Climate System Modeling Group, Lawrence Livermore National Laboratory, Livermore, California

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1 498 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 Effects of Subgrid-Scale Mixing Parameterizations on Simulated Distributions of Natural 14 C, Temperature, and Salinity in a Three-Dimensional Ocean General Circulation Model PHILIP B. DUFFY AND KEN CALDEIRA Climate System Modeling Group, Lawrence Livermore National Laboratory, Livermore, California JERRY SELVAGGI AND MARTIN I. HOFFERT Department of Physics, New York University, New York, New York (Manuscript received 29 April 1996, in final form 29 July 1996) ABSTRACT The effects of parameterizations of subgrid-scale mixing on simulated distributions of natural 14 C, temperature, and salinity in a three-dimensional ocean general circulation model are examined. The parameterizations studied are 1) the Gent McWilliams parameterization of lateral transport of tracers by isopycnal eddies; 2) horizontal mixing; 3) a parameterization of vertical mixing in which the amount of mixing depends on the local vertical density gradient; and 4) prescribed vertical mixing. The authors perform and analyze four ocean GCM simulations that use different combinations of these parameterizations. It is confirmed that the Gent McWilliams parameterization largely eliminates the tendency of GFDL-based models to overestimate temperatures in the thermocline. However, in the authors simulations with the Gent McWilliams parameterization the deep ocean is too cold, in places by more than 3 degrees. Our results are the first known to assess the effects of the Gent McWilliams parameterization on the simulated distribution of natural 14 C. The most important change (compared to results obtained with horizontal mixing) is that interior ocean 14 C values are lower; that is, the water is older with Gent McWilliams. In most locations in the deep North Atlantic, simulated 14 C values are much too low with horizontal mixing and are even lower with Gent McWilliams. Both this problem and the problem of the simulated deep ocean being too cold are probably due, at least in part, to insufficient downward penetration of NADW, resulting in the deep North Atlantic in the model being ventilated primarily via AABW. This problem exists when Gent McWilliams is not used, but Gent McWilliams makes the symptoms it presents (an overly cold and old deep North Atlantic) worse. Gent McWilliams also results in a dramatic reduction in convective adjustment in the model, compared to results obtained with horizontal mixing; as a result, simulated tracer distributions are improved at high latitudes. Finally, Gent McWilliams increases the susceptibility of the authors model to some types of numerical problems. The stability-dependent vertical mixing parameterization causes relatively small changes in simulated distributions of temperature and natural 14 C (compared to results with a prescribed uniform vertical diffusivity), but these changes tend to improve agreement with observations. Assuming they are based on correct physical premises and are properly calibrated, both the stability-dependent vertical mixing parameterization and the Gent McWilliams parameterization should give the model more predictive capability than simpler parameterizations do in that they allow the amount or direction of mixing to change in response to changes in ocean density. 1. Introduction In ocean models used for climate research, parameterizations of the effects of mesoscale ocean eddies will be important for some time to come. Since the timescale for vertical overturning of the large-scale ocean circulation is of order a thousand years, ocean models must be run for several thousand simulated years to reach an approximate steady state. While recent advances in com- Corresponding author address: Dr. Philip B. Duffy, Atmospheric Science Division, L-256, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA pduffy@llnl.gov puting power have allowed eddy-resolving ocean simulations to be run for several simulated years (Semtner and Chervin 1988; Semtner 1995), the ability to run truly eddy-resolving simulations for thousands of simulated years is not anticipated in the near future. Hence, for at least the near future, ocean climate simulations will be run at relatively coarse resolution, and good parameterizations of subgrid-scale motions will be needed. In this paper we examine the effects of two such parameterizations (described below) on simulated distributions of natural 14 C, temperature, and salinity in a three-dimensional global ocean general circulation model. Results of these parameterizations are compared to the results of the simpler alternatives of prescribed hor American Meteorological Society

2 APRIL 1997 DUFFY ET AL. 499 izontal mixing and prescribed uniform vertical mixing. For this purpose, we perform and analyze four ocean GCM simulations, described in detail below. Although this paper looks only at the effects of parameterizations of subgrid-scale mixing on simulated steady-state tracer distributions (i.e., on our model s ability to simulate today s ocean), an important aspect of the more sophisticated parameterizations studied here is that assuming they are based on correct physical premises and are properly tuned they should improve our model s ability to simulate altered ocean climates. This improved predictive capability arises because in these parameterizations the amount or direction of subgrid-scale mixing changes in response to changes in the ocean density structure. By contrast, in simpler parameterizations the amount and direction of mixing are prescribed and thus cannot change as the ocean climate changes. The rest of this paper is organized as follows. The next section describes the parameterizations studied in this paper. Section 3 describes our model and how it was configured for the runs presented here. The results section describes and discusses the results of four simulations with our model. Next we give our conclusions, and in the appendix we discuss nonphysical solutions that appeared in some of the runs presented here. 2. Parameterizations of subgrid-scale mixing In this paper, we compare the effects of two relatively sophisticated parameterizations of subgrid-scale mixing to the simpler alternatives of prescribed uniform horizontal and vertical mixing. The first parameterization studied is the Gent McWilliams parameterization of the effects of subgrid-scale eddies on tracer transport (Gent and McWilliams 1990, hereafter referred to as GM90). This parameterization consists of isopycnal diffusion of tracers, as well as additional advective terms representing an eddy-induced transport velocity. Tracers are transported by a velocity that is the sum of the usual large-scale velocity plus the eddy-induced transport velocity, given by Gent et al. (1995) h h u* t, w* t. (1) z z z TABLE 1 Summary of the treatment of subgrid-scale mixing of tracers in the simulations presented here. Runs 2 and 4 use the Gent McWilliams tracer transport parameterization; the thickness diffusivity determines the magnitude of eddy-induced transport velocities used in this parameterization [see Eq. (1)]. Run Diffusivity (cm 2 s 1 ) Horizontal Thickness Isopycnal Vertical a/n a/n Here u* and w* are the horizontal and vertical eddyinduced transport velocities, t is the thickness diffusivity, h is the two-dimensional gradient operator applied at constant z, is the divergence operator, and is the local water density. The GM90 parameterization has been shown to largely eliminate the chronic tendency of GFDL-based ocean models to overestimate temperatures at intermediate depths [i.e., to have too diffuse a thermocline; Danabasoglu et al. (1994); Danabasoglu and McWilliams (1995)]. In addition, the GM90 parameterization, unlike earlier isopycnal mixing parameterizations (Redi 1982; Cox 1987) does not require residual horizontal mixing for numerical stability. However, we find (as have others; e.g., Hirst and Mc- Dougall 1996) that our model is more susceptible to two types of numerical problems with GM90 than with horizontal mixing (see the appendix). Since model results for any single tracer (such as temperature) can often be brought into reasonable agreement with observations by adjusting model parameters (and without necessarily obtaining realistic model circulation), an essential test of any parameterization is its ability to accurately simulate more than one tracer at once (i.e., with a single set of model parameter values). Results so far for the GM90 parameterization are reasonably encouraging. Duffy et al. (1995a,b) showed that, compared to horizontal mixing, the GM90 parameterization had little effect on a simulated vertical profile of bomb 14 C, while dramatically improving the vertical temperature profile in the same simulation; thus, a net improvement was obtained. Similarly, Robitaille and Weaver (1995) showed that, compared to horizontal mixing, the GM90 parameterization improved simulated distributions of CFC-11 and (on the whole) improved simulated temperatures. On the other hand, compared to results obtained with simple isopycnal diffusion (Cox 1987; equivalent to GM90 with u* and * set to zero), Robitaille and Weaver found that GM90 worsened both simulated temperatures (below about 2-km depth) and salinities but improved simulated distributions of CFC-11. This paper focuses on the effects of GM90 on simulated distributions of natural 14 C (i.e., not bomb 14 Cor 14 C released by deforestation) and temperature. Since the radioactive decay half-life (5730 years) of 14 Cisof the same order as the large-scale overturning time of the ocean, simulated distributions of 14 C are an important diagnostic of the simulated large-scale ocean circulation and, in particular, are sensitive to rates of vertical overturning. As discussed by Broecker and Peng (1982), subsurface 14 C values can be used to quantitatively estimate how long ago the water mass in question was last in contact with the atmosphere. The second parameterization examined in this paper deals with vertical, not isopycnal, mixing of tracers by subgrid-scale motions. This parameterization is based on evidence suggesting that the amount of vertical mixing in the ocean is inversely proportional to the local Brunt

3 500 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 FIG. 1. Maps showing rates of loss of potential energy (W m22) due to convective adjustment in (a: top left) run 1 (horizontal mixing, prescribed vertical mixing), (b: bottom left) run 2 (GM90 parameterization, prescribed vertical mixing), (c: top right) run 3 (horizontal mixing; stability-dependent vertical mixing), and (d: bottom right) run 4 (GM90 and stability-dependent vertical mixing). At each horizontal grid cell, the rate of energy loss shown is summed over all model layers; results shown are annual means. Convective adjustment is more active with horizontal mixing (runs 1 and 3) than with GM90 (runs 2 and 4). In addition, stability-dependent vertical mixing results in less convective adjustment than does prescribed vertical mixing. Global mean rates of loss of potential energy due to convective adjustment are , , , and W m22) in runs 1 through 4, respectively. The color scale is 1000 times more sensitive in (b) and (d) than in (a) and (c).

4 APRIL DUFFY ET AL. FIG. 1. (Continued) Va isa la frequency (Hirst and Cai 1994; Gargett 1984, and references therein). Hence, in this parameterization the coefficient of vertical diffusivity is calculated based on the local vertical density gradient. That is, the part of the tracer evolution equation describing vertical diffusion looks like 1 2 dt ] ]T 5 k 1..., dt ]z v ]z (2) where T is the concentration of any tracer and the vertical diffusion coefficient k v is given by kv 5 a 5 N a! 2g r r0 z. (3) Here a is a constant, N is the Brunt Va isa la frequency, r is the local density, and r0 is a reference density. As

5 502 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27

6 APRIL 1997 DUFFY ET AL. 503 FIG. 2.(Continued) pointed out by, for example, Gill (1982), this definition of N is an approximation that may be inaccurate in the deep ocean. Following Gargett (1984) and Hirst and Cai (1994), we use a value of a cm 2 s 1. Again following Hirst and Cai, we impose upper and lower limits on of 0.2 and cm 2 s 1, to ensure numerical stability. This a/n parameterization has been used before in an ocean basin model (Cummins et al. 1990) and in a global model (Hirst and Cai 1994). Hirst and Cai found that the a/n parameterization has relatively minor effects on simulated distributions of temperature and salinity, compared to using prescribed, depth-dependent vertical diffusivities. In this paper, we look at the effects of the a/n parameterization on simulated temperature and natural 14 C values; in addition we for the first time use the a/n parameterization together with the GM90 parameterization and look at the combined effects of these parameterizations on simulated distributions of temperature, salinity, and natural 14 C. 3. Model description and configurations The model used here is the LLNL ocean circulation model, which is based on the GFDL Modular Ocean Model (MOM), version 1.1 (Pacanowski et al. 1991). The GFDL model and its relatives are the most widely used ocean models in climate research. A number of important physics enhancements have been made to the model at the LLNL; the only important one used here (besides the parameterizations that are the subject of this paper) is the dynamic/thermodynamic sea ice model of Oberhuber (1993). Computationally, our ocean model has been completely redesigned, with the primary goal of allowing it to run on a variety of massively parallel computers. (The simulations discussed here were performed on 32 processors of a Cray T3D.) In addition, the original two-dimensional data structures have been replaced with fully three-dimensional arrays (such as for temperature, salinity, and so on) to make the code easier to read and modify. Computational aspects of our model are discussed by Mirin et al. (1994). Except for the treatment of subgrid-scale mixing, the model configurations are identical in the four simulations presented here. Table 1 summarizes the treatment of subgrid-scale mixing in our four runs. In run 1, we use prescribed horizontal and vertical mixing of tracers, with mixing coefficients of cm 2 s -1 (horizontal) and 0.5 cm 2 s -1 (vertical). In run 2, we eliminate the horizontal mixing and use the GM90 parameterization, with isopycnal and thickness diffusivities of cm 2 s -1. Run 3 reverts to prescribed horizontal mixing and uses the stability-dependent vertical mixing parameterization described above. Run 4 uses both the GM90 and stability-dependent vertical mixing. All four runs use the same treatment of mixing of momentum: horizontal and vertical viscosities of and 20 cm 2 s -1 Fig. 2. Overturning streamfunctions, zonally averaged over the Atlantic Ocean, in (a) run 1 (horizontal mixing), (b) run 2 (GM90 parameterization), (c) run 3 (stability-dependent vertical mixing, horizontal mixing), and (d) run 4 (stability-dependent vertical mixing, GM90). The units are sverdrups (10 6 m 3 s 1 ). The results for runs 2 and 4 include the Gent McWilliams eddy-induced transport velocity. In run 2, there is less vigorous vertical overturning at about latitude 60 N and also at about latitude 70 S, compared to in run 1. Panels (e) (h) are the same as (a) through (d), respectively, except show the global, rather than Atlantic Ocean, streamfunction.

7 504 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 TABLE 2 Simulated and observed ocean flows, in Sverdrups (1 Sv 10 6 m 3 s 1 ). The row labeled Southward NADW at 32 S lists southward flows associated with North Atlantic Deep Water at latitude 32 S. The bottom row gives southward flows in the deep Atlantic associated with either North Atlantic Deep Water or Antarctic Bottom Water; that is, it gives the total southward flow in the deep Atlantic at 32 S. Run Observed Reference Drake Passage Whitworth (1983) Indonesian Throughflow Shmitz (1995) Fieux et al. (1994) 16 4 Godfrey (1989) Southward NADW at 32 S Shmitz (1995) Southward NADW AABWat32 S Shmitz (1995) respectively are prescribed. All four runs use relatively coarse resolution (3 deg by 3 deg with 15 vertical levels). The topography was smoothed to aid convergence of the rigid-lid conjugate gradient solver. This was accomplished via 10 passes of a local two-dimensional symmetric filter supplied by GFDL for this purpose. In addition, some isolated tracer points were filled in to prevent local minima or maxima in tracer values from forming there. Despite this, at least two grid points in the extreme Southern Ocean appear to have nonphysical tracer values in our GM90 runs. These nonphysical values do not appear to have spread to surrounding cells, and we believe that they have no significant effect on our overall solutions (Hirst and Mc- Dougall 1996) and no effect on our conclusions; see the appendix. Climatological wind stresses (Hellerman and Rosenstein 1983) are applied at the surface; the stresses are time interpolated between monthly mean observed values to avoid sudden changes in forcing. Surface salinity values are restored to monthly mean values inferred from observations by Levitus (1982). We used the surface boundary condition for heat described by Oberhuber (1993). This is neither a prescribed heat flux, nor a restoring-type boundary condition. Instead latent, sensible, shortwave and longwave radiative components of the heat flux are calculated, based on monthly climatological atmospheric data (temperature, relative humidity, wind speed, cloud cover, etc.) and modeled ocean temperatures. This is the same sort of boundary condition used in coupled ocean atmosphere models except that here we obtain atmospheric quantities from observations instead of from a model. The treatment of carbon 14 in our simulations is identical to that used in run P of Toggweiler et al. (1989). Here the quantity transported by the model is 14 C. Since 14 C is essentially a ratio, it is not a conserved quantity and strictly speaking should not be treated as such in our model. That we do treat 14 C as a conserved quantity is approximately equivalent to assuming that the ocean 12 C concentration is spatially uniform (since 14 C is essentially a normalized 14 C/ 12 C ratio); in reality, the GEOSECS observations indicate that these concentrations vary by up to about 15% at different locations in the ocean. The model is forced with a spatially uniform and time-independent atmospheric 14 C value of zero. In our model, air sea gas exchange is proportional to the difference between the atmospheric and ocean surface 14 C values and depends linearly on the local wind speed [as in Toggweiler et al. 1989, Eq. (11)]. Biological transport of carbon in the ocean is neglected; the only transport processes modeled are advection, diffusion, and convection. While this treatment of carbon 14 is somewhat simplified, it is adequate for our purpose here, which is to examine the sensitivity of simulated 14 C distributions to different parameterizations of subgrid-scale mixing. All four simulations presented here were initialized from Levitus (1982) observed temperatures and salinities, with the ocean at rest. We used the method of Bryan (1984), in which longer time steps are used in the deeper model layers to accelerate the convergence of the model solution toward equilibrium. Each simulation was run for 1500 simulated years, or the equivalent of 7500 years in the bottom model layer, in order to approach a steady state. At the end of the spinup period, the maximum rate of change of temperature in any individual grid cell in the bottom model layer (in any of our runs) is 0.09 C per century. The final 25 years of each simulation were run without deep-ocean acceleration to diminish distortions in the seasonal cycle (Danabasoglu et al. 1996). Such distortions should be minimal anyway because acceleration was applied only below depth 2.65 km, where there is no measurable seasonal cycle. Results presented here are annual means averaged over the last 5 years of the simulation in question. 4. Results In this section we discuss the effects of the GM90 parameterization on ocean circulation and on simulated tracer values. We find that GM90 improves simulated temperatures and 14 C values in the thermocline but makes the deep ocean too cold and too old. Next we look at the effects of the a/n parameterization on circulation and on simulated tracer values. We find that this parameterization has relatively modest effects on

8 APRIL 1997 DUFFY ET AL. 505 FIG. 3. Latitude depth sections of temperature differences (model minus observed, or model minus model) averaged in longitude over the Atlantic or Indo-Pacific basin. (a) Run 1 minus run 2 in the Atlantic Ocean. (b) Run 1 minus observed (Levitus and Boyer 1994) temperatures in the Atlantic, showing that with prescribed horizontal mixing the simulated ocean is too warm at intermediate depths. (c) The same as in (b) except for run 2. This shows that in our runs the GM90 parameterization largely eliminates the tendency for the simulated thermocline to be too warm but also causes the deep ocean to be too cold, by up to more than 3 C. (d) Run 2 minus observed temperatures in the Indo-Pacific.

9 506 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 FIG. 4. Global-mean vertical profiles of (a) natural 14 C, (b) potential temperature, and (c) salinity in our simulations and (for temperature and salinity) as inferred from observations by Levitus and Boyer (1994). (d) Mean vertical profiles of 14 C at the locations of GEOSECS stations from the GEOSECS observations and from our simulations. The GEOSECS observations, but not our simulations, include bombproduced 14 C. Therefore, GEOSECS stations poleward of 60 latitude, where bomb 14 C penetrates rapidly, are excluded from this comparison. The model and simulated 14 C values should be directly comparable below about 1 km where there should be little bomb 14 C. simulated tracer values but tends to improve agreement with observed temperatures and 14 C values. a. Effects of the Gent McWilliams parameterization on simulated ocean circulation Although this paper focuses on effects of subgridscale mixing parameterizations on simulated distributions of tracers, particularly radiocarbon, we start by looking at the effects of the GM90 parameterization on simulated ocean circulation. In addition to the obvious effect of reorienting diffusive mixing from horizontal to isopycnal, GM90 also has important effects on the other model transport processes (advection and convective adjustment). Danabasoglu et al. (1994), Duffy et al. (1995a), and Hirst and McDougall (1996) all showed that much less convective adjustment occurs with the GM90 parameterization than with horizontal mixing. The main reasons for this are that, as shown below, the simulated deep ocean is much colder with GM90 than with horizontal mixing; thus, with GM90 the ocean is more stably stratified. In addition, as discussed by Hirst and McDougall (1996) the Gent McWilliams eddy-induced transport velocities [u* in Eq. (1)] tend to reduce the slopes of neutral surfaces when those are nearly vertical. As shown in Fig. 1, our results also show that GM90 reduces convective activity. Since convective adjustment mixes vertically adjacent grid boxes when the upper box is denser than the lower one, this process reduces potential energy in the simulated ocean. Here we show maps of the rate of loss of potential energy due to convective adjustment, vertically integrated; this

10 APRIL 1997 DUFFY ET AL. 507 FIG. 5. Latitude depth sections of temperature, averaged over longitude in the Atlantic Ocean for (a) run 1 and (b) run 2. is a more useful diagnostic than the frequency of convective adjustment in that it gives some indication of the size of density instabilities removed by convective adjustment. We find that with GM90 the rate of loss of potential energy by convective adjustment is about three orders of magnitude less than it is with horizontal mixing. Since there is no analog in the real ocean to convectively mixing areas of ocean as large as the grid cells in our model, one suspects a priori that this reduction in convective adjustment is an improvement. We show below by comparing simulated to observed tracer distributions that this is, in fact, the case. Figure 2 shows the effects of GM90 on simulated overturning streamfunctions in the Atlantic basin and globally. GM90 reduces the strength of the overturning streamfunction in at least two important locations. First,

11 508 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 FIG. 6. Latitude depth sections of 14 C. (a) Run 1, Atlantic Ocean; (b) run 2, Atlantic Ocean; (c) run 3, Atlantic Ocean; (d) run 4, Atlantic Ocean; (e) GEOSECS observations, western Atlantic Ocean; (f j) same as in (a e) except for Indo Pacific basin. The observations (e and j) are dominated in the upper ocean by bomb-produced 14 C, which is not included in the simulations. Thus, the observations can be compared to the simulation only at depths below a kilometer or so at midlatitudes and deeper at high latitudes.

12 APRIL 1997 DUFFY ET AL. 509 FIG. 6.(Continued)

13 510 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 FIG. 6.(Continued)

14 APRIL 1997 DUFFY ET AL. 511 the rate of formation of North Atlantic Deep Water (NADW) is reduced; in addition, as noted by Danabasoglu et al. (1994) and by Hirst and McDougall (1996), the strong Deacon cell in the Southern Ocean is eliminated. The reduced vertical overturning in the Atlantic with GM90 is consistent with the interpretation of Gerdes et al. (1991) of the results of Bryan (1987). Bryan showed that the strength of zonally averaged advective vertical overturning decreases with decreasing vertical diffusivity; Gerdes et al. noted that the important factor is actually diapycnal, not vertical, mixing (i.e., that overturning is sensitive to the strength of diapycnal mixing, not vertical mixing). Our results are consistent with this interpretation in that GM90 results in less diapycnal mixing and weaker vertical overturning than does horizontal mixing. Based on observations, Schmitz (1995) estimates the flow of NADW out of the Atlantic at about 14 Sv (Sv 10 6 m 3 s 1 ). This flow is too weak in all our simulations, but especially in those using GM90 (Table 2). On the other hand, the proportion of NADW that exits the Atlantic is higher with GM90 than with horizontal mixing; that is, there is less midlatitude upwelling of NADW with GM90 (Fig. 2). As pointed out by Böning et al. (1995), GM90 is more realistic than horizontal mixing in this respect. Table 2 also shows that GM90 significantly reduces flow through the Drake Passage compared to the flow obtained with horizontal mixing. In both the GM90 simulations we ran, the simulated flows are less than the lower limit on the observed flow (i.e., the simulated flows are too low). However, Danabasoglu and McWilliams showed that simulated flow through the Drake Passage is sensitive to model parameter values (and in some cases is consistent with estimated observed flows); thus, we cannot make the general statement that flow through the Drake Passage is too low with GM90. b. Effects of the Gent McWilliams parameterization on simulated temperatures We start this section by comparing simulated temperatures in run 1 (horizontal mixing) to those in run 2 (GM90). The temperature differences between run 1 and run 2 are the net result of differences in all three modes of transport advection, diffusion, and convection between these runs. As noted above, meridional overturning at high latitudes in the Atlantic Ocean is more vigorous in run 1 (horizontal mixing) than in run 2 (GM90). Since NADW is warmer (and saltier) than Antarctic Bottom Water (AABW), reducing the rate of formation of NADW should make the interior ocean colder (and fresher). Indeed, there is a local maximum in the temperature differences between run 1 and run 2 (Fig. 3a) at the location of the NADW overturning cell. In addition, Fig. 4 shows that our runs with GM90 are fresher than our runs with horizontal mixing at typical depths of NADW in our model (around 2 km). These facts suggest that reduced NADW is one reason why run 2 is cooler than run 1, at least in the upper 2 km or so of the Atlantic Ocean. Nonetheless, Fig. 3a suggests that, over most of the Atlantic Ocean, the temperature differences between run 1 and run 2 are due primarily to circulation changes in the south, not in the north. In the south, GM90 results in major changes (relative to horizontal mixing) in all three modes of transport in the model. The effects of these changes can be seen in Fig. 5, which shows that in the South Atlantic, isotherms are nearly vertical in run 1, but slope significantly toward the low-latitude deep ocean in run 2; this results in the Southern Ocean being much cooler in run 2 than in run 1. Differences in all three modes of transport advection, convective adjustment, and diffusive mixing between runs 1 and 2 likely contribute to this temperature difference (although the relative sizes of the different contributions are not clear). First, the effective cancellation of the Deacon cell by the GM90 eddy-induced transport velocity should make run 2 cooler than run 1 in this area since the Deacon cell supplies relatively warm water to the subsurface ocean. Second, as discussed above, convective adjustment is much more vigorous in run 1 than in run 2. Since much of this reduction is at relatively low latitudes (e.g., 50 S where SSTs are in the neighborhood of 10 C), this change, perhaps counterintuitively, tends to make the interior ocean warmer in run 1 than in run 2. (Adding convective adjustment to run 2 would force the sloping isotherms in the Southern Ocean to become more nearly vertical, increasing temperatures at depths of 1 3 km.) Finally, diffusive changes also tend to make run 2 cooler than run 1 in the interior ocean. Since isopycnal surfaces slope most steeply at high latitudes, isopycnal mixing increases vertical (but not diapycnal) mixing at high latitudes, compared to horizontal mixing. Since isopycnal mixing rates are typically 10 7 to 10 8 times higher than prescribed vertical mixing rates, the vertical component of isopycnal mixing far exceeds the explicit vertical mixing even for typical isopycnal slopes of (This is discussed by Hirst and Cai 1994). Thus, at high latitudes the total vertical mixing (prescribed plus the vertical component of isopycnal mixing) in run 2 is often much greater than in run 1; this cools the interior ocean by increasing heat loss to the cold high-latitude atmosphere. More simply, isopycnal surfaces tend to outcrop (reach the ocean surface) at high latitudes where surface air temperatures are very cold. Thus, isopycnal mixing, unlike horizontal mixing, connects the interior ocean to the very cold high-latitude atmosphere. The importance of this heat-transport mechanism is confirmed by the results of Danabasoglu and McWilliams (1995), who show that temperatures throughout the ocean decrease significantly as the coefficient of isopycnal mixing is increased. In summary, changes in all three modes of transport contribute to the Southern Ocean being colder with GM90 than with horizontal mixing. We now turn to a comparison between simulated tem-

15 512 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 FIG. 7. Scatterplot of observed minus model vs observed 14 C values at locations of GEOSECS stations. Locations poleward of 60 latitude and above 1 km are omitted because at those locations observed 14 C values are dominated by bomb-produced 14 C, which is not included in the simulations. FIG. 8. As in Fig. 7 except the horizontal axis is latitude.

16 APRIL 1997 DUFFY ET AL. 513 FIG. 9. As in Fig. 7 except the horizontal axis is longitude. peratures in run 2 and observed temperatures. As discussed above, it is by now well known that GM90 eliminates the chronic tendency in GFDL-based models for the thermocline region to be too warm (Danabasoglu et al. 1994; Duffy et al. 1995a,b; Robitaille and Weaver 1995). Our simulations also show this effect; for example, in run 1 the Atlantic Ocean is too warm by as much as 4 C (Figs. 3b, 4) at intermediate depths. Substituting the GM90 parameterization for horizontal mixing largely eliminates this problem but also causes the deep ocean FIG. 10. As in Fig. 7 except the horizontal axis is depth.

17 514 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 to be too cold, by more than 3 C in places in the Atlantic (Fig. 3c) and as much as C in the Pacific (Fig. 3d; see also Fig. 4). Other published simulations using isopycnal mixing or the GM90 parameterization also are too cold in the deep ocean, suggesting that this problem is generic to isopycnal mixing parameterizations and is not simply the result of poor model configuration. For example, Robitaille and Weaver (1995) find that their horizontal-mean simulated temperature in their lowest model layer is too cold by about 1.5 C with the GM90 parameterization, and by about half that much with the Cox (1987) isopycnal mixing parameterization (which included no diffusion of isopycnal layer thickness, i.e., no eddy-induced transport velocities). Hirst and Cai (1994) also used the Cox (1987) isopycnal mixing parameterization and found that their bottom model layer was too cold by about 1 C. In addition, Danabasoglu et al. (1994) found that with the GM90 parameterization their simulated mean ocean temperature (in the global mean) was too cold by 0.3 C. More recently, Danabasoglu and McWilliams (1995) found that their simulated deep ocean was too cold in three different simulations with isopycnal and thickness diffusivities ranging from to cm 2 s 1. The overly cool deep ocean obtained with GM90 is likely due at least in part to the fact that the deep North Atlantic is ventilated primarily via AABW rather than NADW. This may be due in part to an insufficient rate of formation of NADW but is likely also a result of insufficient downward penetration of NADW, especially insufficient isopycnal overflow through the Denmark Strait. As discussed below, insufficient downward penetration of NADW also explains why simulated 14 C values in the North Atlantic are much too low in our runs with GM90. c. Effects of the Gent McWilliams parameterization on simulated 14 C values We start this section by briefly comparing simulated 14 C values in our baseline simulation (run 1) to the results of run P of Toggweiler et al. (1989). In the Pacific Ocean, our run 1 results are qualitatively similar to those of Toggweiler et al. As in the results of Toggweiler et al., in our run 1 the minimum in simulated 14 C at about 3-km depth is located too far north (Fig. 6f; it is at about 50 latitude vs about 30 in the observations). Our simulated 14 C value at the location of that minimum is about 225 per mil, a bit higher than the observed minimum of 240 and than Toggweiler et al. s value of between 240 and 260 per mil. This difference between our run 1 and run P of Toggweiler et al. is no doubt due to slight differences in our model configurations. Our results for the Atlantic Ocean are again similar to those of Toggweiler et al. s run P. In both simulations, lines of constant 14 C are nearly vertical in the Southern Ocean (this is true in the Pacific as well; see Toggweiler et al. s Figs. 9 and 10 and our Figs. 6a and 6f); this is a sign of excessive convective adjustment, which accompanies horizontal mixing. This vertically mixed region extends to the ocean bottom in our run 1, but only to 1 or 2 km in Toggweiler et al. s run P. We now turn to the effects of the GM90 parameterization on simulated distributions of natural 14 C. As with temperature, we compare the results of run 1 (prescribed horizontal and vertical mixing) to those of run 2 (GM90, prescribed vertical mixing); we also compare the results of run 3 (horizontal mixing, a/n vertical mixing) to those of run 4 (GM90, a/n vertical mixing). We start with a qualitative discussion of the results. The main effect of GM90 on simulated 14 C values is that interior ocean 14 C values are consistently lower (i.e., the water is older ) with GM90 than with horizontal mixing. This is true in both Atlantic and Indo Pacific basins (Fig. 6) and therefore also in the global mean (Fig. 4). For example, 14 C values in the Pacific Ocean 14 C minimum (discussed above, at about latitude 50 N) are about 275 per mil in run 2 and about 225 per mil in run 1 (again, the observed value is about 240 per mil). Also, in the North Atlantic, the minimum 14 C value in the deep ocean is about 250 per mil in run 2 compared to about 180 per mil in run 1. The general reasons for the lower 14 C values in the GM90 runs can be understood in light of the circulation differences discussed above between horizontal mixing and GM90. The reduction in meridional overturning and in convective adjustment with GM90 both reduce the frequency with which interior water is exposed to the atmosphere. This results in older water (i.e., lower 14 C values) in runs 2 and 4 compared to in runs 1 and 3. The other principal effect of GM90 on simulated 14 C values also has to do with convective adjustment. As discussed above, in our runs with horizontal mixing, high-latitude regions are well mixed vertically (i.e., there are no vertical gradients in 14 C); this is especially true in the south. This is not the case in our runs that use GM90. The reason for this difference is the greatly reduced convective adjustment in runs 2 and 4 compared to runs 1 and 3. Since convective adjustment is an instantaneous mixing process, it leaves the vertical water column with no vertical gradients in any tracer. Our results for salinity (not shown) show the same difference between runs 1 and 3 and runs 2 and 4: in runs 1 and 3, the Southern Ocean is nearly well mixed vertically (by convective adjustment), whereas runs 2 and 4 have vertical salinity gradients in the Southern Ocean. The presence of vertical gradients in observed salinity and 14 C in the Southern Ocean confirms that the reduced frequency of convective adjustment in runs 2 and 4 is an improvement over runs 1 and 3. To start making more quantitative assessments of our results, we compare simulated and observed vertical profiles of 14 C at the locations of GEOSECS stations (Fig. 4d). To eliminate contamination by bomb 14 C (which is included in the observations but not the sim-

18 APRIL 1997 DUFFY ET AL. 515 ulations) we eliminated from this comparison GEO- SECS stations located poleward of 60 latitude, where bomb 14 C penetrates rapidly. Equatorward of latitude 60 there should be little bomb 14 C below about 1 km; thus in Fig. 4d the GEOSECS and model 14 C values should be directly comparable below 1 km. This figure confirms our qualitative impression that deep-ocean 14 C values are lower with GM90 than with horizontal mixing. It also indicates that, in the model configurations we used, GM90 makes simulated 14 C values more realistic in the thermocline but worse (too low) in the deep ocean. To investigate this further, we compare individual GEOSECS 14 C measurements to simulated values at the same locations. (Again, locations poleward of 60 latitude and shallower than 1 km are excluded from the analysis.) A total of 897 geographical locations are included in this comparison; this exceeds the number of GEOSECS stations because at each station measurements were made at multiple depths. Figure 7, which shows scatterplots of model minus observed versus observed 14 C values, indicates that in runs 1 and 3, most simulated 14 C values are slightly too high; in addition, in these runs simulated 14 C values are too low by up to about 100 per mil at a number of locations where observed 14 C values are about 50 or 100 per mil. The GM90 parameterization reduces most of the simulated 14 C values; in the model configurations used here, this largely eliminates the tendency for simulated 14 C values to be too high; in fact, in run 4 almost all simulated 14 C values shown in Fig. 7 are too low. Figure 7 also shows that GM90 exacerbates the tendency mentioned above for modeled 14 C values to be much too low at some locations; whereas in runs 1 and 3 simulated 14 C values are too low by at most about 100 per mil, in run 2 the maximum error is almost 200 per mil. Further insight into this situation is obtained from Figs. 8 10, which show the difference between modeled and observed 14 C values as a function of latitude, and longitude, and depth respectively for all our runs. These figures clearly show that the locations where the model severely underestimates 14 C are confined to the deep North Atlantic Ocean and that the problem appears worse with GM90 than with horizontal mixing. The cause of the problem seems to be that, as discussed in section 4b, the deep North Atlantic in all our simulations is ventilated primarily via AABW rather than via NADW. (Evidence for this is that the 14 C age of NADW is about the same in all our simulations, yet the ages of AABW and of the deep North Atlantic vary substantially among our different runs.) Thus, the deep North Atlantic is too old not because of insufficient rates of formation of NADW, but, rather, because NADW does not penetrate far enough downward. This is true both with GM90 and with horizontal mixing, but the symptoms it produces are worse with GM90. The deep North Atlantic is older with GM90 than with horizontal mixing apparently because with GM90 the deep South Atlantic is older (due to reduced convective adjustment); since the deep North Atlantic (incorrectly) ventilates primarily via AABW, the older South Atlantic with GM90 results in the North Atlantic being older as well. Figure 9 also shows that, except in the North Atlantic, GM90 improves simulated 14 C values in our runs that used prescribed vertical mixing. However, this improvement is probably quite sensitive to values of parameters, especially isopycnal and vertical diffusivities, and thus is probably not a fundamental property of the GM90 parameterization. The fact that simulated 14 C values are almost all too low with the a/n vertical mixing parameterization and GM90 (i.e., in run 4) proves this. Thus far we have not directly addressed the question, does or does not the GM90 parameterization improve simulations of natural 14 C? In fact, that question is not particularly meaningful because of the degree to which model results can be influenced by adjusting model parameter values (or surface forcings). A good simulation of one tracer is relatively easy to obtain and does not necessarily indicate good simulated circulation. It is much harder, however, to tune a model to accurately simulate two or more different tracers at once (i.e., with the same set of parameter values); accurate simulation of multiple tracers is more likely to indicate good model circulation than accurate simulation of only one tracer. Thus, a more useful measure of a mixing parameterization is its ability to simulate multiple tracers with a single set of parameter values. We therefore evaluate GM90 and a/n based on their abilities to simultaneously simulate temperature and natural 14 C. (As discussed below, simulated salinity distributions in all our runs are sufficiently poor that is it probably not useful to discuss which of them is better.) An important feature of our results is that (compared to horizontal mixing) GM90 reduces both temperatures and 14 C values in most areas of the ocean. In the runs presented here, this results in better agreement with observations (for both temperature and 14 C) in the thermocline but worse agreement in the deep ocean, which is both too cold and too old (i.e., 14 C values are too low). Increasing the coefficient of vertical diffusivity would both warm the deep ocean and increase 14 C values there; thus, this change could potentially improve both simulated temperature and natural 14 C, at least in the deep ocean. However, our previous simulations of bomb 14 C (Duffy et al. 1995a,b) which were made with the same model in configurations very similar to those used here suggest that vertical diffusivities higher than those used here would probably result in overestimation of ocean uptake of bomb 14 C. Alternatively, simulated 14 C values could be increased (and brought into better agreement with observations) by increasing the coefficient of isopycnal diffusivity. This would increase communication between the deep ocean and the atmosphere at high latitudes, where isopycnal surfaces tend to outcrop. Sensitivity studies (Danabasoglu and McWilliams

19 516 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 FIG. 11. Latitude depth sections of vertical diffusivity as calculated based on local density gradients in (a: top right, b: bottom right) run 3 and (c: top left, d: bottom left) run 4 in the Atlantic and Pacific basins. Vertical diffusivities are not allowed to go below 0.2 cm 2 s 1 or above cm 2 s 1 for numerical stability. Diffusivities tend toward the minimum value (0.2 cm 2 s -1 ) in the upper ocean and increase

20 APRIL 1997 DUFFY ET AL. 517 FIG. 11. (Continued) with increasing depth. The very high vertical diffusivities sometimes seen with horizontal mixing (run 3) are largely absent with GM90.

21 518 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME ) have shown, however, that increasing the isopycnal diffusivity would worsen the problem of the deep ocean being too cold. Thus, it is hard to imagine how our model parameter values could be adjusted to improve tracer values in the deep ocean simulated with GM90. The obvious way to improve both simulated temperature and 14 C values in the deep ocean in our GM90 runs would be to increase the depth of penetration of NADW; this would bring relatively young warm water into the deep North Atlantic. We know of no way to accomplish this by adjusting model parameters, however. To summarize this section and the previous, we find that GM90 makes simulated temperatures and 14 C values lower in all areas, but especially in the deep North Atlantic. The reduction in simulated 14 C values is due to reductions in convective adjustment and in the vigor of meridional overturning with GM90 compared to horizontal mixing. Both these effects result in older water (i.e., lower simulated 14 C values). Whether these lower 14 C values obtained at depths above 3 km are more or less realistic than those obtained with horizontal mixing depends on values of model parameters that are inaccurately known. In the deep North Atlantic, however, agreement with 14 C observations is poor when horizontal mixing is used and is even worse with GM90 (simulated values are too low). The tendency with GM90 to underestimate temperatures and 14 C values in the deep North Atlantic is apparently due at least in part to an unrealistically low depth of penetration of NADW; this results in the simulated deep North Atlantic incorrectly being ventilated primarily via AABW rather than via NADW. While this problem also exists when horizontal mixing is used instead of GM90, the symptoms it produces (underestimated temperatures and 14 C values in the deep North Atlantic) are worse with GM90. d. Effects of stability-dependent vertical mixing on simulated ocean circulation In this section we begin assessing the effects of the a/n parameterization described above, in which vertical mixing coefficients are based on local vertical density gradients. Results obtained with this scheme will be compared to results obtained with prescribed, uniform vertical mixing. Care must be used in drawing general conclusions from this comparison, however, because we have not optimized values of free parameters in either of the vertical mixing parameterizations we use. [Those parameters are a in Eq. (3) in the case of the a/n parameterization and the vertical diffusivity in the case of prescribed vertical diffusivity.] Thus, the results that we are comparing are all at least somewhat suboptimal. This caveat does not apply to our comparison of GM90 to horizontal mixing. In those parameterizations, the only free parameters are diffusivities; setting all these to the same value makes our GM90 runs directly comparable to our runs with horizontal mixing. The method that we use for calculating stability-dependent vertical diffusion of tracers is described in section 2 and is used in runs 3 and 4 (Table 1). Before looking at simulated tracer values, we look at the effects of this parameterization on simulated diffusion, advection, and convection. Figure 11 shows latitude depth sections of vertical diffusivities obtained this way, in the Atlantic and Pacific Oceans, with horizontal mixing and with GM90 (i.e., in runs 3 and 4). In general, diffusivities tend toward the minimum value (0.2 cm 2 s 1 ) in the upper ocean and increase to 1 or 2 cm 2 s 1 in the deep ocean. These diffusivities are similar to those obtained by Hirst and Cai (1994) and are similar to the depth-dependent vertical diffusivities often prescribed in GCM studies (e.g., Toggweiler et al. 1989; Sarmiento and Orr 1992). Of course, having the model calculate the diffusivities using a realistic physics-based parameterization is preferable to prescribing them in that it allows the diffusivities to change in response to changes in ocean density; that is, it gives the model more predictive capability. A striking difference between run 3 and run 4 is that the very high vertical diffusivities (i.e., very small vertical density gradients) seen in run 3, especially in the highlatitude Southern Ocean, are largely absent in run 4 (Fig. 11). This occurs in part for the same reasons that convective adjustment occurs less frequently in run 4 than in run 3 (section 4a). Another reason is that convective adjustment can cause very low vertical density gradients (and thus very high vertical diffusivities with a/n). While convective adjustment eliminates density instabilities (i.e., eliminates the occurrence of denser water overlying less dense water), it results in vertically adjacent grid cells having exactly the same density; that is, it results in areas having zero vertical density gradient. This in turn results in very high vertical diffusivities when the a/n parameterization of vertical mixing is used (as in run 3). By contrast, with GM90 convective adjustment is dramatically reduced; thus, fewer regions of very high vertical diffusivity exist. The occurrence of very high vertical diffusivities in run 3 but not run 4 can also be seen in maps of the vertical diffusivities between the top two model layers (Fig. 12). Comparing these maps to maps of potential energy loss due to convective adjustment (Fig. 1) shows that, as expected, the high vertical diffusivities in run 3 occur in areas where convective activity is high. With the a/n parameterization, very high vertical diffusivities are to some extent a substitute for convective adjustment. Figure 2 shows that meridional overturning is less vigorous with stability-dependent vertical mixing than with prescribed vertical diffusivities of 0.5 cm 2 s 1. This is true in both ocean basins, and with GM90 as well as with horizontal mixing (i.e., in run 3 compared to run 1, and in run 4 compared to run 2; Fig. 2). Since upperocean vertical diffusivities are less in runs 3 and 4 than in runs 1 and 2, this is consistent with the results of Bryan (1987) and Gerdes et al. (1991), who together

22 APRIL 1997 DUFFY ET AL. 519 showed that reduced diapycnal diffusivities in the thermocline result in less vigorous meridional overturning and less latitudinal heat transport. The rate of formation of NADW obtained in our runs with a/n is probably unrealistically low; as discussed in section 4a, it is estimated from observations that about 14 Sv of NADW flow southward at latitude 32 S; Figure 2 indicates that the simulated flows in runs 3 and 4 are much less than this. (As discussed in section 4a and by Boning et al. 1995, GM90 reduces upwelling of NADW near the equator, in better agreement with observations than results obtained with horizontal mixing.) This problem could be corrected to some degree by increasing the value of a in Eq. (3), which would increase vertical diffusivities everywhere and consequently increase meridional overturning (Bryan 1987). Of course, this adjustment could lead to other problems. Comparing our two runs that use horizontal mixing (runs 1 and 3), we find that energy loss due to convective adjustment is about 20 times lower with stability-dependent vertical mixing (run 3) than with prescribed vertical diffusivities (run 1; Figs. 1a,c). As discussed above, this occurs because with the a/n parameterization, high vertical diffusivities reduce the need for convective adjustment. Comparing our two runs that use GM90 (runs 2 and 4), we find that a/n reduces convective activity by a factor of 5. This relatively small difference is presumably related to the fact, discussed above, that rates of energy loss due to convective adjustment are much lower to begin with using the GM90 parameterization (runs 2 and 4) than with horizontal mixing (runs 1 and 3). Table 2 shows that the a/n parameterization reduces simulated flow through Drake Passage compared to results obtained with a prescribed vertical diffusivity of cm 2 s 1. Whether or not this represents an improvement compared to the observed flow depends on whether GM90 or horizontal mixing is used. When both GM90 and a/n are used, the simulated flow is much too low; when a/n is used with horizontal mixing, the simulated flow is about right. Table 2 also shows that in our runs, a/n reduces the simulated Indonesian Throughflow, resulting in better agreement with estimates of the real flow. e. Effects of stability-dependent vertical mixing on simulated tracer distributions Like Hirst and Cai (1994), we find that switching from prescribed vertical diffusivities to stability-dependent model-calculated vertical diffusivities (a/n mixing) has relatively minor effects on simulated temperatures. Figure 4b shows that, on a global mean basis, our runs with a/n mixing are slightly cooler above about 2 km than our runs that use prescribed vertical mixing; deep ocean temperatures are nearly the same. Agreement with observed temperatures is better with a/n than with uniform, prescribed vertical mixing (at least for the parameter values we used). The cooler temperatures in the thermocline with a/n vertical mixing are consistent with vertical diffusivities in runs 3 and 4 being generally lower in the thermocline than the value of 0.5 cm 2 s 1 used in runs 1 and 2. These lower vertical diffusivities result in less heat transported down from the surface, and thus a cooler thermocline. The most obvious effect of a/n vertical mixing on simulated 14 C distributions is that simulated 14 C values are generally lower with a/n than in the analogous run with prescribed vertical mixing (this can be seen in vertical profiles in Fig. 4d and in point-by-point comparisons between observed and simulated 14 C values in Figs. 7 10). This reflects the reduced rates of meridional overturning, discussed above, found with a/n vertical mixing compared to prescribed vertical mixing, and also that upperocean diffusivities are lower in our runs with a/n than in our other runs. This result is probably quite sensitive to model parameter values; specifically increasing the value of the parameter a in the a/n parameterization would increase vertical diffusivities and increase the rate of NADW formation, both of which would tend to increase 14 C values. Thus, that simulated 14 C values are generally lower in our runs with a/n than in our other runs is probably not a general result or a fundamental effect of the a/n parameterization. What may be fundamental, however, is that, as noted above, the a/n parameterization seems to reduce the scatter in model minus observed 14 C values (i.e., the standard deviation of model minus observed 14 C values is reduced; Figs. 7 10); it is hard to imagine how this could be affected by tuning the model. Thus, this result suggests that the a/n parameterization is a fundamental improvement over a prescribed, uniform vertical diffusivity. The effects of a/n vertical mixing on salinity are significant. However, as discussed below, all our simulations of salinity are sufficiently poor that it is probably not meaningful to draw distinctions between them. Specifically, all our simulations fail to simulate the intermediate-depth salinity minimum related to Antarctic Intermediate Water, and deep-ocean salinities are too low. Without fixing this problem, it is difficult to say whether or not a/n improves simulated salinities. That our results with a/n are quite different from those obtained with prescribed vertical mixing may at first appear to contradict the results of Hirst and Cai (1994), who found that changing to stability-dependent vertical mixing had no significant effect on their results. However, Hirst and Cai compared their a/n results to results obtained by prescribing a nonuniform vertical diffusivity whose vertical profile was nearly identical to that obtained using a/n. Thus, it is not surprising that they saw little change in results. By contrast, we compare our a/n results to results obtained using a uniform, prescribed vertical diffusivity. In terms of agreement with observations, our results with a/n are, on balance, slightly better than our results with prescribed vertical mixing in that simulated temperatures are improved in the thermocline and the scatter

23 520 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 27 FIG. 12. Maps of vertical diffusivities between the top two model layers in (a: top) run 3 and (b: bottom) run 4. The very high vertical diffusivities sometimes seen with horizontal mixing (run 3) are largely absent with GM90. between observed and simulated D14C values is reduced (Figs. 7 10). f. Simulated salinity distributions An inability to realistically simulate salinity is nearly universal in coarse-resolution GCMs unless surface forcing values for salinity are manipulated in an ad hoc way, a practice which has been criticized (Toggweiler and Samuels 1993). The failure to realistically simulate salinity stems from difficulty in simulating Antarctic Intermediate Water (AAIW), which is most clearly seen as a tongue of relatively low-salinity water projecting northward from Antarctica at a depth of about 1 km;