become more eddy active with stronger flows along f/D contours as grid spacing decreases.
 While such results are encouraging, they are also challenging. Can we understand eddy effects well enough to represent them in models that do not resolve eddies? This was the goal of Holloway  as implemented beginning with Alvarez et al.  and in a number of coarse grid models since, including our previous effort [Holloway and Wang, 2009, hereinafter HW09] which considered pan-Arctic effects in the present 1° global model.
 Theory, recently summarized by Holloway , follows from nonequilibrium statistical mechanics. Symbolically, if the Arctic is represented by a set of coarse-grid variables Y, then entropic forces act upon those Y given by P · ∂H/∂Y where P is a projector and H is entropy, H ≡ −∫log(p)dp, with p a joint probability function over all unknown degrees of freedom. The challenge is to turn this symbolic idea into practical parameterization. A first and simplest scheme is called “Neptune” (further described in section 2). Another approach approximates maximum entropy production (“MEP”) after Kazantsev et al. . Nazarenko et al.  used Neptune while Polyakov  used MEP in Arctic Ocean models, with Polyakov  finding MEP results quite similar to Neptune.
 The Arctic Ocean Model Intercomparison Project (AOMIP) [Proshutinsky et al., 2005] compared differences between model results and observations under similar setup and forcing. To evaluate differences of circulation patterns among nine AOMIP models, Holloway et al.  introduced topostrophy τ ≡ f × V · ∇D, where f is Corilolis, V is velocity, and ∇D is the gradient of bottom depth. Averaged over the volumes of Arctic basins, τ of three AOMIP models with Neptune were strongly and persistently positive whereas τ of the remaining six models, with conventional frictional parameterization schemes, were weak and variable. Likewise HW09 report stronger, positive τ comparing Neptune with friction. Such strongly positive τ has the sense reported from fine-grid eddy-active models [Fieg et al., 2010; Holloway et al., 2011], reinforcing the suggestion that the fine-grid models are showing an eddy rectification process. Importantly this is not only tendency for mean flow aligned with f/D; it is tendency for flows with a definite sense τ > 0 or “keeping shallow on right side.” Our present purpose is to further examine this process upon transports through Fram Strait.
Section 2 gives a description of the model and the surface forcing. Results are discussed in section 3 with conclusions discussed in section 4.
2. Model Description
 The global model is based on Nucleus for European Modeling of the Ocean (NEMO) 2.3 which includes an ocean component Océan Parallelisé (OPA) [Madec et al., 1998] (http://www.lodyc.jussieu.fr/opa/) and the sea ice module Louvain Ice Model (LIM) [Fichefet and Morales Maqueda, 1997]. The model grid is a tri-3 polar 1 degree global ocean grid (ORCA1) from National Oceanography Center, Southampton, United Kingdom. The tripolar configuration has two poles in the northern hemisphere, one in Canada and the other in Siberia. The horizontal grid has a nominal resolution of 1° in longitude/latitude. The meridional grid spacing is smoothly reduced to 1/3° at the equator within a band of 3° from the equator. Near Fram Strait the grid spacing is about 50 km. There are a maximum of 46 levels in the vertical, with level thickness increasing from 6 m at the surface to 200 m at a depth of 1750 m and reaching a maximum value of 250 m at the bottom of the deep basins. The maximum depth represented in the model is 5720 m.
 Vertical eddy diffusivity and viscosity coefficients are computed according to an order 1.5 turbulent closure scheme based on a prognostic equation for the turbulent kinetic energy [Blanke and Delecluse, 1993]. Horizontal mixing of momentum is parameterized by Laplacian friction with horizontal viscosity, A, varying in proportion to the third power of grid spacing from a maximum of A = 2000 m2 s−1 at the equator where the zonal grid spacing is the largest. Eddy-induced tracer advection and along-isopycnal diffusion are parameterized following Gent and McWilliams  with lateral mixing coefficient set to be 1000 m2 s−1.
 Atmospheric forcing is taken from the recently compiled data set created for the Common Ocean-ice Reference Experiment (CORE2) [Large and Yeager, 2009]. The simulations were first run for 10 years using the “normal year forcing” (NYF) of CORE2, representing the climatology of the reanalysis period. Continuing from the end of the spin-up we ran simulations for the period 1958–2006. Model input forcing includes 6 hourly 10 m air temperature, 10 m wind velocities and humidity; daily short- and long-wave radiation, and total precipitation (rain plus snow). Turbulent heat and momentum fluxes are computed using bulk formulae available in NEMO 2.3. Monthly climatology is used for the runoff of major rivers. No surface restoring to sea surface temperature is applied. However, the model's sea surface salinity is restored to its monthly climatology with a 90 day restoring time scale instead of 15 days from HW09, since we want study variations of freshwater transports. This spin-up simulation is initialized with the January climatology of temperature and salinity (T-S), combining the Polar Science Center Hydrographic Climatology (PHC3.0, http://psc.apl.washington.edu/Climatology.html) at high latitudes with the T-S climatology of WOA05 (http://www.nodc.noaa.gov/OC5/WOA05/) at middle and low latitudes. An initial sea ice thickness of 3 m with snow thickness of 0.5 m is prescribed in Arctic regions where January sea surface temperature is less than 2°C above freezing point.
 The “Neptune effect,” described in detail by HW09, provides forcing of mean flows by eddy-topography interaction. Where frictional models often assume damping terms such as A∇2u in momentum, Neptune replaces A∇2u with A∇2(u − u*) where u* = −L2f × ∇logD and L is an eddy length parameter taken to be a weak function of latitude, ranging from L = 4 km at 90°N to L = 14 km at the equator. A conventional frictional model is recovered by taking L = 0. We refer to case L = 0 as “friction” and L ≠ 0 as “Neptune.” This implementation is very nearly as Nazarenko et al.  and was seen to be close to the leading term included by Polyakov .
 First we compare velocities fields for the two cases in the vicinity of Fram Strait. The averaging period is the entire 49 year period of the CORE2 reanalysis (1958–2006). The WSC and EGC are present in both simulations. Figure 1 shows the regional extent of WSC and EGC at 226 m in the friction and Neptune cases. The branch of WSC following the shelf edge is obtained by both friction and Neptune cases, while the branch following the northwestern slope of Yermak Plateau is only obtained by Neptune case in this coarse-resolution model. The friction case shows the recirculation of WSC starting at 77°N, to the south of the reported range between 78°N and 80°N, while the Neptune case has the recirculation of WSC extending up to 80°N. The three branches of the WSC described in the introduction are shown in the Neptune case.
 The WSC supplies the Arctic Ocean with Atlantic water, forming a warm (temperature > 0°C) intermediate water. Subsurface circulation in the interior of the Arctic, such as cyclonic rim currents and flows along the Lomonosov Ridge, will redistribute warm and salty water mass from North Atlantic Ocean. Rim currents and flows along the Lomonosov Ridge are missed by the friction case but well represented in the Neptune case (Figure 2), as is consistent with HW09. The 49 year mean velocity and temperature across Fram Strait are shown in Figure 3. Stronger flows entering and exiting the Arctic are seen with Neptune as expressed in stronger horizontal shears and greater depth penetration. Warmer temperature of inflowing WSC is also obtained in Neptune case. To check the impact of differences in heat transport through Fram Strait as a deep connector between North Atlantic and Arctic, we compare the average temperature in a region with latitude greater than 80°N at depth of 650 m (Figure 4). The friction case shows a drop of average temperature of about 0.18°C from 1958 to 2006, while stronger northward currents in the Neptune case result in a relatively stable temperature at this depth over the 49 years. There is also a difference in the initial temperature (1958) that results from the 10 year spin-up.
 To quantify the differences between the 2 cases, we use a current meter data set [Holloway 2008, 2011] to check model performances against observation. We test topostrophy, as defined in section 1.2. The region of Fram Strait defined here from 76°N to 80°N and west of 15°E includes 373 current meter sites spanning 48234 months or 402 years. Observed topostrophy is τ = 0.53. The friction case obtains τ = 0.33 while Neptune yields τ = 0.41.
 The relatively modest increase from τ = 0.33 to τ = 0.41 warrants a particular comment concerning the nature of entropic forcing. As described in section 1, this is a force resulting from the derivative of entropy, H, with respect to the coarsely represented flow, Y. In some regions, external forces configure Y so that some components of the derivative, ∂H/∂Y, are weak. For Neptune, this occurs when external forces already yield model u close to Neptune u*. Thus, external forces which tend to drive inflow to the Arctic on the Spitzbergen side (WSC) and outflow from the Arctic on the Greenland side (EGC) already have u close to u*. Elsewhere, external forcing may leave model u weak and ambiguous, far from u* and hence with larger components in ∂H/∂Y. We see this in Figure 4, showing pan-Arctic flow at 226 m and 650 m for friction and Neptune. While differences in the Fram Strait region are modest, differences elsewhere are larger [cf. HW09] with the Neptune cases in Figure 2b clearly reflecting cyclonic rim currents such as suggested by Rudels et al. [2004, and references therein].
 During the period 1997–2006 there was an intensive observational program along 79°N when S08 studied heat and volume transport, estimating 12 Sv northward and 14 Sv southward. These values are considerably larger than earlier inverse model estimates of 1.1 Sv for WSC and 6.2 Sv for the EGC [Schlichtholz and Houssais, 1999] or by Lique et al.  who reported 6.5 Sv northward and 8.3 Sv southward. Fieg et al.  report 3 Sv northward and 5 Sv southward in their model with a resolution of 27 km, while 10 Sv northward and 12 Sv southward in the model with a resolution of 9 km. Our coarse-resolution model with friction achieves 1.4 Sv northward and 3.7 Sv southward, while Neptune achieves 2.9 Sv northward and 4.8 Sv southward. The transports from the Neptune case are close to the transports by the 27 km resolution regional model by Fieg et al. , but smaller than those in their 9 km resolution regional model and also smaller than the transports from the 1/4° resolution global model of Lique et al. . The net transport through Fram Strait from friction case is 2.3 Sv, while the Neptune case produces 1.9 Sv, which is close to 1.8 Sv reported from the two global models [Maltrud and McClean, 2005; Lique et al., 2009] in Table 2, both of which have much finer resolution than our 1° resolution. The 1.9 Sv net transport by Neptune case is also close to the value of 2 Sv reported by S08.
 Time series of heat with reference temperature of −0.1°C, liquid freshwater with reference salinity of 34.8 PSU and ice transports are shown in Figure 5 from 1958 to 2006 for the friction and Neptune cases. The 49 year mean northward heat transport is substantially less with friction (7.5 TW) compared with Neptune (16.9 TW). Either value is small compared with 47.1 TW reported by Maslowski et al.  from a 1/12° Arctic Ocean model, and is also smaller than the reported 28 TW by Nguyen et al.  from a regional Arctic Ocean model with a resolution of 18 km.
 Southward liquid freshwater transport is slightly reduced from 65 mSv for friction to 55.8 mSv for Neptune. The finer grid model of Lique et al.  obtains a mean value of 54.7 mSv for the period from 1962 to 2002. While modeled freshwater transports by Lique et al.  and this study are higher than the estimate of 45 mSv by Meredith et al.  and that of 28 mSv by Aagaard and Carmack , our study suggests that the freshwater transport through Fram Strait has interannual and decadal variability with a range of 40 mSv to ∼80 mSv by the Neptune case. Lique et al.  also report strong variability of freshwater transports [Lique et al., 2009, Figure 9].
 Transports of freshwater as sea ice are similar for friction and Neptune with the friction case showing stronger ice transports than Neptune, as is consistent with the reduced ice tongue width reported by HW09.
 Insofar as Neptune forces the steady (temporal mean) velocity field, it is important assess whether the use of Neptune has an impact on temporal variability of transports. It is seen that the friction case exhibits temporal variations similar to the Neptune case. Increasing heat transports from mid-1980s to early 1990s (Figure 5) with both friction and Neptune agree with the model results of Zhang et al. [1998a]. While there is a slight increasing trend of heat transports during the last 2 decades, it is difficult to judge whether the trend is due to natural variability or model drift. Spielhagen et al.  report “Basinwide observations since 1980s detected multiyear events of AW (Atlantic water) spreading in the Arctic Ocean that featured both a strong warming and increased inflow to the Arctic.” The maxima of freshwater transports in late 1960s are consistent with Curry and Mauritzen , with reference to the Great Salinity Anomaly [Dickson et al., 1988]. Belkin  reports pulses of excess fresh water emitted from the Arctic in the 1980s and 1990s, as seen also in our model results.
 To allow more direct comparison between model results and observation, Figure 6 expands the portion 1997–2006 including monthly values. This can be compared with Figure 3.10 of S08 and with estimates of freshwater transports by Rabe et al. . Figure 6 (top) shows the monthly heat transports. In order to compare with the observed heat from S08, we used the definition of Atlantic water mass by S08, which is warmer than 1°C. The magnitude of observed annual mean heat transports ranges from ∼25 TW to ∼45 TW [S08, Figure 3.10], whereas the friction case achieves 5 TW to 14 TW. With Neptune the range of the modeled transports increase to 13 TW to 24 TW. Although the coarse-resolution model underestimates heat transport in either case, friction has nearly half the transports relative to Neptune.
Figure 6 (bottom) shows freshwater transports from our simulations. Rabe et al.  report an average liquid freshwater transport of 80 mSv based on the observational data for late summers of the years of 1998, 2004, and 2005. The average modeled mean freshwater transports of the late summers corresponding to the years of 1998, 2004, and 2005 are 87 mSv and 82 mSv for the friction and Neptune cases, respectively.
 From a coarse-resolution global ocean model, we've considered volume, heat and freshwater fluxes through the climatically important Fram Strait, a location where coarse-resolution models often underestimate the fluxes. We test the effect of including Neptune parameterization for unresolved eddy stress in comparison with a traditional frictional closure. Although modeled exchanges remain weak compared with observations and with results from fine-resolution models, we observe that Neptune yields an approximate doubling of volume exchanges and of heat transport while somewhat limiting the excess freshwater transport. Evaluation of regional topostrophy from the model and from current meter data likewise show the coarse-resolution model, while underrepresenting the observations, achieves higher topostrophy with Neptune. We further observe that Neptune has little impact on temporal variability of transports. Our results are consistent with Nazarenko et al. , who applied the Neptune parameterization in a regional model, obtaining much stronger currents through the Fram Strait. Likewise Polyakov , applying MEP (similar to Neptune) achieved more realistic EGC and WSC. Although the models used in these studies, both taking into account of eddy-topography interaction, are different, strengthened EGC and WSC by the parameterizations indicates that Neptune achieves stronger currents in channels which are normally not well represented by coarse-resolution models.
 For annul mean variations of heat transports carried by WSC from 1958 to 2006, the friction case gets 7.5 ± 6.2 TW while the Neptune case obtains 16.9 ± 6.6 TW. Anomalies of heat transports from the 2 cases are consistent with decadal variability. For the 49 years of freshwater transports carried southward by EGC, the friction case obtains a range of freshwater transports of 65 ± 22 mSv, and the Neptune case gets 55.8 ± 19.5 mSv. Either of these freshwater results falls within the range of uncertainty of observational estimates.
 We are grateful to the Department of Fisheries and Oceans (DFO) and its Center for Ocean Model Developments for Applications (COMDA) for supporting the global scale ocean modeling. Communications during the AOMIP meetings helped us to better understand the importance of the topic of the study. We thank anonymous reviewers for their comments which helped us improve the manuscript. We also thank AOMIP project (National Science Foundation Office of Polar Programs, award ARC-0804010) for financial support for the publication of this paper.