• Boris, J. P., , and D. L. Book, 1973: Flux-corrected transport. Part I: SHASTA: A fluid transport algorithm that works. J. Comput. Phys., 11 , 3869.

    • Search Google Scholar
    • Export Citation
  • Bryan, F., 1986: High-latitude salinity effects and interhemispheric thermohaline circulations. Nature, 323 , 301304.

  • Bryan, F., 1987: Parameter sensitivity of primitive equation ocean general circulation models. J. Phys. Oceanogr., 17 , 970985.

  • Danabasoglu, G., , J. C. McWilliams, , and P. R. Gent, 1994: The role of mesoscale tracer transports in the global ocean circulation. Science, 264 , 11231126.

    • Search Google Scholar
    • Export Citation
  • Duffy, P. B., , P. Eltgroth, , A. J. Bourgois, , and K. Caldeira, 1995: Effect of improved subgrid scale transport of tracers on uptake of bomb radiocarbon in the GFDL ocean general circulation model. Geophys. Res. Lett., 22 , 10651068.

    • Search Google Scholar
    • Export Citation
  • England, M. H., 1995: Using chlorofluorcarbons to assess ocean climate models. Geophys. Res. Lett., 22 , 30513054.

  • England, M. H., , and A. C. Hirst, 1997: Chlorofluorocarbon uptake in a World Ocean model. 2. Sensitivity to surface thermohaline forcing and subsurface mixing parameterizations. J. Geophys. Res., 102 , 1570915731.

    • Search Google Scholar
    • Export Citation
  • England, M. H., , and S. Rahmstorf, 1999: Sensitivity of ventilation rates and radiocarbon uptake to subgrid-scale mixing in ocean models. J. Phys. Oceanogr., 29 , 28022827.

    • Search Google Scholar
    • Export Citation
  • Gent, P. R., , and J. C. McWilliams, 1990: Isopycnal mixing in ocean general circulation models. J. Phys. Oceanogr., 20 , 150155.

  • Gent, P. R., , J. Willebrand, , T. J. McDougall, , and J. C. McWilliams, 1995: Parameterizing eddy-induced tracer transports in ocean circulation models. J. Phys. Oceanogr., 25 , 463474.

    • Search Google Scholar
    • Export Citation
  • Gerdes, R., , C. Köberle, , and J. Willebrand, 1991: The influence of numerical advection schemes on the results of ocean general circulation models. Climate Dyn., 5 , 211226.

    • Search Google Scholar
    • Export Citation
  • Gregory, J. M., , O. A. Saenko, , and A. J. Weaver, 2003: The role of the Atlantic freshwater balance in the hysteresis of the meridional overturning circulation. Climate Dyn., 21 , 707717. doi:10.1007/s00382-003-0359-8.

    • Search Google Scholar
    • Export Citation
  • Griffies, S. M., 1998: The Gent–McWilliams skew flux. J. Phys. Oceanogr., 28 , 831841.

  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437471.

  • Ledwell, J., , A. Watson, , and C. Law, 1993: Evidence for slow mixing across the pycnocline from an open-ocean tracer-release experiment. Nature, 364 , 701703.

    • Search Google Scholar
    • Export Citation
  • Manabe, S., , and R. J. Stouffer, 1988: Two stable equilibria of a coupled ocean–atmosphere model. J. Climate, 1 , 841866.

  • Manabe, S., , and R. J. Stouffer, 1994: Multiple-century response of a coupled ocean–atmosphere model to an increase of atmospheric carbon dioxide. J. Climate, 7 , 523.

    • Search Google Scholar
    • Export Citation
  • Manabe, S., , and R. J. Stouffer, 1999: Are two modes of thermohaline circulation stable? Tellus, 51A , 400411.

  • Marotzke, J., 1999: Convective mixing and the thermohaline circulation. J. Phys. Oceanogr., 29 , 29622970.

  • Pacanowski, R., 1995: MOM2 documentation user’s guide and reference manual. GFDL Ocean Group Tech. Rep. 3, NOAA/GFDL, Princeton, NJ, 232 pp.

    • Search Google Scholar
    • Export Citation
  • Rahmstorf, S., 1993: A fast and complete convection scheme for ocean models. Ocean Modell., 101 , 911.

  • Rahmstorf, S., 1996: On the freshwater forcing and transport of the Atlantic thermohaline circulation. Climate Dyn., 12 , 799811.

  • Redi, M. H., 1982: Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr., 12 , 11541158.

  • Saenko, O. A., , and A. J. Weaver, 2003: Atlantic deep circulation controlled by freshening in the Southern Ocean. Geophys. Res. Lett., 30 , 1754. doi:10.1029/2003GL017681.

    • Search Google Scholar
    • Export Citation
  • Saenko, O. A., , A. J. Weaver, , and J. M. Gregory, 2003: On the link between the two modes of the ocean thermohaline circulation and the formation of global-scale water masses. J. Climate, 16 , 27972801.

    • Search Google Scholar
    • Export Citation
  • Sijp, W. P., , and M. H. England, 2004: Effect of the Drake Passage throughflow on global climate. J. Phys. Oceanogr., 34 , 12541266.

  • Sijp, W. P., , and M. H. England, 2006: Sensitivity of the Atlantic thermohaline circulation and its stability to basin-scale variations in vertical mixing. J. Climate, 19 , 54675478.

    • Search Google Scholar
    • Export Citation
  • Sijp, W. P., , M. Bates, , and M. H. England, 2006: Can isopycnal mixing control the stability of the thermohaline circulation in ocean climate models? J. Climate, 19 , 56375651.

    • Search Google Scholar
    • Export Citation
  • Sørensen, J. V. T., , J. Ribbe, , and G. Shaffer, 2001: Sensitivity of a World Ocean GCM to changes in subsurface mixing parameterization. J. Phys. Oceanogr., 31 , 32953311.

    • Search Google Scholar
    • Export Citation
  • Visbeck, M., , J. Marshall, , T. Haine, , and M. Spall, 1997: Specification of eddy transfer coefficients in coarse-resolution ocean circulation models. J. Phys. Oceanogr., 27 , 381402.

    • Search Google Scholar
    • Export Citation
  • Weaver, A. J., and Coauthors, 2001: The UVic Earth System Climate Model: Model description, climatology, and applications to past, present and future climates. Atmos.–Ocean, 39 , 10671109.

    • Search Google Scholar
    • Export Citation
  • Zalesak, S. T., 1979: Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys., 31 , 335362.

  • View in gallery

    (a) Averaging regions used for the NP (dark gray) and the NA (including the Arctic, light gray). The white dashed line in the NA indicates the northern boundary of the FW perturbation region. (b) Temporal development of the FW perturbation applied to the NA. Shown is an example where the maximum perturbation M is 0.75 m yr−1.

  • View in gallery

    Zonally averaged Atlantic salinity and overlaid Atlantic meridional overturning streamfunction (Sv; annual mean) for NADW (a) on and (b) off. Zonally averaged Atlantic potential temperature for NADW (c) on and (d) off. Results are shown for Kρ = 4 × 102. Note that the horizontal axis has a northern limit of 70°N, precluding the Arctic. A surface volume containing all Atlantic water north of 49.5°N and above 292-m depth is indicated by the white rectangle in the upper-right corner of each panel, and this volume is interpreted as the surface layer containing the NADW formation regions.

  • View in gallery

    (a) NADW formation (Sv), (b) NPDW–NPIW formation (Sv), (c) the AABW deep cell, and (d) the FW flux maximum (m yr−1) required to shut down NADW formation. This flux in (d) is determined up to 0.25 m yr−1 accuracy. Values are shown against the log10 of the along-isopycnal diffusion coefficient, i.e., log10(Kρ). No multiple equilibria are found beyond the diffusivity value marked by the vertical line. For comparison, the FW flux threshold required to shut down an equivalent experiment employing only horizontal diffusion (HD) is also shown as the horizontal line marked “HD” in (d). This value (0.4875 m yr−1) gives a sense of the response of the model in the absence of along-isopycnal diffusion. FW perturbations up to a value of 1.5 m yr−1 have been applied. The stability of the NADW formation for diffusivities beyond the vertical line has been further examined using experiments similar to those shown in Fig. 7. Additional experiments employing implicit diffusive vertical mixing instead of the convective adjustment algorithm of Rahmstorf (1993) were also conducted and yielded identical results (not shown).

  • View in gallery

    The NP (a) potential temperature (°C), (b) heat fluxes (J s−1), (c) salinity (psu), and (d) salt fluxes (kg s−1) against the log of the along-isopycnal diffusion coefficient. Heat and salt fluxes are decomposed into along-isopycnal diffusion (iso), advective transport (adv), GM eddy advective transport (adv*), transport by convection and diapycnal diffusion (Kv, conv), and surface tracer flux (stf). The advective transport terms include both the horizontal and vertical components. (e) Also shown are the mean salinity anomaly produced by a 4-yr-long linear pulse attaining a maximum value of 0.30 m yr−1 and (f) the associated anomalous fluxes integrated over a period of 50 yr after the pulse. All values are averaged over a 292-m-deep surface volume in the NP between 49.5° and 63.9°N.

  • View in gallery

    As in Fig. 4 but for the NA (including the Arctic Ocean). All values are averaged over a 292-m-deep surface volume in the NA extending northward of 49.5°N (see also Fig. 2).

  • View in gallery

    The NA response of the experiment where Kρ = 4 × 102 m2 s−1 to a 300-yr FW pulse insufficient to permanently shut down NADW in these experiments (attaining a maximum of 0.75 m yr−1). Time series of (a) salinity (psu), (b) NADW formation (Sv), (c) salt fluxes (Sv) for Kρ = 4 × 102 m2 s−1 (kg m−2), and (d) salt fluxes (Sv) for Kρ = 4 × 103 m2 s−1 (kg m−2). Results are shown for the experiments where Kρ = 4 × 102 m2 s−1 and Kρ = 4 × 103 m2 s−1 in (a) and (b). Salt fluxes (Sv) are decomposed according to the process outlined in Figs. 4 and 5: along-isopycnal diffusion (iso), advective transport (adv), GM eddy advective transport (adv*), and transport by convection and diapycnal diffusion combined (Kv, conv). The advective transport terms include both the horizontal and vertical components.

  • View in gallery

    The NA response of the NADW off state of the Kρ = 4 × 103 m2 s−1 experiment when this case is subjected to a sudden increase in isopycnal diffusivity Kρ from 4 × 103 m2 s−1 to 8 × 103 m2 s−1 at time 0. Time series of (a) NADW formation (Sv), (b) the AAIW reverse cell (Sv; see Fig. 2b), (c) the change in salinity of the NA surface volume, (d) the salinity below the NA surface volume, (e) the anomalous salinity fluxes (Sv) of the NA surface volume, and (f) the anomalous salinity fluxes (Sv) below the NA surface volume against time elapsed since the change in Kρ. Salt fluxes are decomposed according to the process outlined in Figs. 4 and 5, although advection is now combined as the total (Eulerian + GM) vertical and horizontal components of the advection. The water volume below the surface volume (denoted by “surface”) is denoted by deep and extends north of 49.5°N and below 292-m depth.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 8 8 3
PDF Downloads 2 2 0

The Control of Polar Haloclines by Along-Isopycnal Diffusion in Climate Models

View More View Less
  • 1 Climate Change Research Centre, Faculty of Science, University of New South Wales, Sydney, New South Wales, Australia
© Get Permissions
Full access

Abstract

Increasing the value of along-isopycnal diffusivity in a coupled model is shown to lead to enhanced stability of North Atlantic Deep Water (NADW) formation with respect to freshwater (FW) perturbations. This is because the North Atlantic (NA) surface salinity budget is dominated by upward salt fluxes resulting from winter convection for low values of along-isopycnal diffusivity, whereas along-isopycnal diffusion exerts a strong control on NA surface salinity at higher diffusivity values. Shutdown of wintertime convection in response to a FW pulse allows the development of a halocline responsible for the suppression of deep sinking. In contrast to convection, isopycnal salt diffusion proves a more robust mechanism for preventing the formation of a halocline, as surface freshening leads only to a flattening of isopycnals, leaving at least some diffusive removal of anomalous surface FW in place. As a result, multiple equilibria are altogether absent for sufficiently high values of isopycnal diffusivity. Furthermore, the surface salinity budget of the North Pacific is also dominated by along-isopycnal diffusion when diffusivity values are sufficiently high, leading to a breakdown of the permanent halocline there and the associated onset of deep-water formation.

Corresponding author address: Willem P. Sijp, CCRC, University of New South Wales, Sydney, NSW 2052, Australia. Email: w.sijp@unsw.edu.au

Abstract

Increasing the value of along-isopycnal diffusivity in a coupled model is shown to lead to enhanced stability of North Atlantic Deep Water (NADW) formation with respect to freshwater (FW) perturbations. This is because the North Atlantic (NA) surface salinity budget is dominated by upward salt fluxes resulting from winter convection for low values of along-isopycnal diffusivity, whereas along-isopycnal diffusion exerts a strong control on NA surface salinity at higher diffusivity values. Shutdown of wintertime convection in response to a FW pulse allows the development of a halocline responsible for the suppression of deep sinking. In contrast to convection, isopycnal salt diffusion proves a more robust mechanism for preventing the formation of a halocline, as surface freshening leads only to a flattening of isopycnals, leaving at least some diffusive removal of anomalous surface FW in place. As a result, multiple equilibria are altogether absent for sufficiently high values of isopycnal diffusivity. Furthermore, the surface salinity budget of the North Pacific is also dominated by along-isopycnal diffusion when diffusivity values are sufficiently high, leading to a breakdown of the permanent halocline there and the associated onset of deep-water formation.

Corresponding author address: Willem P. Sijp, CCRC, University of New South Wales, Sydney, NSW 2052, Australia. Email: w.sijp@unsw.edu.au

1. Introduction

The stability of the formation of North Atlantic Deep Water (NADW) constitutes an important area of research in physical oceanography. Manabe and Stouffer (1994) find a collapse of NADW under greenhouse gas–induced warming and attribute this to an enhanced hydrological cycle due to warming. Although this scenario is conceivable in the real climate system, there is ambiguity in climate models as to the precise sensitivity of the ocean’s thermohaline circulation (THC) to freshwater (FW) perturbations. Knowledge of this threshold is important for understanding future responses of the THC to greenhouse gas–induced warming and past climatic fluctuations during glacial periods. Important sources of uncertainty can be traced to the diapycnal mixing scheme employed in ocean models (Manabe and Stouffer 1999; Sijp and England 2006) and the inclusion of along-isopycnal mixing to parameterize subgrid-scale effects (Sijp et al. 2006).

Deep convection during winter plays an important role in deep-water formation in the global ocean. This process depends on the presence of sufficiently dense surface water and constitutes an important mechanism whereby surface properties are transferred into the deep ocean. Modeling studies indicate that the cessation of deep convection in the NA under enhanced FW input at the surface due to increased precipitation or ice melt may bring about the general shutdown of the Atlantic THC (Manabe and Stouffer 1988). The process of deep convection is parameterized by a form of fast mixing in ocean models, as the vertical acceleration term is not represented explicitly due to the hydrostatic approximation. Convective adjustment algorithms are used (e.g., Rahmstorf 1993), although the application of very large vertical diffusivities to remove vertical instability is now common in most Intergovernmental Panel on Climate Change (IPCC) class models. Convective instability is highly sensitive to freshwater anomalies at the surface, as the vertical mixing criterion depends on the unstable stratification of the water column. Deep sinking at polar regions generally occurs in net precipitation zones, so that sufficiently large FW anomalies at the surface may grow due to longer residence times associated with decreased convection, leading to a “halocline catastrophy” (Bryan 1986). This positive feedback can culminate in a subsequent cessation of deep sinking.

Large-scale general circulation models of the World Ocean must take account of the transfer of properties due to eddies. Constraints on computing power, and therefore grid resolution, still require these processes to be parameterized for global integrations run for long periods of simulated time. Early parameterizations employed fixed horizontal and vertical diffusion to simulate the effect of subgrid-scale eddies on ocean tracers. However, mixing along isopycnal surfaces is stronger than diapycnal mixing by several orders of magnitude (e.g., Ledwell et al. 1993), and isopycnals can have a significant slope at higher latitudes. To improve the accuracy of ocean models, Redi (1982) introduced the now so-called Redi diffusion scheme, an ocean model parameterization whereby along-isopycnal diffusion represents the tendency of tracers to mix along isopycnal surfaces due to eddies. We will refer to this along-isopycnal diffusion in models simply as isopycnal diffusion in this paper, not to be confused with isopycnal thickness diffusion. A further attempt at improving the realism of ocean models was made by Gent and McWilliams (1990, hereafter GM) and Gent et al. (1995), who introduced a parameterization of the effect of subgrid-scale eddies on isopycnal layer thickness. Further improvements in the GM scheme were made by Griffies (1998), who elegantly unified the tracer mixing operators arising from Redi diffusion and Gent–McWilliams stirring. Unlike the Redi (1982) scheme, the isopycnal thickness diffusion terms enable the horizontal mixing to be set to zero, although naturally the isopycnal diffusion is retained to represent along-isopycnal mixing. The eddy-induced tracer advection terms have a tendency to flatten isopycnal surfaces and also promote downslope flows (e.g., England and Hirst 1997). The flattening of the isopycnals arising from this scheme leads to reduced convection depth and transport (e.g., Danabasoglu et al. 1994; England 1995; Duffy et al. 1995; England and Rahmstorf 1999; Sørensen et al. 2001), with water mass formation occurring in more localized regions.

The Redi (1982) diffusion scheme is generally implemented using a fixed diffusivity coefficient, Kρ. Visbeck et al. (1997) argue for a diffusivity coefficient that varies in space and time. They estimate values of between 3 × 102 m2 s−1 and 2 × 103 m2 s−1 for Kρ, depending on location. Another source of uncertainty associated with isopycnal diffusion is associated with its effect on NADW stability. Surface salinity anomalies arising from FW pulses applied over a limited period of time cause sharp gradients of salinity along outcropping isopycnals, as found by Sijp et al. (2006), who show that this leads to strong isopycnal diffusion of the surface anomaly into the interior. This process is in fact the dominant tracer removal mechanism from the North Atlantic surface in their model, whereby rapid diffusive sequestration of FW anomalies applied to the NA surface leads to enhanced NADW stability with respect to FW perturbations. In other words, isopycnal diffusion leads to a reduced likelihood of a halocline catastrophy, effectively increasing the FW threshold required to shut down NADW formation in models.

The tight connection between NADW stability and the use of isopycnal diffusion in noneddy-resolving models shown by Sijp et al. (2006) introduces the possibility that NADW stability may also depend on the magnitude of the isopycnal diffusion coefficient. This could further infer a strong control of isopycnal diffusion over the polar halocline in ocean models. In this study, we use an ocean–atmosphere–sea ice model of intermediate complexity to examine the impact of the magnitude of the isopycnal diffusion coefficient Kρ on the NADW stability. We vary Kρ over a range of magnitudes, while keeping the other mixing parameters fixed, including the isopycnal thickness diffusivity (4 × 102 m2 s−1). We then examine the resulting NADW stability with respect to FW pulses applied to the North Atlantic. We vary Kρ over a range of magnitudes and examine the resulting NADW stability with respect to FW pulses applied to the North Atlantic. We find that there is a significant dependence of the FW threshold on the isopycnal diffusion coefficient, whereby stable model solutions where NADW is absent are excluded beyond a certain value of diffusion. Furthermore, we examine the control of the isopycnal diffusion over the halocline of the North Pacific (NP) and find that, at sufficiently high values of Kρ, the NP halocline is unable to form, resulting in enhanced North Pacific Intermediate Water (NPIW) formation, deep enough to be more aptly named North Pacific Deep Water (NPDW).

The rest of this paper is divided as follows. In section 2 we describe the model and our experimental design. In section 3 we present and discuss the results of our experiments. Finally, in section 4 we include a summary and the main conclusions.

2. The model and experimental design

We use the intermediate-complexity coupled model [the University of Victoria (UVic) model] described in detail in Weaver et al. (2001). This comprises an ocean general circulation model the Geophysical Fluid Dynamics Laboratory’s (GFDL) Modular Ocean Model (MOM) version 2.2; Pacanowski (1995)] coupled to a simplified one-layer energy–moisture balance model for the atmosphere and a dynamic–thermodynamic sea ice model of equal global domain and horizontal resolution of 1.8° latitude × 3.6° longitude. Air–sea heat and freshwater fluxes evolve freely in the model, yet a noninteractive wind field is employed. The wind forcing is taken from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis fields (Kalnay et al. 1996), averaged over the period 1958–97 to form a seasonal cycle from the monthly fields. No flux corrections are used (for further model details, see Weaver et al. 2001), allowing the surface temperature and salinity to vary freely in the model. This allows the full operation of the thermal and salinity feedback, which enables multiple equilibria of the ocean THC (e.g., Sijp and England 2004). Diapycnal mixing is modeled using a diffusivity that increases with depth, taking a value of 0.3 cm2 s−1 at the surface and increasing to 1.3 cm2 s−1at the bottom. We use version 2.7 of the UVic model. Moisture transport in the atmosphere occurs by way of advection and diffusion. The atmosphere employs a spatially varying moisture diffusion coefficient attaining maximal values in the midlatitudes of the SH (Saenko and Weaver 2003).

The release of potential energy by convective overturning of the water column is modeled using the convective adjustment algorithm described by Rahmstorf (1993; see also Pacanowski, 1995). Neutral physics in regions of steeply sloping isopycnals is handled by quadratic tapering as described by Gerdes et al. (1991). We use a maximum isopycnal slope of 1:100. Isopycnal mixing is implemented after Redi (1982), and eddy-induced advection after Gent and McWilliams (1990). In the standard model configuration, isopycnal diffusion occurs via a constant coefficient of 4 × 102 m2 s−1 and isopycnal thickness diffusion with a constant coefficient of 4 × 102 m2 s−1. In the sensitivity experiments we vary the isopycnal diffusion coefficient over a range of values. We use the flux corrected transport (FCT) scheme (Boris and Book 1973; Zalesak 1979; Gerdes et al. 1991) for advective tracer fluxes. The GM eddy advection contribution is implemented through the FCT advection scheme. The thickness of the surface ocean layer is 50 m, and no mixed layer scheme is employed, other than enhanced diapycnal diffusion across the bottom of the first surface layer. A rigid-lid approximation is used and surface freshwater fluxes are modeled by way of an equivalent salt flux calculated using a fixed reference salinity of 34.9 psu.

We have run the model to equilibrium with respect to the applied forcing over a period of several thousands of years using different values for the isopycnal diffusivity. This resulted in steady states with NADW formation. To examine the robustness of each of these steady states, we applied FW pulses of varying magnitude to the NA for a duration of 300 yr between 49.5° and 76.5°N. Figure 1 shows the averaging regions used for the North Pacific and the North Atlantic (including the Arctic), and the northern boundary of the freshwater perturbation region. Also shown is the temporal development of the freshwater perturbation applied to the North Atlantic. The pulse attains its maximum value of M m yr−1 at year 150. We have subjected each equilibrium to a range of FW perturbations and determined the threshold value for M required to cause a shutdown of NADW with an accuracy of 0.0375 m yr−1. We denote those equilibria where NADW is present by referring to the NADW as “on,” and denote the absence of NADW as NADW “off.” We obtained stable NADW on states for all values of Kρ. As shown below, we obtained stable NADW off states only for values of Kρ below 5 × 103 m2 s−1.

3. Results

a. Meridional overturning response

We first briefly examine the NADW on and off states in our standard model configuration for reference (i.e., with Kρ = 4 × 102 m2 s−1). Figure 2 shows the zonally averaged Atlantic salinity and Atlantic meridional overturning streamfunction overlaid, and the zonally averaged Atlantic potential temperature for the NADW on and off states and Kρ set to 4 × 102 m2 s−1. The overturning in the NADW on state exhibits 21.5 Sv (Sv ≡ 106 m3 s−1) of NADW formation, whereas the NADW off state is characterized by an “AAIW reverse cell” of 10.3 Sv, whereby cool freshwater originating from the AAIW formation regions flows into the Atlantic basin at 1000–1500-m depth, compensated by a warm saline southward return flow near the surface (see also Gregory et al. 2003; Sijp and England 2006). While NADW formation is associated with saline Atlantic conditions (Fig. 2a), the NADW off state (Fig. 2b) exhibits a marked freshening due to the net import of FW by the AAIW reverse cell. We indicate a surface volume containing all Atlantic water north of 49.5°N and above 292-m depth by the white rectangle shown in Fig. 2, and interpret this volume as the surface layer containing the NADW formation regions. Note that the white box shown in Fig. 2 only extends to 70°N. This depth range captures the volume of water affected by summer conditions in the model. We will examine the evolution of the T and S properties of this surface volume throughout the rest of this paper.

A strong and deep halocline and potential temperature inversions can be seen across much of the North Atlantic in the NADW off state (Figs. 2b and 2d). This shows that the stability of the NADW off state is ensured by stable salinity stratification only. In contrast, the NADW on state (Fig. 2a) only exhibits a shallow halocline restricted to the upper 300 m in the annual mean, reflecting summertime stratification in the absence of deep convection (this feature is absent during winter). Summertime surface properties do not penetrate much below 300-m depth in the NADW on case, due to stable stratification arising from warm saline surface conditions during this period. Therefore, deeper layers underneath the denoted surface area reflect wintertime conditions characterized by vertically well-mixed T–S properties associated with deep convection and sinking (Figs. 2a and 2c) in the yearly average.

Figure 3 shows NADW formation, NPIW–NPDW formation, and the AABW deep cell strength at steady state, as well as the FW flux maximum required to shut down NADW formation as a function of the log of the isopycnal diffusion coefficient Kρ. The values of our experiments are denoted by an asterisk (*) and are connected by lines. There is a decrease in NADW overturning rates for values of Kρ beyond 2 × 103 m2 s−1, whereby values below 18 Sv are reached beyond 8 × 103 m2 s−1 (Fig. 3a). This is because of the onset of competing NPDW (Fig. 3d), attaining values of up to 10.5 Sv. As we will see, this is because of the dominance of isopycnal diffusion in the surface salinity budget of the NP, whereby diffusion of warm saline subtropical water into the subpolar surface leads to the removal of the NP halocline. The reduction of NADW formation with an increasing diffusion coefficient Kρ contrasts sharply with experiments where diapycnal diffusion is increased, leading to stronger NADW formation as in Bryan (1987). Compared to NADW and NPIW, AABW remains relatively stable, yielding values of around 10–11 Sv for diffusivity values between 1 × 102 m2 s−1 and 8 × 103 m2 s−1.

To find the threshold whereby NADW collapses for each value of the diffusion coefficient Kρ, we apply 300-yr FW pulses of different magnitudes to each steady state. We determine the flux required to shut down NADW formation, and define the threshold by trial and error up to the nearest 0.0375 m yr−1 for the applied FW flux. The maximum FW flux required to shut down NADW formation increases with Kρ (Fig. 3d). For comparison, Fig. 3d also shows the FW flux threshold required to shut down an equivalent experiment employing only horizontal diffusion (HD) to model the effects of subgrid-scale eddies on ocean tracers. This value (0.4875 m yr−1) gives a sense of the response of the model in the absence of along-isopyncal diffusion. The thresholds for all of the examined diffusivity values of Kρ are higher than that found for the horizontal diffusion (HD) experiment. The collapse threshold of 0.6187 m yr−1 for Kρ = 1 × 10−1 m2 s−1 and Kρ = 1 × 10° m2 s−1 is above that found for the HD experiment. Beyond Kρ = 1 × 101 m2 s−1, the collapse threshold increases with Kρ, reaching a value of 0.8062 m yr−1 at Kρ = 4 × 102 m2 s−1 (Fig. 3d), a 30% increase over Kρ = 1 × 100 m2 s−1. The sensitivity of the collapse threshold to Kρ increases for Kρ above Kρ = 4 × 102 m2 s−1, whereby Kρ = 4 × 103 m2 s−1 requires 1.1437 m yr−1 for a shutdown of NADW formation. This is nearly double the value required for Kρ = 1 × 10° m2 s−1, and nearly 50% more than the value required in the Kρ = 1 × 102 m2 s−1 case. The increasing sensitivity of the threshold values beyond experiment Kρ = 4 × 102 m2 s−1 culminates in the absence of multiple equilibria for Kρ values of 5 × 103 m2 s−1 and higher. Note that the enhanced stability of NADW and the subsequent elimination of NADW off states occur despite a decrease in NADW overturning rates for Kρ beyond Kρ = 2 × 103 m2 s−1 (Fig. 3a). The range of values where no stable NADW off state exists is demarked by the vertical line (Figs. 3a–d). To further confirm the absence of a stable NADW off state, we have subjected the experiments where we could not find this state to pulses of different magnitudes (up to peak values of 1.5 m yr−1) and duration and found no permanent state transitions. Furthermore, we have taken the stable NADW off state of the experiment where Kρ = 4 × 103 m2 s−1, and found that increasing the isopycnal diffusivity to values above 5 × 103 m2 s−1 leads to the rapid and spontaneous reestablishment of the NADW on state. These results were obtained using the convective adjustment algorithm described by Rahmstorf (1993). To examine the sensitivity of our results to the choice of convective adjustment parameterization, we have instead conducted an additional group of experiments employing implicit vertical diffusive mixing. Here, large vertical diffusivities allow rapid mixing of vertically unstable water columns analogous to the Rahmstorf (1993) scheme. The results of these additional experiments (not shown) are identical to the standard results, showing that our results are robust with respect to the parameterization of convective mixing.

b. Mechanisms

We now assess the causes for the formation of NPDW at higher diffusivity values by examining the heat and salt budget of a 292-m-deep surface volume in the North Pacific between 49.5° and 63.9°N. Figure 4 shows the salinity, the temperature, and the salt and heat flux budgets according to process for this surface volume, and the results of a stability analysis that we will discuss shortly. Temperature values remain between 4° and 4.5°C for Kρ between 1 × 10−1 m2 s−1 and 1 × 102 m2 s−1 (Fig. 4a), and then increase above 5°C for higher isopycnal diffusivity values. The heat balance is between heat loss to the overlying atmosphere and advective heat gain for Kρ between 1 × 10−1 m2 s−1 and 1 × 102 m2 s−1 (Fig. 4b). The advective heat gain mainly consists of horizontal advective exchange between the cool NP surface volume and the warmer thermocline water to the south (not shown). This horizontal transport increases for Kρ above 4 × 102 m2 s−1 as a result of the increased NP overturning circulation, whereby warmer subtropical thermocline water enters the NP sinking region. This leads to more heat loss to the overlying atmosphere due to warmer sea surface temperatures. There is also a modest contribution of isopycnal diffusion at higher values of Kρ.

Salinity remains at similar values just below 33.5 psu for Kρ between 1 × 10−1 m2 s−1 and 1 × 102 m2 s−1 (Fig. 4c), followed by an increase in NP surface salinity for Kρ = 4 × 102 m2 s−1 and above. The main balance is between freshening due to dilution with rain, river runoff and sea ice melt, and a net salt input by advective processes for diffusivity (Kρ) values between 1 × 10−1 m2 s−1 and 1 × 102 m2 s−1 (Fig. 4d). Unlike heat, the net addition of salt to the NP surface volume by advective processes arises from vertical advective exchange with the saline water underlying the NP halocline (not shown), and not through horizontal exchange with thermocline water south of the NP surface volume. Isopycnal diffusion increasingly contributes to the salinity budget for diffusivity (Kρ) values above 4 × 102 m2 s−1, while the advective contribution is reduced accordingly. The increased influx of salt by along-isopycnal diffusion at high values of Kρ leads to a reduction in the vertical salinity gradient, thus reducing the vertical advective exchange of salt.

Another way of examining the influence of different processes over NP surface salinity is to look at which processes are responsible for the stability of the salinity values in the NP surface volume. A model state is stable if sufficiently small perturbations, such as salinity anomalies, are prevented from growing and taking the model to a different (quasi-)steady state or an oscillatory regime (larger perturbations generally do take the model to a different state). Model solutions that are unstable with respect to very small perturbations cannot be maintained in the model, as such anomalies arise perpetually from numerical noise. Hence, we now examine which processes are responsible for the removal of small salinity anomalies applied to the NP. We apply a 4-yr FW pulse attaining a brief maximum of 0.30 m yr−1 at year 2 and examine the fluxes responsible for the removal of this salinity anomaly and the restoration of the steady state. We have verified that this pulse does not engender a response in the thermohaline circulation, and the model state remains close to equilibrium. The anomalous flux terms excited by the brief perturbation are calculated relative to a concurrent control integration where no perturbation is applied. The maximum salinity anomaly arising from the pulse takes values between 0.01 and 0.04 psu (Fig. 4e). Figure 4f shows the 50-yr integral of the anomalous flux terms as a function of the isopycnal diffusion coefficient Kρ. Advection removes the salinity anomaly for Kρ values between 1 × 10−1 m2 s−1 and 4 × 102 m2 s−1. Unlike the salt flux balance (Fig. 4d), removal of the FW anomaly here is accomplished by horizontal, rather than vertical, advection (not shown). Convection and diapycnal diffusion play no significant role for any of the values of Kρ, except perhaps 1 × 103 m2 s−1, where advection and isopycnal diffusion are equally important. Then, at higher values of Kρ, the isopycnal diffusion becomes the main restoring force, with advective effects becoming small. Advection even takes on a negative value at Kρ = 6 × 103 m2 s−1. This shows that the stability, and therefore the magnitude, of the salinity values of the NP surface volume for values of Kρ between 6 × 103 m2 s−1 and 8 × 103 m2 s−1 are determined by isopycnal diffusion. In other words, the FW perturbation would persist or grow in the absence of a diffusive response to the short-lived salinity anomalies, leading to the development of a different surface salinity. Therefore, the elevated salinity values, and thus the formation of NPDW when Kρ is large, are a direct result of the control exerted by isopycnal diffusion over the NP surface.

Figure 5 shows a similar analysis for the NA using the 292-m-deep surface volume extending north of 49.5°N shown in Fig. 2. Temperature decreases for higher values of Kρ due to lower NADW formation rates (Fig. 2a). Similar to the NP, advection is a dominant heating term in the NA surface heat budget for all values of Kρ (Fig. 5b) whereby the positive heat contribution arises from the horizontal exchange between the NA surface volume and the warm subtropical regions to the south (not shown). In contrast to the NP, convection (diapycnal diffusion is negligible; not shown) is a dominant term for low values of Kρ. Isopycnal diffusion becomes more important and convection less important as Kρ progressively increases. As above, convection is a dominant factor in the salinity budget for lower values of Kρ (Fig. 5d), whereas advection plays a lesser role. Unlike in the NP, the positive advective salinity contribution in the NA arises from the horizontal exchange between the high-latitude region and the saline subtropics to the south, and sinking of water that has been freshened by precipitation (not shown). This pattern is associated with the North Atlantic THC. The roles of isopycnal diffusion and convection are reversed for higher values of Kρ, whereby convection and isopycnal diffusion have similar values around Kρ = 4 × 102 m2 s−1, and then isopycnal diffusion dominates for high values of Kρ. Unlike the NP, a deep halocline extending beneath the surface box is absent in the NA (when NADW formation is present; see Fig. 2a). Deep convection is an important mechanism whereby deeper warm saline water is mixed upward into the surface volume in winter at low values of Kρ, thus preventing the development of a halocline due to net precipitation (note that the convective term was absent in the NP heat and salt budget). The crossover between convection and diffusion near Kρ = 4 × 102 m2 s−1 in the graph in Fig. 5d illustrates isopycnal diffusion taking on this function of convection at higher diffusivity. In other words, isopycnal diffusion prevents the development of a halocline at high values of Kρ. The salinity remains remarkably similar for all values of Kρ (Fig. 5c), despite a reduction in NADW formation at higher values of Kρ. Convection and advection are the main restoring factors at low values of Kρ (Fig. 5f), whereas isopycnal diffusion constitutes the main mechanism for the removal of small FW perturbations at larger values of Kρ. This indicates that isopycnal diffusion has a strong control over salinity in the NA surface volume at high values of Kρ. This may explain why the surface salinity remains at remarkably similar values while NADW formation is reduced at high levels of Kρ.

We now examine the salt fluxes involved in a recovery of NADW formation in response to a 300-yr FW pulse applied at the surface for different diffusivity values Kρ. Figure 6 shows the NA response at values Kρ = 4 × 102 m2 s−1 and 4 × 103 m2 s−1 to a 300-yr freshwater (FW) pulse insufficient to permanently shut down NADW in these experiments (attaining a maximum of 0.75 m yr−1). The FW perturbation applied in these experiments is significantly larger and of longer duration than those shown in Figs. 4e and 4f and Figs. 5e and 5f. As a result of the larger perturbation, the evolution of the model state deviates significantly from its original steady state. Unlike the small perturbation experiments (Figs. 4 and 5), here we look at the processes that are responsible for the FW pulse thresholds required to obtain an NADW collapse at different values of Kρ (see Fig. 3d). The salinity anomaly has largely been resolved by year 700 for Kρ = 4 × 102 m2 s−1 and 4 × 103 m2 s−1 under the FW pulse (Fig. 6a), whereby the maximum anomaly is smallest for Kρ = 4 × 103 m2 s−1. Similarly, NADW is temporarily suppressed to around 5 Sv, followed by an almost complete recovery by year 700 for Kρ = 4 × 102 m2 s−1 and 4 × 103 m2 s−1 (Fig. 6b).

We have seen that in a steady state, convection and isopycnal diffusion make similarly significant positive contributions to the NA surface salinity for Kρ = 4 × 102 m2 s−1 when NADW is present (Fig. 5), and both flux processes constitute an important factor in ensuring the prevention of the development of a permanent deep halocline. The application of the FW pulse leads to a temporary and nearly complete suppression of the convective transfer of salt from deeper layers into the NA surface volume by year 200 (Fig. 6c) for Kρ = 4 × 102 m2 s−1. Note that convective salt transfer plays no significant role in the steady state of Kρ = 4 × 103 m2 s−1. Oceanic removal of the surface salinity anomaly is, however, achieved by different processes in the two experiments. In Kρ = 4 × 102 m2 s−1, strong anomalous advective salt transport into the NA surface volume peaks at year 150 (Fig. 6c) and is largely responsible for the eventual reestablishment of deep-water formation in the region. In contrast, the salinity anomaly leads to a strong temporary increase in the isopycnal diffusion of salt into the NA surface volume in the experiment where Kρ = 4 × 103 m2 s−1 (Fig. 6d). Advective salt transport exchange also increases here due to increased vertical and horizontal salinity gradients. The increase in isopycnal salt diffusion results from an increased salinity gradient along isopycnals outcropping in the NA due to the negative salinity anomaly at the surface (the diffusive fluxes are proportional to the salinity gradients along the isopycnals), despite a possible reduction in isopycnal slope. This shows that isopycnal diffusion is responsible for the enhanced stability of NADW formation with respect to FW perturbations at higher values of isopycnal diffusivity Kρ, as a similar response is absent at low values of Kρ. Convection helps prevent the development of an NA halocline at low values of Kρ, whereas isopycnal diffusion takes on this role at higher values of Kρ. This is due to the difference in the responses of these two mechanisms that strong isopycnal diffusion leads to more stable NADW formation. Namely, convection responds to anomalies by shutting down, whereas isopycnal salt diffusion into the NA surface volume increases in response to a negative surface salinity anomaly.

c. Lack of multiple equilibria

We now examine the reason for the instability of any NADW off state for values of Kρ above 5 × 103 m2 s−1. To do so, we have taken the stable NADW off state where Kρ = 4 × 103 m2 s−1 and instantaneously increased Kρ to 8 × 103 m2 s−1. This leads to a recovery of NADW whereby we examine the fluxes responsible for this transition. Figure 7 shows the NA response to this change in Kρ magnitude, showing NADW formation, the AAIW reverse cell (see Fig. 2b), changes in the salinity of the NA surface volume, changes in the salinity below the NA surface volume, changes in the salinity fluxes of the NA surface volume, and changes in the salinity fluxes below the NA surface volume against the time elapsed since the initial change in Kρ. The recovery of NADW begins immediately after the change of Kρ (Fig. 7a; time 0), while the AAIW reverse cell enters an immediate decline, culminating in its cessation by year 1300 (Fig. 7b). This reverse cell is generally associated with the absence of NADW formation in ocean models (Manabe and Stouffer 1988; Saenko et al. 2003) and, once established, may be responsible for the continued suppression of NH sinking (Saenko et al. 2003; Gregory et al. 2003; Sijp and England 2006) due to freshwater import into the Atlantic basin. The NADW formation rate increases because the surface salinity increases (Fig. 7c). In its place, this increase in surface salinity is caused by a strong positive anomaly in the isopycnal salt diffusion flux into the surface (Fig. 7e; just after time 0). This anomaly is particularly strong at time 0 when the change in the coefficient Kρ is first applied. Later in the integration, beyond year 500, the anomalous upwelling of salt makes a positive salt contribution as well. Horizontal advection at the surface is reduced throughout the integration due to the decreased horizontal salinity gradient. The salinity of the water volume below the NA surface volume (i.e., north of 49.5°N and deeper than 292-m depth, denoted by “deep”) also increases in response to the increase in Kρ at time 0 (Fig. 7d). This is initially due to an increase in (horizontal) isopycnal diffusion and horizontal advection. As NADW increases and the AAIW reverse cell diminishes, horizontal advection becomes the dominant cause of the increasing salinity of the deep NA water volume (red curve in Fig. 7f). This is due to the fact that the Atlantic THC constitutes a net (advective) import mechanism of salt into the North Atlantic (Rahmstorf 1996), whereas the AAIW reverse cell leads to a net export of salt from the North Atlantic (Sijp and England 2006; Gregory et al. 2003). Eventually, isopycnal diffusion begins to export salt from the NA deep volume around year 500 (black curve in Fig. 7f). This change reflects the steepening of NA isopycnals in response to the removal of the deep halocline, allowing diffusive salt loss from the NA deep volume to the NA surface volume. As no diffusive salt loss from the NA deep volume occurs shortly after time 0, the initial large diffusive salt gain of the surface volume must arise from horizontal isopycnal diffusion. This is in agreement with a reduced slope of the isopycnals associated with the deep NA halocline of the NADW off state. However, eventually, most of the diffusive salt gain in the NA surface volume is derived from the underlying water, as the isopycnals progressively steepen.

These results show that the recovery of the NADW on state in response to an increase in isopycnal diffusivity Kρ arises directly from an increase in isopycnal salt diffusion into the NA surface volume. This leads to increased surface salinity and erodes the deep halocline that is responsible for the original suppression of NA sinking. Therefore, the instability of the NADW off state at high values of Kρ arises from the inability to maintain an NA halocline due to excessive isopycnal diffusion of salt into the surface waters of the region.

4. Discussion and conclusions

We have shown that increasing the value of along-isopycnal diffusivity in a coupled model of intermediate complexity (the UVic model) leads to the enhanced stability of NADW formation with respect to FW perturbations. This is because the North Atlantic (NA) surface salinity budget is dominated by upward salt fluxes resulting from winter convection for low values of along-isopycnal diffusivity, whereas along-isopycnal diffusion exerts a strong control on the NA surface salinity at higher diffusivity values. At low values of Kρ, deep wintertime convection in the NA prevents the development of a permanent halocline, as warm saline subsurface water is mixed into the cool fresh surface layer. Indeed, convection constitutes a dominant positive term in the salinity and heat budgets of the NA surface. Convection shuts down in response to a sufficiently strong FW pulse due to stable vertical stratification arising from the anomalous salinity gradient associated with the FW addition. This prevents the deep winter mixing of cold surface water, leaving water throughout large parts of the water column too buoyant to enter the abyss, thus shutting down NADW formation. At higher values of Kρ, isopycnal diffusion partially takes over this role of convection, whereby the isopycnal diffusion of salt along isopycnals outcropping in the NA during winter prevents the development of a permanent halocline. However, the behavior of isopycnal diffusion is different from that of convection. Unlike convection, the isopycnal salt flux does not rely on the a priori condition of unstable vertical stratification, and so it behaves differently under the application of an FW pulse. At high values of Kρ, the isopycnal diffusion temporarily increases as FW is applied, due to higher isopycnal salinity gradients. Multiple equilibria are altogether absent for sufficiently high values of the isopycnal diffusivity (in the case of our model, this threshold is approximately 5 × 103 m2 s−1). This is because an NA halocline is unable to form due to strong isopycnal diffusion of salt into the NA surface. We note that the presence of convection or isopycnal diffusion is not necessary for the existence of NADW formation in ocean models, as shown by Marotzke (1999). Indeed, in some model configurations, the horizontal advection of salt into the NA may be sufficient to prevent the formation of a polar halocline. Instead, our results show that convection and isopycnal diffusion are instrumental in determining the threshold for NADW collapse. Finally, the surface salinity budget of the North Pacific is also dominated by along-isopycnal diffusion when diffusivity values are sufficiently high, leading to a breakdown of the permanent halocline there, and the associated onset of local deep-water formation.

The values of Kρ estimated by Visbeck et al. (1997) of between 3 × 102 m2 s−1 and 2 × 103 m2 s−1 imply a significant influence of isopycnal diffusion on the NA heat and salt budgets, as well as on NADW stability. The high end of this range in particular implies a dominance of isopycnal diffusion over the salt budget of the NA surface volume. Furthermore, the latest version 2.8 of the UVic intermediate-complexity model employs a value of 1.2 × 103 m2 s−1 for Kρ. Version 3 of the Potsdam-Institut für Klimafolgenforschung’s (PIK) Climate and Biosphere Model (Climber-3), which is a model of comparable complexity, employs values of 1 × 103 m2 s−1 and 2 × 103 m2 s−1 for Kρ. The above values all imply a strong influence of isopycnal diffusion on the steady-state ocean thermohaline circulation. Our results point to isopycnal diffusion as a potential source of uncertainty in the threshold for NADW collapse in climate models. This provides additional motivation for determining suitable values for isopycnal diffusivity in IPCC class models, which are ideally derived which a meaningful physical framework.

Acknowledgments

We thank the University of Victoria staff for support in the use of their coupled climate model. This research was supported by the Australian Research Council and the Australian Antarctic Science Program. We also thank Steve Griffios for his helpful comments.

REFERENCES

  • Boris, J. P., , and D. L. Book, 1973: Flux-corrected transport. Part I: SHASTA: A fluid transport algorithm that works. J. Comput. Phys., 11 , 3869.

    • Search Google Scholar
    • Export Citation
  • Bryan, F., 1986: High-latitude salinity effects and interhemispheric thermohaline circulations. Nature, 323 , 301304.

  • Bryan, F., 1987: Parameter sensitivity of primitive equation ocean general circulation models. J. Phys. Oceanogr., 17 , 970985.

  • Danabasoglu, G., , J. C. McWilliams, , and P. R. Gent, 1994: The role of mesoscale tracer transports in the global ocean circulation. Science, 264 , 11231126.

    • Search Google Scholar
    • Export Citation
  • Duffy, P. B., , P. Eltgroth, , A. J. Bourgois, , and K. Caldeira, 1995: Effect of improved subgrid scale transport of tracers on uptake of bomb radiocarbon in the GFDL ocean general circulation model. Geophys. Res. Lett., 22 , 10651068.

    • Search Google Scholar
    • Export Citation
  • England, M. H., 1995: Using chlorofluorcarbons to assess ocean climate models. Geophys. Res. Lett., 22 , 30513054.

  • England, M. H., , and A. C. Hirst, 1997: Chlorofluorocarbon uptake in a World Ocean model. 2. Sensitivity to surface thermohaline forcing and subsurface mixing parameterizations. J. Geophys. Res., 102 , 1570915731.

    • Search Google Scholar
    • Export Citation
  • England, M. H., , and S. Rahmstorf, 1999: Sensitivity of ventilation rates and radiocarbon uptake to subgrid-scale mixing in ocean models. J. Phys. Oceanogr., 29 , 28022827.

    • Search Google Scholar
    • Export Citation
  • Gent, P. R., , and J. C. McWilliams, 1990: Isopycnal mixing in ocean general circulation models. J. Phys. Oceanogr., 20 , 150155.

  • Gent, P. R., , J. Willebrand, , T. J. McDougall, , and J. C. McWilliams, 1995: Parameterizing eddy-induced tracer transports in ocean circulation models. J. Phys. Oceanogr., 25 , 463474.

    • Search Google Scholar
    • Export Citation
  • Gerdes, R., , C. Köberle, , and J. Willebrand, 1991: The influence of numerical advection schemes on the results of ocean general circulation models. Climate Dyn., 5 , 211226.

    • Search Google Scholar
    • Export Citation
  • Gregory, J. M., , O. A. Saenko, , and A. J. Weaver, 2003: The role of the Atlantic freshwater balance in the hysteresis of the meridional overturning circulation. Climate Dyn., 21 , 707717. doi:10.1007/s00382-003-0359-8.

    • Search Google Scholar
    • Export Citation
  • Griffies, S. M., 1998: The Gent–McWilliams skew flux. J. Phys. Oceanogr., 28 , 831841.

  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc., 77 , 437471.

  • Ledwell, J., , A. Watson, , and C. Law, 1993: Evidence for slow mixing across the pycnocline from an open-ocean tracer-release experiment. Nature, 364 , 701703.

    • Search Google Scholar
    • Export Citation
  • Manabe, S., , and R. J. Stouffer, 1988: Two stable equilibria of a coupled ocean–atmosphere model. J. Climate, 1 , 841866.

  • Manabe, S., , and R. J. Stouffer, 1994: Multiple-century response of a coupled ocean–atmosphere model to an increase of atmospheric carbon dioxide. J. Climate, 7 , 523.

    • Search Google Scholar
    • Export Citation
  • Manabe, S., , and R. J. Stouffer, 1999: Are two modes of thermohaline circulation stable? Tellus, 51A , 400411.

  • Marotzke, J., 1999: Convective mixing and the thermohaline circulation. J. Phys. Oceanogr., 29 , 29622970.

  • Pacanowski, R., 1995: MOM2 documentation user’s guide and reference manual. GFDL Ocean Group Tech. Rep. 3, NOAA/GFDL, Princeton, NJ, 232 pp.

    • Search Google Scholar
    • Export Citation
  • Rahmstorf, S., 1993: A fast and complete convection scheme for ocean models. Ocean Modell., 101 , 911.

  • Rahmstorf, S., 1996: On the freshwater forcing and transport of the Atlantic thermohaline circulation. Climate Dyn., 12 , 799811.

  • Redi, M. H., 1982: Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr., 12 , 11541158.

  • Saenko, O. A., , and A. J. Weaver, 2003: Atlantic deep circulation controlled by freshening in the Southern Ocean. Geophys. Res. Lett., 30 , 1754. doi:10.1029/2003GL017681.

    • Search Google Scholar
    • Export Citation
  • Saenko, O. A., , A. J. Weaver, , and J. M. Gregory, 2003: On the link between the two modes of the ocean thermohaline circulation and the formation of global-scale water masses. J. Climate, 16 , 27972801.

    • Search Google Scholar
    • Export Citation
  • Sijp, W. P., , and M. H. England, 2004: Effect of the Drake Passage throughflow on global climate. J. Phys. Oceanogr., 34 , 12541266.

  • Sijp, W. P., , and M. H. England, 2006: Sensitivity of the Atlantic thermohaline circulation and its stability to basin-scale variations in vertical mixing. J. Climate, 19 , 54675478.

    • Search Google Scholar
    • Export Citation
  • Sijp, W. P., , M. Bates, , and M. H. England, 2006: Can isopycnal mixing control the stability of the thermohaline circulation in ocean climate models? J. Climate, 19 , 56375651.

    • Search Google Scholar
    • Export Citation
  • Sørensen, J. V. T., , J. Ribbe, , and G. Shaffer, 2001: Sensitivity of a World Ocean GCM to changes in subsurface mixing parameterization. J. Phys. Oceanogr., 31 , 32953311.

    • Search Google Scholar
    • Export Citation
  • Visbeck, M., , J. Marshall, , T. Haine, , and M. Spall, 1997: Specification of eddy transfer coefficients in coarse-resolution ocean circulation models. J. Phys. Oceanogr., 27 , 381402.

    • Search Google Scholar
    • Export Citation
  • Weaver, A. J., and Coauthors, 2001: The UVic Earth System Climate Model: Model description, climatology, and applications to past, present and future climates. Atmos.–Ocean, 39 , 10671109.

    • Search Google Scholar
    • Export Citation
  • Zalesak, S. T., 1979: Fully multidimensional flux-corrected transport algorithms for fluids. J. Comput. Phys., 31 , 335362.

Fig. 1.
Fig. 1.

(a) Averaging regions used for the NP (dark gray) and the NA (including the Arctic, light gray). The white dashed line in the NA indicates the northern boundary of the FW perturbation region. (b) Temporal development of the FW perturbation applied to the NA. Shown is an example where the maximum perturbation M is 0.75 m yr−1.

Citation: Journal of Climate 22, 3; 10.1175/2008JCLI2513.1

Fig. 2.
Fig. 2.

Zonally averaged Atlantic salinity and overlaid Atlantic meridional overturning streamfunction (Sv; annual mean) for NADW (a) on and (b) off. Zonally averaged Atlantic potential temperature for NADW (c) on and (d) off. Results are shown for Kρ = 4 × 102. Note that the horizontal axis has a northern limit of 70°N, precluding the Arctic. A surface volume containing all Atlantic water north of 49.5°N and above 292-m depth is indicated by the white rectangle in the upper-right corner of each panel, and this volume is interpreted as the surface layer containing the NADW formation regions.

Citation: Journal of Climate 22, 3; 10.1175/2008JCLI2513.1

Fig. 3.
Fig. 3.

(a) NADW formation (Sv), (b) NPDW–NPIW formation (Sv), (c) the AABW deep cell, and (d) the FW flux maximum (m yr−1) required to shut down NADW formation. This flux in (d) is determined up to 0.25 m yr−1 accuracy. Values are shown against the log10 of the along-isopycnal diffusion coefficient, i.e., log10(Kρ). No multiple equilibria are found beyond the diffusivity value marked by the vertical line. For comparison, the FW flux threshold required to shut down an equivalent experiment employing only horizontal diffusion (HD) is also shown as the horizontal line marked “HD” in (d). This value (0.4875 m yr−1) gives a sense of the response of the model in the absence of along-isopycnal diffusion. FW perturbations up to a value of 1.5 m yr−1 have been applied. The stability of the NADW formation for diffusivities beyond the vertical line has been further examined using experiments similar to those shown in Fig. 7. Additional experiments employing implicit diffusive vertical mixing instead of the convective adjustment algorithm of Rahmstorf (1993) were also conducted and yielded identical results (not shown).

Citation: Journal of Climate 22, 3; 10.1175/2008JCLI2513.1

Fig. 4.
Fig. 4.

The NP (a) potential temperature (°C), (b) heat fluxes (J s−1), (c) salinity (psu), and (d) salt fluxes (kg s−1) against the log of the along-isopycnal diffusion coefficient. Heat and salt fluxes are decomposed into along-isopycnal diffusion (iso), advective transport (adv), GM eddy advective transport (adv*), transport by convection and diapycnal diffusion (Kv, conv), and surface tracer flux (stf). The advective transport terms include both the horizontal and vertical components. (e) Also shown are the mean salinity anomaly produced by a 4-yr-long linear pulse attaining a maximum value of 0.30 m yr−1 and (f) the associated anomalous fluxes integrated over a period of 50 yr after the pulse. All values are averaged over a 292-m-deep surface volume in the NP between 49.5° and 63.9°N.

Citation: Journal of Climate 22, 3; 10.1175/2008JCLI2513.1

Fig. 5.
Fig. 5.

As in Fig. 4 but for the NA (including the Arctic Ocean). All values are averaged over a 292-m-deep surface volume in the NA extending northward of 49.5°N (see also Fig. 2).

Citation: Journal of Climate 22, 3; 10.1175/2008JCLI2513.1

Fig. 6.
Fig. 6.

The NA response of the experiment where Kρ = 4 × 102 m2 s−1 to a 300-yr FW pulse insufficient to permanently shut down NADW in these experiments (attaining a maximum of 0.75 m yr−1). Time series of (a) salinity (psu), (b) NADW formation (Sv), (c) salt fluxes (Sv) for Kρ = 4 × 102 m2 s−1 (kg m−2), and (d) salt fluxes (Sv) for Kρ = 4 × 103 m2 s−1 (kg m−2). Results are shown for the experiments where Kρ = 4 × 102 m2 s−1 and Kρ = 4 × 103 m2 s−1 in (a) and (b). Salt fluxes (Sv) are decomposed according to the process outlined in Figs. 4 and 5: along-isopycnal diffusion (iso), advective transport (adv), GM eddy advective transport (adv*), and transport by convection and diapycnal diffusion combined (Kv, conv). The advective transport terms include both the horizontal and vertical components.

Citation: Journal of Climate 22, 3; 10.1175/2008JCLI2513.1

Fig. 7.
Fig. 7.

The NA response of the NADW off state of the Kρ = 4 × 103 m2 s−1 experiment when this case is subjected to a sudden increase in isopycnal diffusivity Kρ from 4 × 103 m2 s−1 to 8 × 103 m2 s−1 at time 0. Time series of (a) NADW formation (Sv), (b) the AAIW reverse cell (Sv; see Fig. 2b), (c) the change in salinity of the NA surface volume, (d) the salinity below the NA surface volume, (e) the anomalous salinity fluxes (Sv) of the NA surface volume, and (f) the anomalous salinity fluxes (Sv) below the NA surface volume against time elapsed since the change in Kρ. Salt fluxes are decomposed according to the process outlined in Figs. 4 and 5, although advection is now combined as the total (Eulerian + GM) vertical and horizontal components of the advection. The water volume below the surface volume (denoted by “surface”) is denoted by deep and extends north of 49.5°N and below 292-m depth.

Citation: Journal of Climate 22, 3; 10.1175/2008JCLI2513.1

Save