Effects of tidally driven mixing on the general circulation in the ocean model MPIOM

Transcription

1 Effects of tidally driven mixing on the general circulation in the ocean model MPIOM E. Exarchou a,b,, J.-S. von Storch b, J. Jungclaus b, a International Max Planck Research School on Earth System Modeling, Hamburg, Germany b Max Planck Institute for Meteorology, Hamburg, Germany Abstract A mixing parameterization, which produces spatial variations of diapycnal diffusivity depending on the locations of tidal energy dissipation over rough topography, is implemented in the MPI-Ocean Model. A simulation with this mixing parameterization is compared with two control experiments using the standard configuration, each one with different spatially constant background diffusivity. The diffusivity in the first experiment is strong above rough topography and weak over smooth regions. The experiment with tidal mixing reduces density bias and improves representation of the water masses. The deep enhanced mixing due to tides increases the deep and bottom circulation in the Pacific Ocean, and produces stronger western boundary currents. The Atlantic circulation is sensitive to tidal mixing, and the differences with the control runs are significant, but not dramatic. Tidal mixing induces stronger horizontal gradients of the deep and bottom water properties which, in turn, are responsible for the increase of the mass transport through the Drake Corresponding author. Address: Bundestrasse 53, Hamburg, Germany. Tel.: address: eleftheria.exarchou@zmaw.de (E. Exarchou) Preprint submitted to Ocean Modelling June 2, 2010

2 Passage. Regional effects of tidal mixing are also investigated. Significant changes are observed in the Nordic Seas: the tidal run produces Sv larger overflows than the two control runs. The results of the stronger overflows in the Nordic Seas and the stronger circulation in the Pacific Ocean are more comparable with the observations, and underline the importance of using a spatially variable diapycnal mixing for more realistic and physically based simulations. Keywords: Tidal mixing, Overflows, Nordic Seas Introduction Tidally driven mixing is thought to play a major role in driving the ocean general circulation, in the sense that it provides a large part of its energy supply. Estimates of earlier studies (Munk and Wunsch, 1998) indicate that tides account for half of the total energy that is required to sustain the deep ocean circulation, so tides are estimated to provide approximately 1 TW of the total 2 TW needed. These estimates are further supported by recent findings based on satellite altimetry (Egbert and Ray, 2003) and in-situ observations (Dushaw et al., 1995). In the vast area of the ocean, according to the observational studies, there is only weak turbulent mixing. Diapyncal diffusivity, which quantifies turbulent mixing, has over most of the ocean area a weak background value around 10 5 m 2 s 1. Over rough topography, on the other hand, diffusivity has values that are several orders of magnitude larger than the weak background diffusivity (Toole et al., 1994, Ledwell et al., 2000, Rudnick et al., 2003). The principal process that could account for the observed enhanced mixing over rough topography is generation of internal 2

3 tides (Laurent and Garrett, 2002). When barotropic tidal flow encounters rough topography, internal tides are generated, thus converting barotropic energy into baroclinic. Some of these internal tides are unstable and break immediately, creating locally enhanced turbulent mixing. The remaining tides radiate away from their location of generation, transferring energy into regions far away from their generation site, contributing to the weak background mixing. The resulting diffusivity, thus, is highly variable in space, with small background values over smooth regions and greatly enhanced values over rough topography. Both together, the locally enhanced turbulent mixing and the weak background mixing should account for the value of 1 TW that is needed to close the energy problem of the ocean s circulation (Munk and Wunsch, 1998). In most Ocean General Circulation Models (OGCMs) this spatial variability of diapycnal diffusivity that is connected to tides is not taken into account. The effects of tides is merely represented in the form of a spatially homogeneous background diffusivity. Several recent modeling studies (Simmons et al., 2004, Saenko and Merryfield, 2004, Montenegro et al., 2007, Hasumi and Suginohara, 1999, Huang and Jin, 2007, Schmittner et al., 2005) indicate that using more physically based spatially variable diffusion coefficients instead of using fixed constant values has a significant effect on the modeled ocean s circulation and noticeably improves the simulations of the ocean state. Simmons et al. compared two simulations with a OGCM, one with a spatially uniform diffusion coefficient and the other with spatially variable diffusion coefficient, representing the effect of tidal mixing over rough topography. In the latter case, diffusion was greatly enhanced close to the bottom, 3

4 depending on the bottom topography and the tidal amplitudes, and decayed exponentially to the weak value of 10 5 m 2 s 1 towards the surface. The two simulations had the same global average diffusion coefficient. This implies that the uniform mixing case has larger, spatially homogeneous, diffusivity values over smooth regions and far away from the bottom, whereas closer to the ocean floor and over rough topography it has weaker values compared to the variable mixing case. The tidal mixing scheme produced significantly better representation of the water masses. Large differences in the modeled meridional mass transports between the two cases were observed. The overturning of the Pacific in the tidal mixing case was found to be weaker and more in agreement with observational estimates. The Atlantic overturning was reduced by almost 50% compared to the uniform mixing case. This decrease can be attributed to the lower diffusivity value in the thermocline, which in the tidal mixing case is significantly smaller compared to the uniform mixing case. Saenko and Merryfield used the same tidal mixing scheme as Simmons et al.. In their study they compared a tidal mixing case with a simulation that had a weak background mixing equal to 10 5 m 2 s 1, thus deviating in their approach from Simmons et al. who instead compared two simulations with the same globally averaged diffusivity. Saenko and Merryfield found that without the tidal mixing scheme the deep North Pacific became nearly stagnant, whereas including topographically enhanced mixing produced inflow of abyssal waters into the Pacific from the south. The simulation with tidal mixing produces results that are closer to observational estimates. The strength of the North Atlantic overturning, however, remained almost the same in both cases. They also found that tidal mixing 4

5 was responsible for a deeper and stronger Antarctic Circumpolar Current, which is in better agreement with observations. The present study deals with the implementation of the tidal mixing parameterization proposed by Laurent et al. (2002) in the MPI-Ocean Model (MPIOM, Marsland et al. 2003) and investigates its effects on the large scale ocean circulation. This is the same tidal mixing scheme that was imple- mented in the studies of Simmons et al. and Saenko and Merryfield discussed above. Two questions will be addressed. First, whether the globalscale effects reported by Simmons et al. and Saenko and Merryfield can be reproduced by another OGCM. Secondly, what are the regional effects of the tidal scheme, which has not been discussed by the two aforementioned studies. Tidal mixing produces enhanced diffusivity attached to rough topography, hence, one expects direct effects on overflows and generation of regional water masses. Here, we will concentrate on the Nordic Seas. The Nordic Seas is an important deep water formation region, which supplies the global overturning circulation with deep dense water. Thus, it is of particular importance to assess and improve the ability of the model to reproduce the main characteristics of Nordic Seas climate. The impact of tidal mixing on the formation of the overflows has not been studied so far with an OGCM. The paper is organized as follows: the mixing parameterization, the OGCM and the experiments are described in Section 2. Section 3 describes the effects on the temperature and salinity distributions. The effects on the circulation are described in Section 4. The changes of the overflows in the Nordic Seas are discussed in Section 5. Finally, in the last section, the summary and the conclusions are given. 5

6 Methods 2.1. Model Description The model used in this study is the Max Planck Institute Global Ocean/Sea Ice Model MPI-OM (Marsland et al., 2003). It has an orthogonal curvilinear grid, with horizontal resolution 3 by 3 near the equator that increases towards the model poles, placed over Greenland and Antarctica. The model resolution is about km 2 in the Nordic Seas. There are 40 vertical levels. The subgridscale parameterizations of the model include a convective adjustment scheme (Marsland et al., 2003). We do not use enhanced diffusivity to parameterize convection because this would mask enhanced diffusivity due to tidal mixing. For the vertical eddy viscosity and diffusivity, the model follows the so-called PP scheme, suggested by Pacanowski and Philander (1981). According to the PP scheme, the total vertical diffusivity is given by k = k winds + k ri + k bg + (k tidal ), (1) where k winds accounts for the turbulent mixing close to the sea surface due to the wind, k ri is a Richardson number dependent term, and k bg is the background mixing term and accounts for other sources for mixing, predominantly due to internal waves. The last term, k tidal, represents the mixing due to tides and is added in one of the experiments. The model is forced by the OMIP climatological forcing dataset (Marsland et al., 2003). 6

7 Tidal mixing parameterization The tidal mixing parameterization, which determines the term in parenthesis in Eq. 1, was proposed by Laurent et al. (2002) and was used in the modeling studies of Simmons et al., Montenegro et al. and Saenko and Merryfield. The parameterization relates the diapycnal diffusivity k v to the energy flux per unit area that is lost from barotropic tides to internal tides E(x, y), according to k v (x, y, z) = k bg + k tidal = k bg + qγe(x, y)f (z) ρn(x, y, z) 2. (2) The term k tidal represents mixing due to local dissipation of waves over rough topography. The term k bg is the background diffusivity and represents mixing due to other internal waves, in particular those which, after being generated by barotropic tides, radiate away and dissipate outside the generation sites. Additionally, q = 0.4 is the portion of the tidal energy that dissipates locally, Γ = 0.3 is the mixing efficiency, ρ is the density, and N(x, y, z) is the buoy- ancy frequency. The values for the parameters k 0, Γ and ζ are the same used in the study of Simmons et al. We deviate, however, in our choice for the values of q and Γ, which were taken to be q = 0.3 and Γ = 0.2 in Simmons et al. Here we mention that we perform in total three tidal experiments with qγ = 0.06, as in Simmons et al., qγ = 0.08, and qγ = 0.12 (q and Γ appear together in Eq. 2, thus we consider their product). The three experiments have very similar behavior, but there are differences in the amplitude of the changes that occur when compared to the control runs. Our choice to show the results for the latter experiment (qγ = 0.12) is motivated by the more clear demonstration of the impact of the local dissipation of tides on the 7

8 ocean s circulation. Both parameters q and Γ are uncertain, and in a more detailed study it would be worth to investigate the sensitivity of the tidal mixing parameterization in each of their values (Jayne, 2008). F (z) of Eq by is a vertical structure function, which satisfies 0 H F (z)dz = 1, and is given F (z) = e (H+z)/ζ ζ(1 e H/ζ ), (3) where H is the total depth of the water column, and ζ = 500m is the vertical decay scale of turbulence. The meaning of the function F (z) is that the energy that originates from local mixing decays exponentially with height. The term k tidal scheme (Eq. 1). of Eq. 2 is added to the diffusivity calculated by the PP The energy flux per unit area that is lost from barotropic tides to internal waves E(x, y) is given by E(x, y) = 1 2 ρ 0N b (x, y)κh(x, y) 2 u(x, y) 2, (4) where ρ 0 is a reference density, N b (x, y) is the bottom buoyancy frequency, u 2 is the mean square tidal velocity, taken from a tidal model (Zahel and Müller, 2005), κ is the wavenumber of topography and is taken constant and h(x, y) 2 is the bottom roughness. The value for h(x, y) 2 is calculated by using the high resolution (2 minute) topography data from ETOPO2 1 1 U.S. Department of Commerce, National Oceanic and Atmospheric Administration, National Geophysical Data Center, minute Gridded Global Relief Data (ETOPO2v2) 8

9 dataset. Over each model grid cell a polynomial sloping surface is fitted to the bottom topography. The bottom roughness h(x, y) 2 is defined as the mean square of the residuals over the grid cells. The value for κ is diagnosed from the constraint that the area integral of E(x, y), with N b (x, y) taken from Levitus dataset (World Ocean Atlas 1998, hereafter WOA98; Levitus et al. 1998), represents an energy flux of 1 TW. In principle, however, κ should be calculated directly from topography data. The tidal mixing scheme, thus, depends on bottom roughness, mean tidal velocity amplitudes and stratification. It also evolves as part of the model solution, through its dependence on the buoyancy frequency N and the density ρ Experiments We performed three simulations that span 1000 years each. One simulation (hereafter called Tidal ) adds in the diffusion coefficient calculated from the PP scheme k the tidal term k tidal given in Eq. 2. The tidal effect, hence, is described by a spatially variable term, representing the local dissipation of tides over rough topography, and a weak background term k bg, representing the weak background mixing due to breaking of internal waves. The second simulation (hereafter called Ctr-high ) uses the PP scheme diffusivity k with the background term k bg equal to the sum of the global average of k tidal and the background term of Tidal: k bg ctr high m 2 s 1 = k bg tidal + k tidal. The tidal effect here is represented only by the constant background term. The third experiment (called Ctr-low ) is the same as Ctr-high, but with k bg = 10 5 m 2 s 1. The reason that motivates the choice of two, instead of one, control experiments, is that earlier studies (Scott and Marotzke, 2002) 9

10 suggested that the diffusivity value at thermocline depths strongly controls the MOC strength. The diffusivity in the thermocline is about the same in experiments Tidal and Ctr-low and stronger in experiment Ctr-high, whereas the diffusivity near the bottom is stronger in Tidal and weakest in Ctr-low. Therefore, the two control runs allow us to differentiate between results caused by increased mixing in the thermocline and results caused by deep mixing due to tides. The experiments are summarized in Table 1. The analysis that follows in the next sections uses time means of the last 200 years of the simulations. Hereafter, the term diffusivity refers to the whole term, i.e. the PP scheme coefficient plus the tidal term of our experiments, which is spatially variable in the tidal run and constant in the control runs. The PP scheme term is stratification-dependent. Since the stratification is also affected by the tidal mixing parameterization, the PP scheme term should be different among the three experiments. The tidal parameterization produces a three dimensional field of diffusivity k tidal that varies horizontally and vertically. In the vast ocean area, away from topography, the tidal scheme produces small diffusivity values. Above the mid-ocean ridges, however, where enhanced mixing due to internal tides is expected to occur, diffusivity values of the Tidal run are enhanced. An example of how the diffusivity increases with depth above rough topography in the Tidal run is shown in the vertical sections of diffusivity (Fig. 1, left panel). The two control runs, in contrast, have constant diffusivity (Fig. 1, middle and right panel). We note here that some grid points have increased values of diffusivity due to Richardson number dependencies at the bottom. 10

11 Figure 2 shows maps of diffusivity at 2000 m depth revealing the horizontal differences among the three experiments and how the spatial variability of the Tidal experiment occurs over the mid-ocean ridges. Common characteristics among all three experiments shown in this figure are the large diffusivity values in the Labrador Sea, Drake Passage and Ross Sea in Antarctica. These values are related to different dynamic ocean features, such as strong convection and mesoscale eddies, which are mainly wind driven and/or connected to particular topographic conditions. For the purpose of intercomparison of the current study with previous similar studies, we mention here that the experiments in Simmons et al. correspond to Tidal and Ctr-high, and the experiments in Saenko and Merryfield correspond to Tidal and Ctr-low Effects on temperature and salinity distributions The tidal mixing scheme affects the vertical distribution of temperature and salinity. The globally averaged temperature bias, defined as the departure from WOA98 data, is shown in the upper panel of Fig. 3. Experiments Tidal and Ctr-low produce significantly reduced bias above 3000 m compared to Ctr-high. At large depths, however, Tidal and Ctr-high have smaller bias compared to Ctr-low. The differences are not that clear in the salinity bias (3, bottom panel). Experiment Tidal has smaller bias everywhere when compared to Ctr-low. However, when compared to Ctr-high, Tidal has smaller bias above 1000 m and below 3500 m depth, but larger bias at m. There are some similarities with the Simmons et al. study, in which they compare their tidal simulation with a control run equivalent to our Ctr-high. 11

12 The temperature bias in the tidal simulation of this study is reduced in the whole water column, instead of the upper 3000 m. Their salinity bias is reduced significantly everywhere, in contrast to our results. Horizontal maps of the temperature bias at 960 m depth, which is the depth of the maximum bias of the three experiments, are shown in Fig. 4. The maps reveal that Tidal and Ctr-low have almost the same horizontal distribution of temperature bias, whereas Ctr-high has amplified positive bias over both the Atlantic and Pacific Ocean. A similar conclusion is derived from the map of the salinity bias at 645 m depth (Fig. 5), the depth of the larger salinity bias in all three runs. Ctr-high has amplified, but with similar structure, salinity bias, compared to the other two experiments. Ctrhigh, therefore, has the largest temperature and salinity bias of the three experiments at the depth of the largest bias amplitude. We can conclude that, at these depths, the thermocline value of diffusivity is the decisive factor that controls the magnitude of the bias. Since it is not clear from the differences in temperature and salinity biases among the three experiments whether there is an improvement in the water masses due to the introduced parameterization, a more consistent method to test this is to check both temperature and salinity errors, manifested in the density field. The globally averaged vertical density profile (Fig. 6) shows that Ctr-high has a significantly larger negative bias above 2000 m depth, suggesting that a strong diffusivity value in the thermocline amplifies the model drift from the WOA98 climatology and is not advisable for a realistic representation of the ocean. Ctr-low and Tidal are performing in a similar manner, with Tidal having larger density bias above 2000 m, but smaller 12

13 density bias below that depth, compared to Ctr-low. The difference between these two experiments is small, but, by checking the rms error in the density bias averaged over the ocean volume, we see that the Tidal run has smaller rms error than Ctr-low. The experiment Tidal, hence, represents better the water mass properties compared to both control runs. Horizontal maps of the density bias at 560 m depth (not shown) reveal that, at this depth, the Ctr-high density bias is the largest among the three runs, whereas the other two runs are comparable. It is worth noticing that, in the Nordic Seas, which is an important region for the global circulation, the density bias is negative in Ctr-high and positive in the other two runs. This, as to be investigated in more detail in the next section, is expected to have an impact on the production of the dense overflows that are formed in this region Effects on large scale circulation 4.1. The global meridional overturning circulation Atlantic In the Atlantic Ocean there are moderate, but significant differences in the meridional overturning streamfunction among the three runs (Fig. 7). The experiment Ctr-high has the strongest Atlantic MOC (hereafter referred as AMOC), defined here as the value of the overturning streamfunction at 48 N and 1000 m depth. The mean AMOC for the last 100 years is 19.9 Sv for experiment Ctr-high (1 Sv = 10 6 m 3 s 1 ), 18.4 Sv for Tidal and 16.6 Sv for Ctr-low. The difference of 1.5 Sv in AMOC strength between experiments Ctrhigh and Tidal, according to the study of Scott and Marotzke, could be 13

14 attributed to the larger diffusivity in the thermocline of Ctr-high. This result is consistent with Simmons et al. but less dramatic, since they find a 50% reduction in their tidal experiment compared to their control experiment, which is equivalent to experiment Ctr-high. This could be because the difference in the diffusivity values in the thermocline, between their tidal and control experiment, is m 2 s 1. In our case, however, the difference between Tidal and Ctr-high is m 2 s 1, thus, the resulting difference in AMOC strength between Tidal and Ctr-high is not very large. The difference of about 2 Sv between experiments Tidal and Ctr-low, which have the same diffusivity in the thermocline, indicates that the tidal mixing parameterization does have an effect in increasing the strength of the AMOC. However, this effect results in smaller increase in AMOC strength compared to the increase occurring when increasing the background diffusivity, as the 3.3 Sv difference between the two control runs indicates. Our result is in contrast to the Saenko and Merryfield study, where they find that the tidal mixing parameterization has no effect in their modeled AMOC. Another difference to notice is that experiment Ctr-low produces less northward transport of Antarctic bottom water compared to the other two experiments, which indicates that the deep/bottom circulation in Ctr-low is weak. Notice also the difference in the streamfunction at 70 N where the Nordic Seas deep water flow enters the North Atlantic. In the experiment Tidal the contribution of the Nordic Seas is about 0.35 and 0.9 Sv larger compared to the Ctr-low and Ctr-high. To examine whether the increase of the streamfunction value at 70 of Tidal is statistically significant, we perform a t-test, with the null hypothesis that the time means of the last 500 years of the 14

15 experiments are equal. The null hypothesis is rejected, with the probability of a false reject being 1%. The effect of the tidal mixing on the Nordic Seas overflow is further investigated in the following section Indopacific The overturning circulation in the Indopacific Ocean is quite different among the three experiments (Fig. 8). The experiment Tidal has overall a stronger overturning circulation overall, Ctr-high and Ctr-low transports are significantly weaker than the Tidal and of comparable magnitude, with Ctrhigh being slightly stronger than Ctr-low. There are qualitative differences among the experiments. More specifically, in the experiment Tidal there are isolines at 4500 m depth that reach the surface at about 50 N, indicating mass transport of 3 Sv from large depths to the surface. In contrast, in the experiment Ctr-high, a similar mass transport from the abyssal depths to the surface at this latitude is much weaker (1 Sv). In the experiment Ctr-low this effect is entirely absent. In the deep and abyssal equatorial Pacific flow at 4000 m depth, Tidal produces about 2 Sv stronger transport than the two control runs. This transport reaches about 50 N in Tidal, but only 35 N in the two control runs. The results produced from the tidal scheme are closer to observations (Schmitz, 1995), and similar to the study by Saenko and Merryfield, in which the North Pacific is stagnant in their control case, while their tidal case has significantly enhanced circulation. We note here that they compare their tidal simulation with a control run which is equivalent to our Ctr-low. In Simmons et al. on the other hand, the deep circulation in the Pacific is weaker in their tidal case compared to their control run, in contrast to our result. 15

16 The differences in the Indopacific meridional streamfunction between Tidal and the two control runs indicate that we should expect significant changes in the velocity field of these experiments. The circulation at intermediate depths is much more rigorous with a stronger western boundary current in the Tidal experiment (Fig. 9, upper panel), than in the two control runs (Fig. 9, middle and bottom panel) The Antarctic Circumpolar Current The Southern Ocean is an important region for the global ocean circulation. It connects all three oceans and affects their water masses. It is, thus, worth investigating how the circulation in this region is affected by the tidal mixing parameterization. A way to achieve this is to check the mass transport through the Drake Passage, which indicates in turn how the transport in the Antarctic Circumpolar Current (ACC) is affected. Previous studies (Gent et al., 2001) demonstrated that the Drake Passage transport of a coarse resolution global ocean model is sensitive to the value of background vertical diffusivity. This is the case, as shown by the Drake Passage mass transports (Table 2). All three experiments produce an unrealistically strong ACC transport, which, according to observations, is about 135 Sv (Cunningham et al., 2003). The problem of the strong ACC may be caused by other processes that are not of direct importance for the present study. The largest mass transport through the Drake passage occurs in the experiment Ctr-high, and is approximately 30 Sv larger than the transport in the experiment Ctr-low, which, in turn, has the weakest transport of all three experiments. The difference between the mass transports of Ctr-high and Ctr-low accounts to 15 % of the total mass transport of the Ctr-low experi- 16

17 ment. The magnitude of the mass transport produced by Tidal is in between the magnitudes of the mass transports of the two control experiments, and 8 % larger than the total transport of Ctr-low (see Table 2). Russell et al. (2005) suggested that the strength of the ACC transport is related to the westerly winds, the air-sea heat flux gradient and the depthintegrated density gradient over the latitude band around Drake Passage. All three experiments have the same forcing, thus the differences in the Drake Passage mass transports of the three experiments must lie in differences in the gradient of the depth-integrated density across the ACC latitude band. Indeed we find out that the depth-integrated density gradient across ACC is strongest in Ctr-high, weakest in Ctr-low, and in-between the two control experiments in Tidal (Table 2). The differences in the horizontal density gradient can arise from differences in the horizontal temperature or salinity gradient. Examining the T, S gradients at different depths between 40 and 60 S in the Atlantic Ocean (not shown) reveals that both T, S gradients of Ctr-high, which is the experiment with the strongest Drake Passage transport, are the strongest of all three runs above 1500 m depth. However, below 3000 m depth, the strongest T, S gradients occur in Tidal. The depth-dependence of the horizontal T, S gradients, suggests that even if the ACC strength increases in both experiments Tidal and Ctr-high relative to Ctr-low, there is a qualitative difference between them: the increase in the ACC strength in Ctr-high is mainly caused by an increase in the T, S gradients above 1500 m depth, whereas the increase in the ACC strength in Tidal is mainly caused by an increase in the T, S gradients below 3000 m depth. This is also consisted with the result of the more energetic deep and bottom 17

18 375 circulation of Tidal in the Indopacific ocean Effects on the overflows in the Nordic Seas There are two proposed mechanisms for the formation of the dense overflows in the Nordic Seas. One mechanism is open ocean deep convection in the Greenland and Iceland Seas. Recent studies, however, contradict this view and suggest an alternative view (Mauritzen, 1996). The dense overflows are a product of gradual densification of warm and saline Atlantic water as it flows northwards in the Nordic Seas and, through the Barents and Fram Straits, enters the Arctic Ocean. These water masses are further diapycnally modified in the Arctic Ocean and re-enter the Nordic Seas via the Fram Strait, and constitute, along with the water masses formed from convection events in the Greenland Sea and Iceland Sea, the deep overflow that exits the Greenland-Scotland Ridge. This latter scenario can be further explained as the following: Atlantic Water flows along the Norwegian Coast and gets gradually denser, primarily due to heat loss to the atmosphere. By the time this water mass reaches north of the Lofoten Basin it separates into three branches. One branch, known in the literature as return Atlantic Water, returns in the west south direction, meets the East Greenland Current and flows along the Greenland coast where it finally exits the Nordic Seas as overflow via the Denmark Strait (DEN). The second branch enters the Arctic Ocean through the Fram Strait. During its transit in the Arctic Ocean, this mass gets modified and returns back into the Nordic Seas and exits through DEN into the North Atlantic as a second overflow mass, known as Arctic Atlantic Water. The third branch enters the Barents Seas and the Arctic 18

19 Ocean, it gets denser through diapycnal modifications and enters back into the Nordic Seas through the Fram Strait. This mass exits the Nordic Seas as an overflow across the Iceland-Scotland Ridge (ISR) (Hansen and Osterhus, 2000, Dickson and Brown, 1994). According to this latter scenario, the deep convection in the Greenland Sea is not the main player for the production of the dense overflows across DEN and ISR, but rather the heat loss to the atmosphere and turbulent diapycnal mixing in the intermediate and deep waters in the Nordic Seas. This view is supported by observational findings from a tracer-release experiment in the Greenland Sea (Watson et al., 1999). Convection, according to the results, was found to be responsible for only a limited portion of the water masses that were vertically transported. These findings imply that turbulent mixing may be the dominant factor for the vertical mixing in the region. This possibility was explored by Visbeck and Rhein (1999), who quantified how large vertical mixing should be in a bottom boundary layer with thickness equal to 150 m, so that there is ventilation of the deep and bottom waters of the Greenland Sea, in the absence of deep convection. The order of magnitude of the values of diffusivity they calculated is 10 2 m 2 s 1 and is feasible in a tidal mixing scenario. Observations of the actual values of diffusivity in the Nordic Seas (Garabato et al., 2004) found elevated diffusivities below 500 m in the eastern basin of the Nordic Seas and below 2000 m across the whole area of the Nordic Seas. In the Greenland Sea the observed diffusivities were m 2 s 1, thus smaller than the estimate of Visbeck and Rhein ( 10 2 m 2 s 1 ), but, not confined into a thin bottom layer, instead being spread in regions even 1000 m above the ocean bottom. In the 19

20 study of Garabato et al., the suggested energy source for the elevated turbulent mixing in the deep layers is the breaking of tidal internal waves that are not locally generated over rough bottom topography. This suggestion deviates from our study, which addresses the role of the direct dissipation of tides on bottom topography. However, the local tidal dissipation results in elevated diffusivities in up to 1000 m above the ocean bottom in our model. Thus, apart from difference in the interpretation, the vertical distribution of diffusivity here does not qualitatively deviate from the one found in the above observational study. To summarize, it is suggested by the aforementioned studies that turbulent mixing, and more specifically, the turbulent mixing in deep waters due to tides, plays an important role in shaping the stratification of the water masses and contributing, complementary to the atmospheric heat loss, to the diapycnal transformation of the water masses to dense overflows. Modifying the mixing scheme in the model, hence, is expected to result in an impact on the dense water formation in the Nordic Seas. Before we look into the changes among the experiments induced by the differences in the diffusivities, we consider the basic differences between the experiment with the tidal mixing scheme and the two control experiments for the particular region of the Nordic Seas. The map of the converted barotropic energy into baroclinic energy E(x,y) in the Nordic Seas, estimated from Eq. 4, is shown in Fig. 10. The majority of the barotropic tidal energy conversion takes place above the Greenland-Scotland Ridge, above the Mohn Ridge, in the coastal shelves along Greenland and Norway and in the Arctic Ocean. In these places, hence, we should expect elevated values of diffusivity close 20

21 to the bottom, in the experiment Tidal. In Fig. 11 the diffusivities in 1440 m depth are shown for all three experiments. We remind here that these diffusivities are the whole term in Eq. 1, thus differences among the three experiments are not only due to the tidal and background terms, k tidal and k bg in Eq. 1, but also because of the Richardson number term k ri. The latter is expected to be quite different, because of the different stratifications in the experiments. The diffusivity shown in Fig. 11 is only August values, and the reason is that we want to exclude the effect of elevated diffusivities due to the homogeneous water column that follows the winter convection. Ctr-low has the highest diffusivities at the Greenland Sea, implying that the Richardson number dependent term k ri is higher. At the Greenland-Scotland Ridge, the Tidal experiment has the highest values, which are clearly due to tidal mixing at this region (Fig. 10). Hence, in Tidal we have large values in the Greenland-Scotland Ridge, close to the Norwegian shelves, and in the Arctic Ocean. The enhanced values are within the range of values found in the observations of Garabato et al.. In the Ctr-low run, on the other hand, we have high values in the Greenland Sea. To see how the overflows change, we examine the last 200 years time series of the overflow transport, which is defined as transport of water with potential densities σ 0 > 27.8 kg m 3 (σ 0 is potential density with reference pressure at the sea surface). We choose 27.8 kg m 3 as a density threshold value for defining the overflows because it is widely used in the literature. Why we use a common threshold value for all three experiments and in both DEN and ISR may not seem obvious. Using 27.6 or 27.7 kg m 3 as threshold value yields different results. However, even if we relax the constraint of common 21

22 density threshold value, and instead choose different threshold value for each experiment and each overflow channel, according to which value gives the highest overflow transport, the relative differences in total overflow transports among the three experiments do not change. Thus, to avoid complication, and since the conclusions remain the same, we continue this analysis using the 27.8 kg m 3 threshold value. The locations of the transects in DEN and ISR where the transports are calculated are shown in Fig. 10. Table 3 summarizes the transports. The Tidal experiment produces 0.7 and 0.3 Sv stronger total overflow compared to Ctr-high and Ctr-low, respectively. Tidal converts 52.6% of its total inflow to overflows, compared to 50.2% for Ctr-low and 43% for Ctr-high. The Tidal experiment is, thus, more effective in diapycnally transforming light incoming water to dense overflows compared to both control experiments. The differences in overflow between Ctr-low and Tidal are, although not very large, persistent for at least 400 years of the simulations (not shown), implying that the stronger overflows are a solid result of the Tidal simulation, related to the differences in diffusing temperature and salinity due to tidal mixing. The total transport of 5.3 Sv in Tidal presents an improvement over the control runs, although it is still smaller than the 6 Sv of total overflow estimated from the observations (Hansen and Osterhus, 2000). The differences in overflows are not related to atmospheric changes, since the forcing is the same for all three experiments. The reasons for the changes are related to the differences in the mixing scheme. Mixing affects temperature and salinity, thus also the density of the water masses. The density distribution, in turn, affects the height of the 27.8 kg m 3 isopycnal surface. 22

23 The latter is the interface between overflows and upper lighter water masses. The height of this interface is considered to be an indicator of the potential energy stored in the Nordic Seas, and potential energy in the Nordic Seas is the driver of the overflows (Jungclaus et al., 2008). Larger overflows in the experiment Tidal imply that there should be more potential energy, hence larger interface height, in Tidal compared to both control runs. To test this hypothesis, we plot the height of the interface (Fig. 12) from a reference level (here, 700 m). The differences between Tidal and Ctr-high are significant and evident in the whole region of the Nordic Seas, consistent with the large differences in the overflows in DEN and ISR between Tidal and Ctr-high. The differences between Tidal and Ctr-low, however, do not occur over the entire Nordic Seas. Instead, the Tidal experiment has larger interface height in few grid points close to ISR. We point out here that it is in the ISR that the differences between Tidal and Ctr-low in the time series of the overflows (not shown) are more distictive through out the whole last 200-year period. The relation between overflow strength and the height of the 27.8 kg m 3 isopycnal surface is consistent with previous work, according to which a strong relation between overflow and interface height exist only close to the overflow channels (Jungclaus et al., 2008). The grid points that have the most pronounced differences in interface height between Tidal and Ctr-low are above the ISR overflow channel, as shown in a vertical transect slightly north of the sills of DEN and ISR (Fig. 13). The question arises about the role of convection in changing the density distribution, and from that the interface height in our experiments. Convection can be sensitive to mixing. Mixing alters stratification, which, in turn, 23

24 can potentially alter convection. According to this hypothesis, one would expect that the Tidal experiment, since it has the largest overflow, it would have more intensive convection. One way to examine this is to check convection depth. Here, we note that the convection depth has the drawback that it does not necessarily give information about the convection strength, or the potential energy released during convection. The experiment Tidal, which has the strongest overflow, does not have the largest convection depth (not shown). Quite the contrary, the Ctr-low run is the one with the largest convection depth in the Greenland Sea, which is also consistent with its elevated diffusivities in this region. The convection, which is one of the suggested mechanisms for overflow formation, does not seem to be responsible for the overflow changes in our experiments. Our results support the second suggested mechanism, according to which the overflows are a product of gradual conversion of light water to overflows via atmospheric heat loss and diapycnal mixing (Mauritzen, 1996). The latter, enhanced in the Tidal simulation close to the bottom in some grid points, leads to a more effective diapycnal tranformation of light water to dense overflows. The second mechanisms does not exclude differences in circulation in the Nordic Seas. Fig. 14 shows velocities averaged over the σ 0 isopycnal surfaces kg m 3 (these are the densities of the densest water masses in DEN). In this figure we can see the pathways of water masses that create the densest part of the DEN overflows. There is an important difference between Ctr-high and Tidal (the circulation patterns between Ctr-low and Tidal are comparable). The dense part of DEN overflows in the Tidal run (and Ctr-low) are originating partly from Atlantic water circulating in the 24

25 Nordic Seas, and partly from Arctic water that enters through the Fram Strait. In Ctr-high, in contrast, the Arctic branch is missing. The lack of contribution from Arctic water masses in the DEN overflows in Ctr-high can explain why its overflows are the lowest of all three experiments Summary and discussion The current study discusses the effects of the tidal mixing parameterization proposed by St. Laurent et al. (2002) on the MPI-Ocean Model MPIOM. This scheme produces spatial variations of diapycnal diffusivity depending on the locations of tidal energy dissipation over rough topography. Three experiments were carried out: one experiment with the tidal mixing scheme (Tidal), a second experiment with the standard configuration and background diffusivity equal to the global average of the diffusivity of the Tidal experiment (Ctr-high), and a third experiment with the standard configuration and the same background diffusivity as in the Tidal experiment (Ctr-low). Tidal and Ctr-high have the same globally averaged diffusivity, but different diffusivity at intermediate depths. Tidal and Ctr-low have different globally averaged diffusivity, but equal diffusivity at intermediate depths. Changes occur on the temperature and salinity distribution, the large-scale circulation, and on the formation of the overflows in the Nordic Seas. The Tidal experiment has reduced density bias, thus improved representation of the water masses, compared to both control runs. When it comes to the large-scale circulation, there are changes in all three major oceans. The Atlantic MOC increases in both Tidal and Ctr-high, compared to Ctr-low, by about 2 and 3 Sv, respectively. This result implies that the Atlantic MOC 25

26 is sensitive to both factors that can affect MOC strength: enhanced mixing in the thermocline in Ctr-high, and enhanced deep mixing due to tides in Tidal. Moreover, mixing in the thermocline is more efficient in controlling the AMOC than the mixing due to tides. In the Indopacific Ocean, on the other hand, deep tidal mixing seems to play a larger role than enhanced mixing in the thermocline. This is specially evident in the deep and bottom waters. The increase in the Indopacific circulation of the Tidal experiment is more comparable with observations, and emphasizes the role of tidal mixing for more realistic simulations. Regarding the circulation in the Southern Ocean, Ctr-high and Tidal produce 15% and 8% stronger mass transport of the ACC in the Drake Passage than Ctr-low, respectively. The increased transports are caused by enhanced horizontal temperature and salinity gradients. The increase in the horizontal gradients in Ctr-high and Tidal occur at different depths: above 1500 m depth in Ctr-high, and below 3000 m depth in Tidal run. This result underlines the changes in the water properties at large depths, due to deep tidal mixing. Tidal mixing affects the diapycnal transformation of warm and saline Atlantic water into dense overflow. The dense waters cross the Greenland- Scotland Ridge and supply the North Atlantic with dense water masses. The effect of the tidal mixing is to increase the overflow by Sv compared to Ctr-low and Ctr-high, respectively. The stronger overflows produced in the experiment with tidal mixing (5.3 Sv) are still less than the observations (6 Sv), but they are an improvement over both control runs. The increase in the overflows is caused by an increase of the potential energy stored in the Nordic 26

27 Seas, indicated by the height of the 27.8 kg m 3 isopycnal surface. This surface is the interface between overflows and upper lighter water masses, and is lifted in the Tidal experiment due to changes in the stratification. The connection between the lift of the interface and the overflows seems to be important only in regions close to the overflow channels. Other reasons for the overflows changes can be identified in changes in the circulation field. It seems that changes in the pathways of the water masses in Ctr-high are partly responsible for its weak overflows in DEN. As the results in overflows of Ctr-low and Tidal are comparable, the question arises why should one consider the tidal simulation the preferable choice. The answer lies in the large-scale changes. Ctr-low Atlantic MOC (AMOC) is not very strong. To make AMOC stronger, an obvious solution would be to increase the background diffusion. Such solution indeed increases AMOC. However, it gives unsatisfactory results in the Nordic Seas. Using the tidal mixing scheme, on the other hand, increases AMOC strength, and improves the Nordic Seas overflows. In combination with the other changes which improve the representation of the water masses and the large-scale circulation, the results of the tidal parameterization suggest that it should be recommended for future simulations and further emphasize the importance of using a variable mixing scheme in ocean models Acknowledgments This work is partly funded by the DFG through the research project Sonderforschungsbereich 512. We thank Daniela Matei and Ismael Núñez- Riboni for their useful comments. This work is supported by the Max Planck 27

28 Society and the International Max Planck Research School on Earth System Modelling. 28

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