The Impact of a Bottom Boundary Layer Scheme on the North Atlantic Ocean in a Global Coupled Climate Model

202 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 35

YONG MING TANG AND MALCOLM J. ROBERTS Met Office, Hadley Centre for Climate Prediction and Research, Exeter, United Kingdom

(Manuscript received 8 September 2003, in final form 7 July 2004)

ABSTRACT

Although the overflow and descent of cold, dense water across the Greenland–Iceland–Scotland ridge is the principal means for the maintenance of the thermohaline circulation in the North Atlantic Ocean, this feature is not adequately treated in global ocean numerical models. In this paper, a bottom boundary layer scheme is introduced into the HadCM3 coupled atmosphere–ocean–sea ice general circulation climate model, in order to give an improved representation of cold water formation in the North Atlantic Ocean. The scheme uses a simple terrain-following bottom boundary layer incorporated into the ocean general circulation model; only the tracer tendencies are evaluated in the bottom boundary layer, with the velocities taken from the near-bottom interior values. It is found that with the bottom boundary layer scheme, there are several significant effects on the deep water formation and flow. The overflow of dense water from the Nordic Seas into the North Atlantic Seas is improved with the introduction of the authors’ bottom boundary layer scheme. Further, the thermohaline circulation is reduced in strength, but is also deeper, when compared with simulations without any bottom boundary layer scheme. There is also a stronger flow along the northwestern boundary, a more southerly location of the North Atlantic Current, and a stronger and larger subpolar gyre. Overall, these effects are an improvement when compared with climatology, although some differences remain.

1. Introduction the northern Atlantic. Unfortunately, global ocean numerical models currently being used for climate studies The thermohaline circulation (THC) in the North do not yet deal with this process adequately (e.g., Hirst Atlantic Ocean plays a fundamental role in the global and McDougall 1996), primarily because the model climate system (Broecker 1991). The THC transports resolution does not sufficiently resolve the continental warm water from low to high latitudes, where it is slopes (Roberts and Wood 1997). In addition, the z- cooled, releasing heat into the atmosphere. The cooling coordinate models cannot properly represent a down- of the water makes it sufficiently dense that it mixes to slope flow, and even when dense overflow water is pro- great depth, and then returns equatorward as a deep duced, it is artificially diluted through convective ho- and cold current. One consequence of this is the rela- mogenization instead of being transported downslope tively mild climate of the high-latitude northern regions (Winton et al. 1998). relative to the analogous regions elsewhere. It has been suggested that these problems can be The overflow and descent of cold, dense waters alleviated by incorporating a bottom boundary layer across the Greenland–Iceland–Scotland (GIS) ridge is (BBL) parameterization scheme (e.g., Hirst and Mc- the principal means by which the deep North Atlantic Dougall 1996). While the importance of bottom bound- Ocean is ventilated and renewed. This overflow is an ary layers has been recognized for many years, it is only important control point for the THC and the conse- recently that consideration has been given to incorpo- quent production and spreading of deep water with the rating parameterizations of them into ocean general cir- correct properties is of critical importance for a valid culation models (OGCM). We note here, in particular, description of the large-scale thermohaline circulation, the approaches adopted by Beckmann and Döscher and thus for an understanding of the climate system in (1997), A. Gnanadesikan (1997, unpublished manuscript), Killworth and Edwards (1999), Döscher and Beckmann (2000), Song and Chao (2000), and Nakano Corresponding author address: Yong Ming Tang, Met Office, and Suginohara (2002). Each of these couple a BBL Joint Centre for Mesoscale Meteorology (JCMM), Meteorology Building, University of Reading, P.O. Box 243, Earley Gate, model to a z-coordinate OGCM, and find various im- Reading, Berkshire RG6 6BB, United Kingdom. provement over simulations with no BBL parameter- E-mail: [email protected] ization present.

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Beckmann and Döscher (1997, hereinafter BD97) the BBL allowed strong downslope flows to develop. couple a terrain-following (␴ coordinate) BBL to a z- However, the code requires a Rayleigh friction term in coordinate OGCM, but simplify the full BBL equations the momentum equations, with a coefficient equal to by evaluating only the tracer tendencies, with the ve- the Coriolis parameter f in order to ensure that the locity field taken from the near-bottom interior values. bottom boundary layer thickness was of the same order

The BBL depth hBBL cannot evolve in time, being de- as the Ekman depth. termined by the lowest ␴ level. They also introduce an Song and Chao (2000) use the KE99 formulation, but empirical parameter ␥ to measure the relative coupling with a different method of evaluating the pressure gra- between the BBL and the interior, 0.0 Յ ␥ Յ 1.0, where dient in the BBL, in which they apparently assume that ␥ ϭ 0.0 represents a simple z-coordinate system, and the pressure gradient is constant across the BBL; this ␥ ϭ 1.0 means that the BBL is fully implemented in the differs from KE99 who calculate a depth-averaged ␴-coordinate system; there is a corresponding modifi- pressure gradient. They also use a terrain-following co- cation to the BBL tracer equations. This approach is ordinate, which takes account of the bottom slope in a appealingly simple, although it does not give the correct different way. They report some results from idealized velocity field in the BBL and uses a fixed bottom model simulations that are broadly similar to the results boundary layer depth. BD97 applied their scheme to an of KE99, but have some differences. idealized box model, and showed that including a BBL The approach of Nakano and Suginohara (2002, resulted in enhanced downslope tracer transport. Loh- hereinafter NS02) is similar to G97, but they include the mann (1998, hereinafter L98) inserted the BD97 advection terms in the momentum equations. Again scheme into a coupled atmosphere–ocean–sea ice hBBL is a constant, set equal to 100 m, and the code, like model with idealized geometry for the North Atlantic G97, requires a Rayleigh friction term with a coefficient Ocean, and with climatological fixed wind forcing, in a equal to the Coriolis parameter f. They incorporate sensitivity study of the thermohaline circulation. Later their BBL scheme into an OGCM, and find that they Döscher and Beckmann (2000, hereinafter DB00) ap- can produce a realistic overslope/downslope flow in the plied a slight modification of their method to the for- Northern Atlantic and around Antarctica. mation of North Atlantic Deep Water (NADW) and As was pointed out in Winton et al. (1998) and G97, obtained some improvement over an OGCM without level coordinate models in particular have trouble rep- any BBL. resenting the thin boundary layer flows down sloping Killworth and Edwards (1999, hereinafter KE99) topography. This is because of 1) an inability to repre- represent the BBL as a two-dimensional slab boundary sent the correct pressure gradient for a thin slope; 2) an layer, which occupies some temporally and spatially inability to resolve the Ekman layer, which breaks geo- varying layer at the ocean floor in a continuous model. strophy to the point where the downslope flow can oc- The BBL equations consist of the tracer equations, cur; and 3) excessive convective entrainment, which di- depth-integrated momentum equations with an aver- lutes the properties of the overflow water. Some of the aged pressure gradient term, and an equation for the above schemes attempt to address all of these prob- evolution of hBBL, the bottom boundary layer depth. lems. However, we choose to implement the BD97 for- Entrainment/detrainment is implemented through a mulation into a fully coupled atmosphere–ocean–sea turbulence closure parameterization. The numerical ice general circulation model as a first step in investi- version of this KE99 scheme is presented for a z-coor- gating the impact of a BBL model on the coupled cli- dinate system, but it has yet to be fully implemented in mate. This formulation only addresses point 3 above, an OGCM, although some idealized box model simu- particularly given the resolution limitations imposed by lations were reported (see also Song and Chao 2000, long climate integrations, but it is possible that this is discussed briefly below). sufficient to represent the most important aspects of Worker A. Gnanadesikan (1997, unpublished manu- deep overflows for climate. script available online at http://www.gfdl.noaa.gov/ Therefore the purpose of this paper is to describe the ϳa1g/bbl.html, hereinafter G97) proposes a generaliza- impact of the Beckmann and Döscher (1997) BBL tion of BD97 in which the BBL momentum equations model in our climate model. Since the atmosphere and are reinstated, albeit without the advective terms, and ocean are fully coupled, we only need to specify the driven by a pressure gradient computed within the initial state of the atmosphere, in contrast to simula- BBL, thus in essence following the KE99 approach. tions with an OGCM alone where the atmospheric forc-

However, hBBL is not allowed to evolve in time and ing is always specified. There is also no need to provide instead is fixed at a constant value of 50 m. Conse- any artificial supply of dense water at the northern quently, turbulence is modeled with a vertical turbulent boundary of the model, as would be the case for a eddy coefficient, rather than with a entrainment/ regional version of an OGCM. Our primary aim here is detrainment specification. Except for the constraint to investigate the effect of a BBL on the representation that hBBL is a constant, the BBL pressure gradient is of the dense overflows, and how this affects the THC calculated as in KE99. The code is tested on some 2D and associated oceanic heat transport in the North At- and 3D model problems, and it is shown that including lantic Ocean. In section 2 we describe the coupled

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model, and our BBL scheme, while in section 3 we proach, in which diffusion is applied between bottom present some results from our simulations. Section 4 cells only if the bottom is not flat, and if denser water contains a summary and discussion. overlies less dense water on the slope. Thus the Lapla- cian diffusivity coefficient A␴ is expressed as Model description A␴ if ٌ␳ · ٌh Ͻ 0 .2 ␴͑ ͒ ϭ ͭ max b A x, y, t ␴ , a. HadCM3 coupled climate model Amin otherwise ␳ The HadCM3 model is a coupled atmosphere– where b is potential density in the bottom tracer box, ocean–sea-ice general circulation model developed for h is depth, and ␴ indicates the bottom-following coor- climate studies at the Hadley Center, part of the Met dinate. This is applied separately to the two horizontal ␴ 2 2 Office. The atmospheric component of HadCM3 (Pope directions. The minimum value Amax is set to be 10 cm Ϫ et al. 2000) has a regular horizontal longitude–latitude s 1,asintheDöscher and Beckmann (2000) study. ␴ 7 2 grid spacing of 3.75° ϫ 2.5°, and 19 vertical levels, with However, here we set Amax to the fixed value of 10 cm Ϫ a detailed specification of physical processes. The s 1, less than the set of values used by DB00, for rea- ocean component is a 20-level Bryan–Cox-type model sons set out below. (Bryan 1969; Cox 1984) with a horizontal grid spacing 2) CONDITIONAL ADVECTION of 1.25° ϫ 1.25°. Thus there are six ocean grid boxes to each atmospheric grid box, chosen so that the land–sea We apply a conditional advection scheme as sug- boundaries match precisely. The sea-ice model has the gested by DB00. In an analogous way to the above, same resolution as the ocean model, and is based on the advection is allowed only if the bottom is not flat, and Semtner (1976) scheme. A detailed description of the if dense water overlies less dense water on the slope; HadCM3 ocean and sea-ice models, including the pa- further, we now add the condition that advection is rameterizations of along isopycnal and vertical mixing, allowed only if the velocity is directed toward a greater can be found in Gordon et al. (2000). depth. With these conditions, the cross-isobath bottom The atmospheric initial conditions are those appro- layer flow of the level model is partially rotated into the priate for mid-September, and are taken from an early terrain-following system (␴-coordinate system): atmosphere-only model integration. The ocean is ini- 1 x y z ␴ tialized from rest, with initial September temperature ␳ ϭϪ ͓͑␣ hu ␳͒ ϩ ͑␣ h␷ ␳͒ ϩ ͑␣ h⍀ ␳͒␴͔ t h BBL x BBL y I and salinity fields taken from the climatology of Levitus and Boyer (1994) and Levitus et al. (1994). The ocean– Ϫ ͓͑ Ϫ ␣x͒ ␳͔ ϩ ͓͑ Ϫ ␣y͒␷␳͔ ϩ ͓͑ Ϫ ␣z͒ ␳͔ z ͕ 1 u x 1 y 1 w z͖ atmosphere coupling period is 1 day. ϩ D␴. b. The BBL scheme Here subscripts denote derivatives, and superscripts are In these studies, the HadCM3 model is linked with a used to distinguish between the ␴-coordinate and z- ␴ ␴ BBL model based on the BD97 scheme (Beckmann coordinate systems; D ϭٌ(A ٌ␳) is the conditional ⍀ and Döscher 1997). A terrain-following bottom bound- tracer diffusion in the BBL, described above, and I is ary layer model is coupled to the ocean general circu- the vertical velocity in the ␴-coordinate system of the z lation model component of the coupled model. The bottom layer. The vertical diffusion D in a z-coordi- BBL connects the bottom boxes of the OGCM, thus nate system is not included here, but it is of course enabling advection and transport along the bottom. present in the OGCM component. For a two-layer ver- Only tracer tendencies are evaluated, and the advection sion of such a model the vertical velocity at the layer velocities are taken from the OGCM bottom boxes. interface ␴ ϭϪ1 ϩ h/H is ⍀ ϭϪ͑ ͒ Ϫ ͑ ␷ ͒ The BBL depth hBBL is fixed. Later Döscher and Beck- h I huBBL x h BBL y, mann (2000) modified this scheme by introducing a and u, ␷, and w represent the zonal, meridional, and conditional advection in the BBL (see below) to ensure vertical velocities, respectively. Tracer fluxes are calcu- that the BBL tracer fluxes are implemented only when lated in the topography-following coordinate only if the there is downslope flow of dense water, thus preventing dense downslope condition is satisfied: some unrealistic vertical homogenization in their x ␥ if ٌ␳ · ٌh Ͻ 0, u · ٌh Ͼ 0␣ OGCM simulations of the North Atlantic. In this study, ͩ ͪ ϭ ͭ we use a similar BBL scheme, which is described below. ␣y 0 otherwise

1) CONDITIONAL DIFFUSION and ␣z ϭ ␣x ␣y The diffusive part of the BBL is slope convection and max͑ , ͒. represents a conditional diffusion. As pointed out by Here ␥ is a tuning factor, ranging from 0 to 1, as de- Döscher and Beckmann (2000), an unrestricted diffu- scribed in BD97. As in the HadCM3 OGCM, we use a sivity would result in an overall smoothing of tracer central differencing discretization for the BBL advec- fields in the bottom layer. Here we adopt their ap- tion scheme.

Unauthenticated | Downloaded 09/30/21 12:11 AM UTC FEBRUARY 2005 T A N G A N D ROBERTS 205 c. Parameters for the BBL scheme sharp topographic “cliff” at 65°N, 28°W; this was introduced in HadCM3 in order to minimize the convective To emphasize the role of the BBL in taking dense mixing of the dense overflow by reducing the number water downslope, it is desirable to keep the diffusion ␴ of topographic steps. Given that we wanted to be able coefficient A as small as possible, and to set ␥ ϭ 1.0 max to compare with the basic HadCM3 model, this was to allow the advective part of the BBL to play an im- ␴ Ϫ unaltered in the current experiments, though one might portant role. Hence, we set A ϭ 107 cm2 s 1 for all max expect the introduction of the BBL to remove the need the runs showed here. Simulations (in an idealized ␴ for such “topography tuning.” The impact of removing ocean-only model) with a larger value of A indicated max this cliff, and topography issues in general, are dis- that the BBL then spread the dense water plume hori- cussed further in appendix A4 of Gordon et al. (2000) zontally as well as in the downslope direction, and also and in Thorpe et al. (2004). tended to suppress the along-seafloor current. Further, ␴ ϭ 7 2 Ϫ1 the value for Amax 10 cm s is consistent with the value of 0.6 ϫ 107 cm2 sϪ1 estimated by Straneo et al. a. Impact of BBL scheme on dense overflows (2003) from an analysis of Lagrangian floats in the La- The most immediate impact of including the BBL brador Sea, and with the slightly lower estimates of scheme is likely to be in the representation of dense Khatiwala et al. (2002) from hydrographic data. Most of overflows from the Nordic seas into the North Atlantic. the results shown here have ␥ ϭ 1 (run BBL-G1), al- This process is often poorly represented in z-coordinate though we also performed simulations with ␥ ϭ 0 (run models (see, e.g., Roberts et al. 1996), and we expect BBL-G0) and ␥ ϭ 0.5 (run BBL-G05), and some results that including a BBL scheme will improve it. Since the for these cases are shown as well. Overall, the case ␥ ϭ outflow from the Nordic seas into the North Atlantic is 0.5 showed little difference from the case ␥ ϭ 1.0. the source of the coldest water, the simplest way to show its penetration is to plot minimum temperatures 3. Numerical experiments and results at each latitude, and this is done in Fig. 2. From the cold source waters at the Greenland–Iceland–Scotland Our analysis is based upon four model simulations, a ridges at 65°–68°N with temperatures around 0°C, as HadCM3 control run with no BBL scheme, and three one moves south there is a distinct difference between other simulations, which include a BBL parameteriza- the runs with an advective component to the BBL and tion scheme as discussed in the previous section. The the others. The control run together with run BBL-G0 model is run out for 60 yr, and the results shown are (␥ ϭ 0) show a fast increase in minimum temperature based on averages over the last decade. As might be south of 65°N, as the overflow crosses the ridges and is expected, the most significant effects of the BBL occur mixed into the surrounding water, primarily through in the North Atlantic, and hence we shall concentrate convective mixing. The advective BBL runs (BBL-G05 our attention on that region. and BBL-G1, i.e., ␥ ϭ 0.5 and 1.0) show a smaller For reference, the model bathymetry of the region change (which looks similar to an advective overshoot/ around Iceland is shown in Fig. 1, with depth contours undershoot between 65° and 63°N) and distinctly coinciding with the bottom of model tracer boxes. This colder temperatures by more than 1°C down to around is the standard HadCM3 bathymetry, which has not 50°N. These advective BBL cases are in much better been altered in any of these experiments. Note the agreement with the World Ocean Atlas 1998 (WOA98)

FIG. 1. Ocean model bottom depths around the Greenland–Iceland–Scotland ridges. The dashed lines indicate the sections through which fluxes are calculated (see text). The contours are at 164.8, 242.6, 359.4, 534.7, 797.9, 1193.2, 1808.5, 2423.8, 3039.0, 3654.3, 4269.5, 4884.8, 5500.1 m.

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FIG. 2. Minimum temperature at each latitude in the North Atlantic for points deeper than 200 m. climatology (Antonov et al. 1998), though care must be south of 55°N, which is in much better agreement with taken in interpreting the latter since the observed data WOA98 climatology (Fig. 3c). The difference between is sparse and much may come from interpolation. control and BBL-G1 runs is shown in Fig. 3d, making The preservation of the overflow water is shown even clear the path of the overflow spreading from the Den- more clearly in Fig. 3, which shows the temperature at mark Strait and the Iceland–Scotland ridges. The BBL- the lowest model grid point. Compared to the control G05 case (not shown) is very similar to BBL-G1, while run in Fig. 3a, BBL-G1 (Fig. 3b) has considerably the BBL-G0 case shows a small amount of more dense colder temperatures over most of the ocean interior overflow being preserved than in the control.

FIG. 3. Temperature (°C) at the lowest model grid point in the North Atlantic for (a) control run, (b) BBL-G1 (␥ ϭ 1), and (c) WOA98 climatology. (d) The temperature difference, control Ϫ BBL-G1. For (a)–(c), temperatures colder than 3°C are shaded, and for (d), differences ՅϪ1°C are shaded.

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The introduction of the BBL scheme has an impact with a total entrainment of 4.7 Sv in water of density on the large-scale circulation of dense water in the Ն27.8 in the outflow. The BBL-G0 experiment has a North Atlantic. In the control case, the total amount of smaller level of entrainment (3 Sv) and similarly mixes overflow of water denser than 27.8␴␪ from the Nordic the dense water into lighter categories. The advective seas into the North Atlantic, measured across the BBL cases are better at retaining outflow water near to ridges at their shallowest point (i.e., before convective the original density, and consequently have smaller en- entrainment) is around 8.2 Sv (where 1 Sv ϵ 106 m3 trainments (2.5 and 1.7 Sv for BBL-G05 and BBL-G1, sϪ1), whereas for BBL-G1 the value is 6.1 Sv, and 7.2 respectively). These results can be compared with the and 6.2 Sv for BBL-G0 and BBL-G05, respectively. observations of Dickson and Brown (1994), which sug- These compare to observed values of around 5.6 Sv gest that 2.9 Sv of overflow denser than 27.8 from the from Dickson and Brown (1994). This suggests that, Denmark Strait is converted to 5.2 Sv after entrain- even before entrainment and other processes can op- ment. erate, the BBL scheme has reduced the amount of By the time the dense flow reaches Cape Farewell at dense outflow from the Nordic seas. These overflows 45°W, it will have mixed with outflow water from the have temperatures ranging from Ϫ1° to 4°C, but with Iceland–Scotland overflow region, may well have un- salinities that are much too high, at around 35.0 to 35.2 dergone more entrainment, and part of the flow may be psu. This is related to the hydrological cycle of recirculating in the subpolar gyre. In comparison with HadCM3, and is described more thoroughly in Gordon observations in Dickson and Brown (1994) of 13.3 Sv of et al. (2000) and Pardaens et al. (2003). water with ␴␪ Ն 27.8 in this region, all models have a As discussed in the introduction, the BD97 BBL larger flux of between 18 and 20 Sv. Slightly surpris- scheme really only addresses the problem of excessive ingly the fluxes in the BBL runs are at least as large as convective entrainment of dense overflows in level co- those without a BBL, though the advective BBL runs ordinate models. The previous two figures suggest that retain denser water than the others. indeed this is improved with the BBL, but a more de- The impact of the overflows on the overturning ad- tailed look at the fluxes, and particularly the entrain- jacent to the ridges is shown in Fig. 4, which shows the ment by the overflow water (which plays an important overturning in potential density space. The control run part in setting the meridional overturning circulation), has very strong entrainment at 65°N, consistent with is now described for the Denmark Strait overflow wa- the above, with hardly any water denser than 28.0 ter. Care should be taken in interpreting these values, surviving to 40°N. The BBL-G0 run also shows some since advection and other schemes can generate grid- entrainment at 65°N but retains more dense water, point noise, which given the narrowness of the over- and has two distinct southward flows, one at 28.1 and flows, can skew the pointwise values. the other at 27.8–27.85, the latter from water formed Table 1 shows the fluxes in the most dense categories, in the Labrador and Irminger Seas (see later). In con- calculated from the temperature, salinity, and velocity trast, there is very little entrainment evident in the on the standard model grid through sections shown in BBL-G05 and BBL-G1 at 65°N, and both these runs Fig. 1, one upstream and one downstream of the large have strong outflow of water denser than 28.0 through “cliff” in the bathymetry at (65°N, 28°W) and one off 40°N, as well as the Labrador/Irminger Sea Water cell Cape Farewell at the southern tip of Greenland. The at 27.8–27.85. impact of convective entrainment on the dense flows in One impact of the different entrainment rates for the the control run is evident, with the 6.2 Sv of water with overflow water can be seen in the mixed layer depths density Ն28.1 being converted into less dense water, for the different experiments shown in Fig. 5. All of the

TABLE 1. Fluxes across the Denmark Strait (Sv). Inflow is the westward flux across the 21°W section; outflow is the westward/ southward flux across the 62°N, 32°W section; and Farewell is the westward flux across the 35°W section. Potential density categories are defined as being within 0.05 ␴␪ of the central density. Model Density 27.85 27.95 28.05 28.15 28.25 Total Control Inflow 0.1 0.8 0.1 2.5 3.7 7.2 Outflow Ϫ5.0 6.6 10.3 0.0 0.0 11.9 Farewell 2. 6.8 9.7 0.0 0.0 18.5 BBL-G0 Inflow 0.6 0. 0.6 1.6 3.2 6.0 Outflow Ϫ0.8 2.3 7.5 0. 0. 9.0 Farewell 5.2 3.7 9.1 0. 0. 18.0 BBL-G05 Inflow 0.5 0.1 1.2 1.1 2.6 5.5 Outflow 1.7 Ϫ0.1 3.2 3.2 0. 8.0 Farewell 6.7 7.5 4.3 1.6 0. 20.1 BBL-G1 Inflow 0.4 0.1 1.1 1.0 2.5 5.1 Outflow 1.7 Ϫ0.5 2.8 2.8 0. 6.8 Farewell 2.9 9.8 0. 5.6 0. 18.3

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FIG. 4. Overturning in potential density space in the North Atlantic for (a) control, (b) BBL-G0, (c) BBL-G05, and (d) BBL-G1. integrations have similar patterns of deepest mixed lay- tology) and Fig. 7 (BBL simulations vs WOA climatol- ers, and hence convection, in the Nordic seas. However, ogy) we compare the potential density gradients in the in the North Atlantic the mixed layer regions are rather Labrador Sea and North Atlantic Ocean. From these different. The control experiment has deep mixed lay- figures we see that overall the BBL run has produced ers to the south of the Iceland–Scotland ridges, produc- denser water at depth than in the control run, and in ing a water mass with density 27.7–27.8 (surface density this respect, is more consistent with the WOA98 clima- not shown). The other three runs, which have less en- tology. For instance, from the north–south density con- trainment, have their deeper mixing further west in the tours of Figs. 6a and 7a, we see that the density con- Irminger Sea (with the advective BBL cases having tours below 1000-m depth are consistently deeper in the some deep mixing in the Labrador Sea), and these re- BBL case than in the control, and are more consistent gions produce the water masses of densities 27.7–27.8. with the WOA98 climatology. Similarly, for the east– The reason for these differences can be seen by study- west density contours of Figs. 6b–c and 7b–c, we again ing the vertical density structure. see that the BBL run produces a deepening of the den- The improved representation of dense overflow has sity contours; for instance, a comparison of the 27.8 an important impact on the vertical density structure in density contour shows that the BBL run places this a the North Atlantic. In Fig. 6 (control vs WOA98 clima- few hundred meters deeper than in the control run, and

FIG. 5. Model mixed layer depth for Mar, averaged over years 51–60, for (a) control, (b) BBL-G0, (c) BBL-G05, and (d) BBL-G1. Contours are at 0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 600, 700, 800, 900, 1000, and 2000 m, with shading for depths greater than 400 m.

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FIG. 6. Comparison of isopycnals in (a) Labrador Sea at cross section 50°W and North Atlantic Ocean at cross sections (b) 55° and (c) 45°N, from control run (solid line) and WOA98 climatology (dashed line).

generally at a level more consistent with the WOA98 b. Meridional overturning and northward climatology. heat transport The maintenance of the denser water in the BBL runs and smaller entrainment into lighter layers means In Fig. 8 we show a time series of the maximum that the stratification in the Labrador Sea is altered. A transport carried by the meridional overturning circu- doming of the isopycnals seen at 54°N in Fig. 7a and lation in z space for all four model cases. We see that 50°W in Fig. 7b indicates stronger Labrador Sea cir- the BBL significantly lessens the strength of the over- culation and convection in the BBL run. This is consis- turning. The effect is present for all three values of the tent with the thicker layers of water with density 27.75– tuning parameter ␥ and is most marked for the BBL-G1 27.8, which is formed in the Labrador and Irminger case, where the reduction is around 15%–20% over the Seas and can also be seen in the climatology. In the course of the 60-yr run. Note that the BBL-G05 case is control run, where more of the dense water is entrained not very different from BBL-G1, but the BBL-G0 case into lighter layers, the stratification is stronger nearer gives a noticeably smaller change from the control run. the surface, and convection is not as strong in the La- This is consistent with the change in overflow noted brador Sea. above.

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FIG. 7. Same as Fig. 6 but from model simulation with BBL (solid) and WOA98 climatology (dashed).

Figure 9 shows contour plots of the decadal mean while the BBL-G1 and BBL-G05 runs have only one meridional overturning streamfunction, for the four maxima of 15 Sv at about 30°N. In effect, the deeper runs. The overturning in the control run has reasonable flow of the BBL case at the northern end has elimi- features, with the NADW transport agreeing well with nated the more northerly maxima in the control run. observations at Cape Farewell and at 24°N (Wood et al. 1999), where the value of 18 Sv is in line with an estimate of 19 Sv from Hall and Bryden (1982). The greatest departures from the control run occur in BBL-G1 and BBL-G05, with BBL-G0 rather closer to the control run. Comparing the BBL-G1 case with the control run, we see that the effect of the BBL is to produce a weaker maximum overturning, but with the 5 Sv of dense overflow water flowing southward at deeper levels in BBL-G1 and BBL-G05 than in the FIG. 8. Time series of the maximum overturning streamfunction control. There is also a change in the structure of the in the North Atlantic Ocean for four cases; control (solid line), overturning at 1000 m, with the control run having two and runs with a BBL, where ␥ ϭ 0, 0.5, 1.0 (dot, dash–dot, and overturning maxima of 18 Sv at about 30° and 40°N, dashed lines, respectively).

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FIG. 9. Atlantic meridional overturning streamfunction for (a) control, (b) BBL-G0, (c) BBL-G05, and (d) BBL-G1. Contour interval is 1 Sv.

Similar features can be seen in the results of DB00 and the AABW appears to reach only 10S and the flux is NS02 in their studies of the effect of a BBL scheme in reduced to only 2 Sv. A similar feature was also found an OGCM and in the L98 idealized sensitivity study. by DB00 in their OGCM simulations. Another consequence of the stronger southward flow In studying overturning in level space, it is impossible at depth when the BBL scheme is present is the sup- to separate changes in flow geometry and changes in pression of the northward flow of Antarctic Bottom the properties of the flow. In Fig. 10 the overturning in ␴ Water (AABW). In the control run (Fig. 9a) this water density space, relative to 2000 m ( 2000), is shown for has penetrated to about 10°N and has a flux of nearly 4 all models. This confirms many of the features seen in Sv, but in the BBL run (Fig. 9d), the cell associated with level space—the maximum overturning at 50°Nisre-

␴ FIG. 10. Atlantic meridional overturning streamfunction in 2000 density space relative to 2000 m for (a) control, (b) BBL-G0, (c) BBL-G05, and (d) BBL-G1. Contour interval is 2 Sv.

Unauthenticated | Downloaded 09/30/21 12:11 AM UTC 212 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 35 duced in the BBL cases, as entrainment is reduced, and lead to a smaller layer depth, and indeed, this can be the large-scale overturning at 24°N decreases from 17.4 discerned in Fig. 9, where the layer depth at the over- Sv in the control run to 14.5 Sv in BBL-G1. turning latitudes (40°–60°N) is in the range 1100–1200 Spall and Pickard (2001) have argued that the m for the control run (Fig. 9a), whereas it is around strength of the THC can be simply estimated from the 1000 m for the BBL run (Fig. 9d). This reduction of depth of the oceanic mixed layer at the northern 10%–20% in the layer depth h would produce a reduc- boundary. They proposed that the total downward flux tion in the flux MB of at least 20%, as we have found. at the northern boundary can be estimated as Similar estimates of h can be made from Fig. 7b, which shows the potential density contours at 55°N. g⌬␳ h2 ϭ B Here, let us define the layer depth h by the 27.75 iso- MB ␳ . 8 0 f pycnal contour as it is approximately located at 1000-m Here h is the depth of the northward-flowing layer at depth. Then, when the BBL scheme is included, we see ⌬␳ that h is reduced; the reduction varies significantly with the northern boundary, B is the density change along ␳ latitude, but at about 30°W has a peak value of about the northern boundary, and 0 is a reference density. The most sensitive dependence here is due to the layer 50%, and we can estimate an average reduction of depth h. Spall and Pickard (2001) used this expression around 10%–20%, consistent with our estimate of h to explain why idealized OGCM simulations with a directly from Fig. 9. sloping topography at the northern boundary gave a Figures 11a–c show the meridional heat transport weaker THC than analogous simulations with a vertical (the total transport in Fig. 11a, that due to the meridi- wall at this boundary [but we note that Park and Bryan onal overturning streamfunction in Fig. 11b, and that (2000) have shown in a model study that the differences due to the gyres in Fig. 11c), while in Fig. 11d we show between the sloping topography case and the flat bot- the maximum flux of the meridional overturning tom case are not so apparent in density coordinates]. streamfunction as a function of latitude. In each case we The reason advanced by Spall and Pickard (2001) was show the four cases. Again we see that the differences that the effect of the sloping topography was to allow from the control run are most marked when ␥ ϭ 1.0. for rim currents in the subpolar gyre, with a consequent The significant feature here is that the total heat trans- reduction in the boundary mixing and layer depth, thus port (Fig. 11a) is not greatly affected by the BBL, with reducing MB above. Although here all simulations, the only noticeable difference being a slight reduction both the control and the runs with a BBL scheme, have in the region 0°–30°N. Here, the main role of the BBL the same topography, there is a similar effect. As we is apparently to increase the northward heat transport have noted above, the presence of the BBL has resulted carried by the subpolar gyre in the region 30°–60°N, in stronger flows along the northwestern boundary. and correspondingly to reduce the heat transport car- Spall and Pickard (2001) have argued that this should ried by the THC in the region 0°–60°N. Both of these

FIG. 11. The meridional heat transport: (a) the total transport, (b) that due to the meridional overturning streamfunction, and (c) that due to the subpolar gyre; (d) the maximum flux of the meridional overturning streamfunction as a function of latitude.

Unauthenticated | Downloaded 09/30/21 12:11 AM UTC FEBRUARY 2005 T A N G A N D ROBERTS 213 effects of the BBL can clearly be related to the weak- The barotropic streamfunction for the four model ening of the meridional overturning flux, and the runs is shown in Fig. 12. The control run shows a rea- strengthening of the subpolar gyre. Interestingly, the sonable circulation, with the subpolar gyre strongest on net effect is felt only in the subtropical region 0°–30°N, the western side of the basin and a strong subtropical as in the more northerly region 30°–60°N the two ef- gyre with maximum transport of 35 Sv. There are two fects are in almost complete balance. major changes to this circulation when the BBL is introduced. The strength of the subtropical gyre decreases in all cases, with particularly large differences c. Horizontal circulation around 35°N. Conversely, the strength and extent of the Having studied the impact of the BBL scheme on subpolar gyre increases, with stronger circulation in processes involving deep water and their impact on the both the Irminger Sea and on the western side of the thermohaline circulation, we now turn to the impact on gyre. These features were also found in the L98 sensi- the horizontal circulation. Maintaining a realistic ocean tivity study with idealized topography. surface climatology is essential in coupled climate mod- The difference in the barotropic streamfunction be- els, since the atmospheric component is most sensitive tween the control and the BBL cases BBL-G0 and to this aspect of the ocean circulation. BBL-G1 is shown in Fig. 13. Much of the difference can

FIG. 12. Barotropic streamfunction for (a) control, (b) BBL-G0, (c) BBL-G05, and (d) BBL-G1. The contour interval is 5 Sv, with dark shading for values greater than 20 Sv, and light shading for values less than Ϫ20 Sv. Dashed contours signify positive values. The fields have been put through a 1–2–1 filter to remove gridpoint noise.

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FIG. 13. Barotropic streamfunction differences for (a) BBL-G0 Ϫ control and (b) BBL- G1 Ϫ control The contour interval is 5 Sv, differences greater than 10 Sv have dark shading, and differences less than Ϫ10 Sv have light shading. be explained with reference to the bottom velocities also to a marked northward turn in the subpolar gyre (not shown). The enhancement of deep flow from the boundary. Nordic seas into the Labrador Sea, and then equator- In Fig. 14 we show the sea surface temperature (SST) ward in the DWBC would give an increase in the for the HadCM3 control simulations (Fig. 14a), BBL- strength of the subpolar gyre, particularly on the west- G1 (␥ ϭ 1.0) (Fig. 14b), and the WOA98 climatology ern side, and the decrease in the subtropical gyre seen (Antonov et al. 1998; Fig. 14c). Clearly, the most no- around 35°N. This is more noticeable for the BBL-G1 ticeable effects are around the Labrador and Irminger case than for the BBL-G0 case. It is less clear why the Seas, where overflow over the geographical ridges is subpolar gyre becomes so much stronger on the eastern most active. In general, the numerical simulations are side of the basin, making the contour lines more zonal comparable with the climatology, although the region than they are in the control—at least part of this may of high temperature gradient to the south of Newfound- be due to the joint effect of baroclinicity and relief land that is associated with the NAC is too far north in (JEBAR). This has important consequences for the the control simulation, and the NAC is rather too zonal, path of the North Atlantic Current (NAC) and the sea with a correspondingly weaker northward deflection. It surface temperature. These features are consistent is suggested (Cooper and Gordon 2002) that this is be- with the case studies of Cooper and Gordon (2002) who cause the model Gulf Stream does not separate from pointed out there is a complex dynamical response of the North American coast at Cape Hatteras, as ob- the NAC system to Labrador Sea Convection (LSC); served in reality, but instead separates farther north. an enhanced LSC can lead to a stronger NAC and The simulations with a BBL alter some of these fea-

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FIG. 14. Sea surface temperature (SST) in the North Atlantic Ocean (°C). tures. When compared with the control run, the high- Overall, from these streamfunction and SST fields, temperature gradient to the south of Newfoundland is we see that the subpolar gyre is larger in extent for the rather weaker, and as noted above, the NAC is dis- runs with the BBL scheme; its eastern boundary is fur- tinctly more zonal, while there is a slight northward ther to the east, and the northward deflection at the deflection around 45°N, 40°W, which is not evident in eastern boundary is more marked. However, when the control run in the SST plots (Fig. 14a). compared with the climatology, there does not appear

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to be a consistent trend resulting from the introduction in taking dense water in the downslope direction when of the BBL. Thus, the stronger zonal flow of the NAC ␥ ϭ 1, so that advection plays a full role. However, all ␴ ϭ with the BBL scheme is not reflected in the climatol- runs shown here have the diffusion coefficient Amax ogy, but the slight northward deflection at 45°N, 40°W, 107 cm2 sϪ1, which although it is consistent with the mentioned above and not seen in the control run, is Labrador Sea estimates of Khatiwala et al. (2002) from consistent with the much stronger northward deflection hydrographic data and Straneo et al. (2003) from ve- seen in the climatology at this location (cf., e.g., the 10° locity data, is an order of magnitude less than the value ␴ ϭ 8 2 Ϫ1 contour in the SST plots in Fig. 14). In the temperature of about Amax 10 cm s typically used by Döscher and streamfunction fields, the eastern boundary of the and Beckmann (2000) in their analogous study of the subpolar gyre is further to the east for the BBL runs impact of a BBL scheme. As we have mentioned ear- than for the climatology, while the control run places lier, we would expect that a larger value of the diffu- this boundary further to the west. On the other hand, sivity would lead to more horizontal spreading of the the BBL runs give better agreement with climatology dense water, that is a flow in the downslope direction, for the temperature fields along the western boundaries and suppression of the along-seafloor current. Further, ␴ of the Irminger and Labrador Seas. as Straneo et al. (2003) have pointed out, in reality Amax will vary spatially in response to current fluctuations about the time-averaged state. Hence, one might expect ␴ 4. Summary and discussion a localized increase in Amax in regions of strong currents. In the present context we speculate that such a In this paper, we have introduced a bottom boundary localized increase might reduce the strength of the layer (BBL) scheme into the HadCM3 coupled atmo- North Atlantic Current and subpolar gyre that we have sphere–ocean–sea ice general circulation climate mode. found here, when using a BBL scheme, thus bringing The BBL scheme is based on the model of Döscher and these features rather closer to climatology. Beckmann (2000), in which tracer tendencies are par- Clearly this work is only a first step in introducing tially evaluated in a terrain-following coordinate system bottom boundary layer physics into ocean models, be- in order to enhance downslope flow of dense water. cause the parameterization does not include the direct Our aim was to improve the representation of the effects of the BBL momentum advection and pressure spreading of cold, dense water in the North Atlantic gradient terms, and does not allow the boundary layer Ocean from its primary source in the Nordic seas. depth to vary spatially and temporally, as it would in We find that with the bottom boundary layer scheme, reality. Several schemes with some or all of these more there are several significant effects on the deep-water complex features have been tested in idealized models, formation and flow in the North Atlantic. The BBL and although their impacts have been similar to those runs show a marked improvement in the representation reported for the simpler schemes, it remains to be seen of the dense overflows from the Nordic seas into the how they might impact in a fully coupled global climate North Atlantic. The bottom temperature is colder and model. in better agreement with climatology, and the overflow Another problem with current climate models is their fluxes are smaller, again consistent with climatology. inability to adequately resolve the complex topography The thermohaline circulation is reduced in strength by through which the important dense flows navigate. This about 15%, and has only a single maximum with lati- is a difficulty for the results presented here, both for the tude, when compared with simulations without any bot- runs with and without a BBL. Clearly the implementa- tom boundary layer scheme. The lower branch of the tion of increased horizontal and vertical resolution, as circulation is also deeper, with a consequence that the well as an improved representation of the topography northward penetration of Antarctic Bottom Water is itself, is a key step in future progress in evaluating the curtailed. There is a stronger flow along the northwest- impact of this and other BBL schemes. ern boundary around the Labrador Sea, a greater penetration of cold water into the Labrador Sea from the Acknowledgments. The authors thank the two re- Irminger Basin with a stronger Labrador Sea circula- viewers for their very helpful comments, which im- tion, a more zonal North Atlantic Current with a more proved the paper considerably. 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