*3.3. Stratification*

In the simulation with interior mixing, the GLOM generates a region of water that is substantially warmer than that in the rest of the ocean, which is largely contained in the upper 1 km between 50◦ S and 50◦ N (Figure 8a).

**Figure 8.** Stratification along 30◦ W. (**a**) Temperature (◦C) in the simulation with mixing. (**b**) Temperature (◦C) in the simulation without mixing. (**c**) Potential density in nature, with the upper four isopycals referenced to the surface, and the lower four isopycnals referenced to their approximate depths. The lower isopycnals are shown only in the vicinity of the depth to which they are referenced.

The vertical temperature gradient in the tropics within a few hundred meters of the surface is especially high. These aspects of the simulated thermocline structure are like those in the pycnocline in nature (Figure 8c). In both the model and in nature, the densest water forms in the Antarctic, and it undercuts the deep water formed in the north (Figure 8a,c). When interior tracer mixing is removed, the upper thermocline structure is very similar to that in the simulation with mixing (Figure 8b). However, at greater depths, the ocean warms substantially, with many isotherms rising around 1 km or more. The two simulations (with and without the mixing of tracers), have a similar slope in most of the Atlantic (Figure 8a,b), which is also similar to that of isopycnals in nature (Figure 8c).

#### *3.4. Water Mass Distributions*

One advantage of the GLOM is that it is easy to identify locations where water masses form. In Figure 9, we color code parcels along 30◦ W by the latitude at which they were last modified by the surface forcing (the model saves this information as a parcel variable and updates it it every time surface fluxes alter the parcel temperature). We compare the water masses in the GLOM (Figure 9a,b) to those in nature, as revealed by the salinity field (Figure 9c). In the simulation with mixing, each of the main water masses in the Atlantic is represented (Figure 9a): warm tropical and sub-tropical water near the surface that forms between 40◦ S and 40◦ N (red dots); Antarctic Intermediate Water (AIW) that forms between 40◦ and 60◦ S and moves northward along the main thermocline (cyan dots); North Atlantic Deep Water (NADW) that forms north of 40◦ N and reaches depths of about 4 km (green dots), and Antarctic Bottom Water (ABW) that forms south of 60◦ S, and spreads to cover most of the ocean bottom. Each of these water masses has a similar positioning to its counterpart in nature (Figure 9c), as inferred from the salinity field. In the simulation without tracer diffusion (Figure 9b), the general distribution of water masses is similar, except that the AIW penetrates farther north, the NADW is shallower, and the ABW is deeper.

**Figure 9.** Water masses along 30◦ W. Parcels are color coded by the latitude of last surface contact in (**a**) the simulation with mixing. and (**b**) the simulation without mixing. (**c**) Observed water masses are inferred from the salinity field.

#### *3.5. Atlantic Meridional Overturning Circulation*

Most of the deep overturning the model generates is in the Atlantic Ocean, and we now examine this circulation in detail, both because of its importance to ocean heat transport and to follow up on the previous Lagrangian modeling results of HF12. When interior mixing is included in the model, the AMOC has a mid-latitude amplitude of about 21 Sv (Figure 10a), of which about 11 Sv upwells in the Southern Ocean. When interior tracer mixing is removed, the peak amplitude of the overturning is reduced to 13 Sv, but almost as much water (10 Sv) upwells in the Southern Ocean (Figure 10b). The overturning also becomes more shallow, with the deepest streamlines reaching around 3 km. The other difference is that there is a lack of streamlines crossing the thermocline between 27◦ S and 40◦ N. We also examine the AMOC using temperature as a vertical coordinate in Figure 11—both because this more directly illustrates heat transport by removing adiabatic overturning cells [15,33], and because it also more clearly illustrates shallow wind-driven cells. When interior mixing is included, the GLOM generates 24 Sv of deep overturning in the North Atlantic (Figure 11a), with roughly 12 Sv of water upwelling in the Southern Ocean. There is little temperature change following four streamlines (each representing 3 Sv of transport) from 70◦ N to 30◦ S. However, multiple streamlines indicate warming of water in the interior of the deep cell with roughly 6 Sv of upwelling near the equator (Figure 11a). When interior mixing is removed (Figure 11b), the amplitude of the deep cell is reduced to 15 Sv, but once again roughly 12 Sv of water sinks in the North Atlantic and makes a long journey to the Southern Ocean with very little temperature change. Also note that removing interior mixing has little impact on the shallow wind-driven cells for T > 10 ◦C. These results sugges<sup>t</sup> that the basic character of the AMOC is maintained without interior mixing, but that mixing deepens the circulation, and generates transport across the equatorial thermocline.

**Figure 10.** Meridional overturning streamfunction (3 Sv contour interval). (**a**) Simulation with mixing. (**b**) Simulation without mixing. Positive (negative) contours are drawn with solid (dashed) lines, with contour values ranging from −10.5 to 22.5 Sv.

**Figure 11.** Meridional overturning streamfunction with temperature as a vertical coordinate (3 Sv contour interval). (**a**) Simulation with mixing. (**b**) Simulation without mixing. Positive (negative) contours are drawn with solid (dashed) lines, with contour values ranging from −10.5 to 22.5 Sv.

#### *3.6. Sample Trajectory Analysis*

One advantage of the GLOM is that it provides trajectory information for every wass mass element (WME) in the ocean. Each WME has a unique identification number (ID) that does not change during the course of a simulation. To compute a trajectory for a given WME, the modeler simply uses the ID to look up parcel positions for that WME for the times that data is saved. Moreover, for low-resolution runs, it is easy to construct trajectories for *every* WMI in the ocean. These can then be objectively partitioned to illustrate particular water pathways. We now perform such an analysis for the subsurface pathway of the AMOC.

Figure 12a shows downwelling (blue) and upwelling (red) locations of all WMEs that sink in the North Atlantic and upwell south of 30 N during the last 300 years of simulation with interior mixing. Water generally sinks (i.e., loses contact with the surface) in the Labrador or Norwegian Seas and upwells (i.e., regains contact with the surface) near the Gulf of Guinea or in the Southern Ocean. Regions most frequented by WMEs are contoured, revealing that the preferred pathway to upwelling is through a deep western boundary current just to the east of the Americas, which takes an eastward turn south of 20◦ S (see dashed and solid black contours in Figure 12a). When interior tracer mixing is removed, the downwelling locations are similar, as is the preferred pathway to the Southern Ocean, but water no longer upwells near the Equator (Figure 12b). Presumably, this is because without interior mixing, there is no longer any mechanism to warm the water once it loses contact with the surface, which would be necessary for equatorial upwelling.

**Figure 12.** Horizontal pathway to upwelling of North Atlantic Deep Water. (**a**) Simulation with mixing. (**b**) Simulation without mixing. Blue (Red) dots indicated downwelling (upwelling) locations. Contouring indicates the percent of WME pathways that pass through each 3 by 3 degree grid box (10, 30, and 50 percent).

A y–z cross-section of the water pathways in shown in Figure 13.

In both simulations, water typically downwells just south of 70◦ N, and upwells near 60◦ S. In the simulation with interior tracer mixing, the pathway to upwelling is slightly deeper (Figure 13a), and includes a branch to equatorial upwelling that is not present in the simulation without interior mixing (Figure 13b). The pathways shown in Figures 12 and 13 are generally consistent with the streamfunctions shown in Figure 10; although the preferred pathway to upwelling is slightly shallower than the streamlines indicate, which may indicate a bias towards shallower paths because of the relatively short sampling time (300 years).

**Figure 13.** Vertical cross-section of pathway to upwelling of North Atlantic Deep Water. (**a**) Simulation with mixing. (**b**) Simulation without mixing. Blue (red) dots indicate downwelling (upwelling) locations. Contouring indicates the percent of WME pathways that pass through each 3 degree by 300 m grid box (10, 30, and 50 percent).

#### *3.7. Pacific Water Masses*

As in nature, the deep circulation in the GLOM in the Pacific Ocean differs greatly to how it is in the Atlantic Ocean. In particular, for both the simulations, with and without interior mixing, Antarctic Bottom Water fills almost all of the ocean at depths greater than 1 km (Figure 14). In the southern hemisphere, there are a few scattered parcels of North Atlantic Deep Water (green dots) at depths between 1 and 2 km that apparently come around the southern tip of Africa and through the Indian Ocean to reach the central Pacific. We conclude that there is essentially no deep water formation in the Pacific in the GLOM, which is not surprising considering the ocean geometry (Figure 3b) and the zonally symmetric temperature restoring (Figure 5b).

**Figure 14.** Water masses along 170◦ W. Parcels are color coded by the latitude of last surface contact in (**a**) the simulation with mixing, and (**b**) the simulation without mixing.
