1. Introduction
Double-diffusive phenomena, that is, salt fingering and diffusive convection, contribute to diapycnal mixing in extensive regions of the oceans. However, their effects generally are not accounted for in ocean circulation models, which typically represent diapycnal mixing as diffusion with coefficients that are constant or prescribed functions of depth. In this paper we include a parameterization of double-diffusive mixing in a global ocean model and examine its effects.
Double diffusion occurs when relatively warm, salty water overlies cooler, fresher water, or vice versa. The former condition leads to salt fingering and the latter to diffusive convection. When driven strongly, salt fingering occurs in strongly stratified interfaces separating thicker, well-mixed layers (Schmitt et al. 1987). When driven more weakly, it appears in intermittent patches (Gargett and Schmitt 1982). Salt fingering has been observed in the central waters of the subtropical gyres, in the western tropical North Atlantic, and in the northeast Atlantic beneath the Mediterranean outflow (Schmitt 1994).
Diffusive convection occurs primarily at high latitudes where surface waters tend to be cold and fresh due to ice melt (e.g., Padman and Dillon 1987, 1988; Muench et al. 1990). Diffusive convection is observed as sequences of well-mixed layers separated by extremely thin interfaces, across which density changes abruptly and temperature and salinity are transported mainly by molecular diffusion.
Ocean models that ignore these processes risk misrepresenting the structure and transformation of water masses (Schmitt 1994). In addition, it has been suggested that large-scale thermohaline circulation may be sensitive to such transports, particularly insofar as they may differ between heat and salt. [Salt fingering transports salt more effectively than heat, whereas diffusive convection transports heat more effectively than salt. A related possibility, raised by Gargett (1988), is that microscale turbulence may transport heat more effectively than salt under some doubly stable conditions, as certain laboratory experiments suggest (Turner 1968; Altman and Gargett 1987).]
An initial exploration of these issues was performed by Gargett and Holloway (1992, hereafter GH92) in the context of an idealized ocean circulation model consisting of a Northern Hemisphere basin forced by zonal-mean climatology. They considered very simple forms for the vertical salinity and temperature diffusivities KS and KT. In a first set of experiments in which KS and KT differed but were spatially uniform, they observed a remarkable sensitivity of thermohaline circulation to the ratio KS/KT. With the usual choice KS/KT = 1, a conventional meridional cell with high-latitude sinking filled the domain. When KS/KT = 0.5, this cell strengthened by some 50%. However, when KS/KT = 2, the cell weakened substantially, and the abyssal circulation reversed sense. In a second set of experiments, KS was doubled only in locations favorable to fingering. Nonfingering regions were assigned KS = KT in one run and KS = 0.5KT in another. The run with KS = 0.5KT exhibited a stronger meridional cell, as well as greater abyssal salinities and density stratification.
In a model similar to that of GH92, Zhang et al. (1998, hereafter ZSH98) treated double diffusion more realistically, assigning KS and KT values based on the local intensity of fingering or diffusive convection. Meridional circulation was then 22% smaller than in a comparison run having spatially uniform KS = KT, and the occurrence of double diffusion was more prevalent. Use of double diffusive KS and KT also increased horizontal-mean salinity and temperature at most depths.
To determine the extent to which these idealized model results apply under more realistic geometry and forcing, we examine in this study the influence of double-diffusive mixing parameterizations in a coarse-resolution global model. In section 2 we describe the global model, including the parameterizations of salt fingers and diffusive convection. We then compare model runs with and without double diffusive mixing. To assess the generality of our results in view of the wide range of global model configurations in use, we perform such comparisons with different choices of surface forcing: model runs subject to annual-mean forcing are considered in section 3, whereas in section 4 we apply surface forcing which is seasonally varying. In section 5 we compare our results with those of GH92 and ZSH98. Conclusions are presented in section 6.
2. Global ocean model
Our ocean model is adapted from the MOM 2 version of the Bryan–Cox primitive equation model (Bryan 1969; Pacanowski 1995). The model represents the global ocean to 66.8°N, with resolution 3.71° in latitude and 3.75° in longitude. The maximum depth of 5500 m is spanned by 15 levels, ranging smoothly from 20 m in thickness at the surface to 870 m at the bottom. Coastlines and bathymetry are realistic to within grid resolution, aside from standard modifications required to prevent isolated grid cells.
In configuring the model, we have sought to produce passably realistic circulations and water masses, adhering to usual choices for parameters other than the diapycnal (vertical) mixing parameters, which are the focus of this work. For isopycnal (horizontal) diffusion, both the mixing scheme of Redi (1982) and Cox (1987) and that of Gent and McWilliams (1990) were considered initially. The Redi–Cox scheme is based on a coordinate rotation that aligns the axes of the diffusion tensor with local isopycnal tilt. It has been found in practice that a relatively small amount purely horizontal diffusion can be needed to maintain numerical stability (Cox 1987). A side effect is significant and unintended diapycnal fluxes in regions of strong isopycnal tilt, which nonetheless are much smaller than when horizontal–vertical mixing is employed. The Gent–McWilliams scheme also performs such a rotation, and represents eddy advection of tracers under the assumption that eddies tend to smooth thicknesses between neighboring isopycnals. Our final selection of the Redi–Cox scheme was based upon two factors. First, the Redi–Cox scheme skillfully represents Antarctic Intermediate Water and the associated salinity minimum (England 1993), whereas runs using the Gent–McWilliams scheme yielded middepth salinity minima that were relatively indistinct and too shallow. In addition, use of the Gent–McWilliams scheme in coarse-resolution models with the a0/N diapycnal mixing described below leads to a sluggish Antarctic Circumpolar Current: a comparison run (similar to run II of section 4) using Gent–McWilliams mixing provided transport across Drake Passage of only 59 Sv (Sv ≡ 106 m3 s−1), as compared to 81 Sv for the Redi–Cox model run. Such behavior also was noted by Duffy et al. (1997).
We also tried using the fingering diffusivities proposed by Large et al. (1994). These decrease with Rρ more rapidly than (7)–(8), and consequently produce only very small effects in our model. Also, Large et al. specify
Implementing (7)–(13) requires computing Rρ at each grid point and time step. This in turn requires knowledge of thermodynamic functions α and β and the vertical gradients of T and S. For computational efficiency, we evaluate α and β, which are functions of temperature, salinity and pressure, by means of trilinear interpolation from a table. Gradients ∂zT and ∂zS are computed by second-order centered differences between adjacent grid levels. The double-diffusive mixing scheme increases execution time by approximately 10%.
To reiterate, the diapycnal diffusivities for salt and temperature are assigned the forms (3)–(13) in model runs with double-diffusive mixing. In runs without double-diffusive mixing, KS =
Subgrid scale mixing of momentum is parameterized by uniform horizontal viscosity 2.5 × 109 cm2 s−1 and vertical viscosity 50 cm2 s−1.
To represent exchange of water with the Arctic Ocean, Baffin Bay, the Mediterranean and Red Seas, and the Persian Gulf, we relax temperatures and salinities of grid points adjacent to these regions to annual-mean Levitus (1982) climatology with a timescale of 200 days. The remaining side boundaries are insulating and no-slip. Bottom boundaries are insulating and free-slip.
The occurrence of double diffusion depends on details of water mass structure, which in turn are sensitive to surface forcing. Therefore, we consider two types of surface forcing, reflecting two types of surface boundary conditions in common use. The first, consisting of relaxation to annual-mean climatology with enhanced Antarctic salinities to imitate the influence of wintertime conditions, is described in section 3. The second, consisting of seasonally varying conditions, is described in section 4.
Initial conditions are annual-mean Levitus (1982) climatology. Time steps are 2 days for T and S, and 30 minutes for the equations advancing internal and external mode velocities, where the acceleration technique of Bryan (1984) is used. Model runs are terminated when horizontally averaged T and S change by less than 0.005°C and 0.001 psu per century at all grid levels. This occurs after about 2000 years in the runs with annual-mean forcing, and about 4000 years in the seasonally forced runs. The Bryan (1984) acceleration technique can distort the latter solutions at shallower levels where seasonal variations are perceptible. The seasonally forced runs thus are run for an additional 25 years with a 30-min time step for all prognostic variables, allowing these levels to relax to true stationarity. We then compute annual means, which serve as a basis for the analysis in section 4.
The model runs are summarized in Table 1.
3. Influence of double diffusion under annual-mean forcing
In this section, we first compare runs I (no double diffusive mixing) and Id (double-diffusive mixing with K∗ = 10 cm2 s−1 and the Federov diffusive convection parameterization) to each other and to annual-mean Levitus (1982) climatology. We then consider sensitivity to double-diffusive mixing parameterization, describing run Id1 (K∗ = 1 cm2 s−1) in section 3b and run Id1k (K∗ = 1 cm2 s−1 and Kelley diffusive convection parameterization) in section 3c. In section 3d we describe run Idd, which features double-diffusive mixing as in run Id, together with reduced background turbulent diffusivity
Surface forcing for runs I and Id consists of annual-mean Hellerman and Rosenstein (1983) wind stress, together with relaxation to annual-mean Levitus (1982) temperature and salinity on a 12-day timescale. To mimic wintertime conditions necessary for deep-water formation, we increase the reference salinities toward which surface values relax to 35.0 psu in the southernmost row of grid cells, comprising the southernmost Ross and Weddell Seas. In the next four rows, restoring salinity is set to 35.0r + Slev(1 − r), where r is a weight that decreases linearly from 1 at 74.2°S to 0 at 63.1°S. This practice of enhancing polar salinities to represent brine rejection in models lacking sea ice submodels (England 1993; Hirst and Cai 1994; Weaver and Hughes 1996) has been criticized by Toggweiler and Samuels (1995) on the grounds that the implied equatorward export of sea ice far exceeds observational constraints. While mindful of this caveat, we adhere to the above procedure on the basis that it is frequently used, and Antarctic Bottom Water formation is inadequate (and abyssal waters much too fresh) without it.
a. Run Id (K∗ = 10)
1) Circulation
In contrast to the idealized model results of GH92 and ZSH98, circulation differences between runs I and Id are very minor: barotropic transports are nearly identical, whereas the formation rate of North Atlantic Deep Water is slightly reduced and that of Antarctic Bottom Water slightly increased when double diffusion is active (Table 2).
2) Incidence of double diffusion
The intensity and extent of double diffusion, as diagnosed from stability ratio Rρ, are indicated in Fig. 2 for runs I, Id, and climatology. In computing Rρ, ∂zT and ∂zS are found by differencing between adjacent grid cells. Climatological data has been interpolated to the model grid for this purpose. At depth 180 m (Figs. 2a–c), both model runs exhibit fingering-favorable conditions in the Atlantic and Pacific subtropical gyres, the equatorial Atlantic and eastern Pacific, and a 180° longitudinal swath of the southern Pacific and Indian Oceans. Fingering-favorable locales deduced from climatology are grossly similar, although they are somewhat more compact in the Pacific and Indian Oceans, and conditions favorable to fingering are largely absent in the equatorial Pacific. (Such similarity is not surprising, given that the surface grid cells are restored toward climatological fields.) In climatological Rρ there is a greater incidence of very strong fingering, corresponding to values of Rρ close to (but greater than) unity.
At this depth, model locales favorable to diffusive convection are much less extensive than for fingering. In runs I and Id, such locales in the sub-Arctic are very similar to those implied by climatology. However, the climatological belt of diffusive-convection favorable locales surrounding Antarctica is nearly absent in the model runs. This is likely due to the enhanced surface salinities, intended to simulate wintertime conditions, in the annual-mean forced runs.
At 700 m (Figs. 2d–f) fingering-favorable locales in the model bear less resemblance to climatology. A climatological region of favorable Rρ straddling southern Australia and New Zealand is present in runs I and Id. However, such regions in the western Indian Ocean and South Atlantic are virtually absent in the model runs. In the North Atlantic, fingering-favorable Rρ is concentrated westward relative to climatology, and is much more extensive in run Id than in run I.
Climatology indicates very little diffusive convection at these depths, whereas the model runs exhibit diffusive convection-favorable conditions in the Antarctic south of eastern Africa and Madagascar.
At an abyssal depth of 2420 m (Figs. 2g–i), runs I and Id exhibit fingering-favorable conditions across virtually the entire Atlantic due to the relatively warm and saline Mediterranean outflow water and North Atlantic Deep Water overlying colder, fresher Antarctic Bottom Water. Such conditions are also seen where the Antarctic Circumpolar Current disperses Atlantic waters into the Southern Ocean. Climatological Rρ exhibits a similar pattern, except that fingering-favorable conditions in the southern Atlantic tend to occur somewhat deeper due to a lesser volume of Antarctic Bottom Water. Introduction of double-diffusive mixing in run Id leads to fingering-favorable conditions in the Gulf of Arabia, in agreement with climatology.
In runs I and Id and in climatology, diffusive convection is virtually absent at these abyssal depths.
The apparent tendency for double-diffusive activity to be less intense in the models than is implied by climatology is confirmed by Fig. 3, which shows volume censuses of Rρ over various ranges in depth. The thin solid lines represent run I, the thick solid lines run Id, and the dashed lines climatology. Regions where double diffusion is most intense (Rρ close to 1) are significantly less extensive in run I than is implied by climatology, particularly at greater depths. Introducing double-diffusive mixing in run Id tends to shrink such regions further. Moderately active fingering (2 ≲ Rρ ≲ 4) is more extensive in the run I than in climatology, and double-diffusive mixing as in run Id makes such conditions more extensive still.
3) Temperature and salinity
Figure 4 shows horizontally averaged T and S as functions of depth. As compared to climatology (dashed curves), run I (thin solid curves) without double-diffusive mixing is slightly too warm in the thermocline, and somewhat too cold beneath, as is commonly found in models using isopycnal mixing schemes (Hirst and Cai 1994; Danabasoglu and McWilliams 1995; Robitaille and Weaver 1995). Horizontally averaged salinities are reasonably close to observed values at all depths. Introducing double-diffusive mixing in run Id (thick solid curves) leads to a very slight increase in T at all depths, as well as substantially larger abyssal S. This is possibly because high near-surface values diffuse downwards more effectively due to the increased diapycnal diffusion.1
Conspicuous effects of double-diffusive mixing appear regionally. To evaluate regional influences of double-diffusive mixing in the model, we first consider differences between run I and climatology (Figs. 5a,c,e,g). The numerous regional disagreements likely have many causes, such as underresolution by the model of western boundary currents. To identify which (if any) of the model deficiencies might be ascribed to neglect of double-diffusive mixing in run I, we also examine differences between run Id and run I (Figs. 5b,d,f,h). By comparing such pairs of difference maps, we can determine whether introducing double-diffusive mixing improves or degrades the model.
Because fingering is more prevalent than diffusive convection and transports salt somewhat more effectively than heat (Fig. 1), we concentrate on the salinity distribution. At depth 67 m (Fig. 5a), run I is fresher than climatology in the subtropical gyres, the eastern equatorial Pacific, and the Gulf of Arabia and Bay of Bengal. Introducing double diffusion (Fig. 5b) counteracts these tendencies by increasing salinity throughout most of these regions. Run I is saltier than climatology in the far-north Pacific, which double-diffusive mixing makes slightly saltier still. Run I is also too salty in much of the Southern Ocean, particularly in the Ross and Weddell Seas where surface salinities are artificially enhanced; introducing double-diffusive mixing has relatively little effect on these locales.
At 227 m, all subtropical gyres are again too fresh in run I (Fig. 5c). In contrast to Fig. 5a, the Southern Ocean is now mainly too fresh, except in the southernmost Ross and Weddell Seas. The far-north Pacific and equatorial Atlantic are still too salty at this depth. Introducing double diffusion (Fig. 5d) makes midlatitudes saltier, especially in the North Atlantic and Pacific subtropical gyres. The eastern tropical Pacific, which is too fresh in run I, becomes significantly saltier, but the equatorial Atlantic, which already is too salty, becomes saltier still.
At 832 m, run I is too fresh throughout the Southern Ocean and the tropical and southern Pacific (Fig. 5e). The northern Pacific, as well as most of the Atlantic and Indian Oceans, is too salty. Introducing double-diffusive mixing in run Id mostly increases salinity, particularly in the tropical Atlantic, which is already too salty, and the western Indian Ocean (Fig. 5f).
At 2732 m (Fig. 5g), the pattern of deep-water formation in run I is such that the Pacific is too saline and the Atlantic and Indian Oceans too fresh. In run Id, fingering has diffused salt downward from the relatively warm and saline Mediterranean and North Atlantic Deep Waters, making the Atlantic more saline by up to 0.1 psu (Fig. 5h). By contrast, salinity in the Pacific and eastern Indian Oceans increases only by around 0.01 psu.
Differences between run I and climatological temperatures (not shown) exhibit many of the same trends as the salinity difference field, in the sense that regions that are too fresh, such as the subtropical gyres, tend also to be too cold. (This trend is superimposed on the overall tendency to be too warm in the upper thermocline and too cold in the abyss.) Similarly, temperature differences between runs Id and I mirror many of the trends of the corresponding salinity differences, in the sense that regions made more saline by double-diffusive mixing are also warmed.
As a quantitative measure of whether our treatment of double-diffusive mixing improves or degrades the model, we consider at each depth the correlation between the run I minus climatology and run Id minus I difference fields. Where double diffusive mixing tends to correct the modeled temperature and salinity, so that run Id minus I differences oppose those of run I minus climatology, the correlation is negative. Figure 6 shows these correlations for salinity (solid lines) and for temperature (dashed lines) as functions of depth. The correlations are mostly negative, as would occur if some of the run I errors were due to neglect of double diffusion, and were counteracted in run Id. The correlations turn positive at depths near 1000 m, where run I exhibits a large positive salinity anomaly in the Atlantic (Figs. 6e, f). This anomaly appears to result from an underdevelopment in the model of the salinity minimum associated with Antarctic Intermediate Water, particularly after it rounds the coast of Brazil. In run Id, these too-salty waters are made saltier still by increased diffusion due to fingering. The dominance at these depths of intermediate waters, which are difficult to model realistically, overshadows effects related to double diffusion. In the abyss, large negative correlations arise because double-diffusive mixing counteracts the tendency for Atlantic deep waters to be too cold and fresh (Figs. 6g–h).
b. Run Id1 (K∗ = 1)
Like run Id, run Id1 exhibits only very minor differences in barotropic and overturning circulation (Table 2). As compared to run Id, these differences have the same sign but are smaller in magnitude. An exception is transport of Antarctic Bottom Water, which has intensified by 0.56 Sv in run Id1, but only 0.06 Sv in run Id.
In run Id1, the effects of double diffusion on stability ratio Rρ are qualitatively similar to those seen in Figs. 3–4, but are much smaller.
Run Id1 minus I differences in T and S resemble the run Id minus I differences in Figs. 5–6, but again are somewhat smaller (Fig. 7; note that scale on color bar has been halved). But for their smaller magnitude, regional effects are qualitatively similar to those shown in the right-hand panels of Fig. 5. An exception occurs within the thermocline of the far northeast Pacific: double-diffusive mixing now lowers S in this region, which in run I is too saline (Figs. 7a–b). Also, salinities in the deep Pacific and Indian basins are now slightly reduced by double-diffusive mixing rather than enhanced as in run Id (Fig. 7d). As a result, the run Id1 minus I T and S are better anticorrelated with the run I minus climatology errors than are run Id minus I T and S (Fig. 8). Although double-diffusive mixing in run Id1 tends to correct modeled T and S overall, the improvements typically are smaller than the run I minus climatology errors by an order of magnitude.
c. Run Id1k (K∗ = 1, Kelley diffusive convection)
Run Id1k using the Kelley diffusive convection parameterization differs very slightly from run Id1, reflecting the relatively infrequent occurrence of diffusive convection as compared to salt fingering. The largest differences occur above 700-m depth in the far north Pacific and in the Southern Ocean near the Greenwich meridian, locales of diffusive–convection favorable Rρ in the model (Fig. 2). Run Id1k is slightly cooler and fresher than run Id1 above where diffusive convection occurs and slightly warmer and saltier below, the largest differences amounting to about 0.4°C and 0.1 psu. This apparently is because the Kelley parameterization prescribes less mixing (Fig. 1), reducing the extent to which the cold–fresh over warm–salty conditions that give rise to diffusive convection are smoothed out.
d. Run Idd (K∗ = 10, reduced turbulent KS)
In run Idd, we halved the background turbulent diffusivity
4. Influence of double diffusion underseasonal forcing
Our evaluation of the effects of double-diffusive mixing in model runs with annual-mean forcing in section 3 relied largely upon comparison of salinity and temperature distributions, which are sensitive to surface boundary conditions. To assess the generality of these results, we repeat such a comparison using seasonally varying forcing.
The surface boundary conditions for runs II (no double-diffusive mixing) and IId (double-diffusive mixing with K∗ = 10 cm2 s−1, Federov diffusive convection parameterization) consist of seasonally varying Hellerman and Rosenstein (1983) wind stress, together with relaxation on a 12-day timescale to seasonally varying Levitus (1982) temperature and salinity. Temperature and wind stress are interpolated linearly between monthly mean values, and salinity between seasonal-mean values. No further adjustments to represent wintertime conditions are made, despite large uncertainties in high-latitude wintertime climatology.
a. Circulation
As for the runs described in section 3, differences in global circulation between runs II and IId are relatively minor (Table 2), in contrast to the idealized model results of GH92 and ZSH98.
b. Incidence of double diffusion
The incidence of double diffusion in the uppermost levels in runs II and IId closely resembles that in runs I and Id, shown in Figs. 3a–b.
At greater depths, differences become more substantial. At 700 m, fingering-favorable conditions exist in most of the northern and eastern equatorial Atlantic (Figs. 9a–b). This range is somewhat more extensive than climatology (Fig. 9c). In the Indian and Pacific basins, fingering-favorable conditions grossly resemble climatology, although they are somewhat too weak in the eastern Indian Ocean.
At 700 m, conditions favoring diffusive convection are prevalent in much of the Southern Ocean bordering Antarctica. This is in contrast with climatology, which exhibits such conditions at much shallower depths (Fig. 2c). The discrepancy arises because the model entirely lacks the sharp Antarctic halocline at 100–200 m, exhibiting instead a more diffuse halocline centered at around 1500 m. The widespread incidence of diffusive convection in the Antarctic is nonetheless an improvement upon runs I and Id, where Antarctic diffusive convection is suppressed by the enhanced surface forcing salinities.
At 2420 m (Figs. 9d, e), the distribution of fingering-favorable conditions is again qualitatively similar to climatology (Fig. 9f), although the influence of the Mediterranean outflow is somewhat weaker in the model, and that of Red Sea and Persian Gulf outflows somewhat stronger. This is in contrast to runs I and Id (Figs. 3g–h), in which the relatively warm and saline North Atlantic waters are undercut at this depth by somewhat overdeveloped Antarctic Bottom Water, giving rise to fingering-favorable conditions throughout the Atlantic.
The Rρ volume censuses (Fig. 10) is more realistic than for runs I and Id (Fig. 3). Runs II and IId again tend to feature smaller volumes having Rρ very close to unity than climatology, although this trend is less pronounced than in runs I and Id.
c. Temperature and salinity
Figure 11 shows horizontally averaged T and S as functions of depth for runs II and IId. Both runs exhibit fairly realistic mean T. Mean salinities show a well-developed mid-depth salinity minimum, although abyssal waters are much too fresh. This is characteristic of most models in which Antarctic salinity forcing is not enhanced as described in section 3 (e.g., England 1993;Danabasoglu and McWilliams 1995). Introducing double-diffusive mixing in run IId increases deep temperatures by ∼ 0.25°C and deep salinities by ∼ 0.05 psu.
In the upper thermocline, regional salinity errors in run II resemble those in run I (Figs. 3a,c,e). At abyssal depths, run II is too fresh (and cold) throughout most of the Pacific and Indian basins, and too salty (and warm) throughout most of the Atlantic. This is in contrast to run I, which is too salty in the Pacific and too fresh elsewhere.
Run IId minus II differences are fairly similar to those for run Id minus I, with some significant distinctions. In run IId double diffusion makes the eastern North Atlantic subtropical gyre fresher instead of more saline at depths less than 500 m. At 2732 m, double diffusion makes the Pacific and Indian basins saltier. This trend is opposite to that in run Id, but brings the model closer to observations. On average, introducing double diffusion counteracts the model temperature and salinity errors at nearly all depths, as seen from the mainly negative correlations of the run II minus climatology and run IId minus II differences, shown in Fig. 12.
5. Comparison with ZSH98 and GH92
We now compare our results with those of ZSH98 and GH92, who examined the effects of double-diffusive mixing in a model of a single idealized Northern Hemisphere basin.
Four types of comparisons are made among these three studies: runs in which double-diffusive mixing is “turned on” versus runs with no double-diffusive mixing; runs in which the magnitude K∗ of mixing by salt fingering is varied; runs in which the magnitude of mixing due to diffusive convection is varied; and runs in which the background turbulent diffusivity for KS is reduced. Comparisons of resulting effects on meridional transport, abyssal temperature, and abyssal salinity are reported in Table 3.
As remarked previously, meridional circulation in the present study is much less sensitive to double-diffusive mixing than in ZSH98, even in instances where we have employed larger diffusivities for salt fingering (K = 10 cm2 s−1). As in ZSH98, however, it is generally reduced when double-diffusive mixing is present. Introducing double-diffusive mixing increases abyssal T and S in all cases, although for given K∗ the effects are still somewhat smaller here than in ZSH98.
In our study and in ZSH98, mixing by diffusive convection is found to have very little effect on global properties. This is evidently because of the relatively small volumes over which diffusive convection is active.
In GH92 and the present study, reducing the background turbulent diffusivity KS for salt leads to increased meridional overturning and increased abyssal T and S. However, the effects are much smaller in the present study than in GH92.
One possible reason for the relative insensitivity of large-scale circulation to double-diffusive mixing in our model is that the GH92 the ZSH98 models are forced by zonal-mean surface climatology, which gives rise to a thermohaline cell whose strength is intermediate to the strong Atlantic and weak Pacific meridional overturnings. These relatively sluggish meridional cells (∼ 5 Sv in ZSH98 and ∼ 2 Sv in GH92 runs 135 and 136) might be more susceptible to perturbation than a more realistic North Atlantic cell.
It should be cautioned that different methodologies were used in this study and ZSH98. In this study, the functional form of background turbulent diffusion is not altered when double-diffusive mixing is turned on. The volume-averaged diffusivities thus are somewhat larger with double diffusion than without (Table 2). In ZSH98, the constant background diffusivities in experiment CDD without double diffusion are set to the mean of KT and KS in double-diffusive experiment DDP. Mean KT consequently is smaller in the former experiment, whereas mean KS is larger. Because meridional circulation tends to increase with increasing KT and decreasing KS (GH92), the modifications to KT and KS in the ZSH98 double-diffusive experiment both contribute to the 22% reduction in overturning that they report.
6. Conclusions
We have found that parameterizations of double-diffusive mixing in a global ocean model, while only slightly affecting large-scale circulation patterns, can significantly influence regional distributions of temperature and salinity. Our results indicate that salt fingering is much more widespread than diffusive convection and that double diffusion tends to increase deep temperatures and salinities. The changes brought about by double-diffusive mixing also tend to bring modeled temperatures and salinities closer to observations in both annual-mean and seasonally forced models. The improvements are particularly pronounced at large depths.
Although double-diffusive mixing apparently can improve model representations of the formation and structure of water masses, other influences must also be considered. In particular, deep-water properties appear to be very sensitive to high-latitude surface forcing, as is evident from comparing model runs I (annual-mean forcing with enhanced Antarctic salinities; Fig. 4) and II (seasonally varying forcing; Fig. 11).
Acknowledgments
This work was supported by the Office of Naval Research (N00014-96-I-0518), and by a NOAA Fellowship in Climate and Global Change to WJM. We thank two anonymous reviewers whose suggestions led to improvements in this paper.
REFERENCES
Altman, D. B., and A. E. Gargett, 1987: Differential property transport due to incomplete mixing in a stratified fluid. Proc. Third Int. Symp. on Stratified Flows, Pasadena, CA, American Society of Civil Engineers, 454–460.
Bryan, K., 1969: A numerical method for the study of the circulation of the world ocean. J. Comput. Phys.,3, 347–376.
——, 1984: Accelerating the convergence to equilibrium of ocean-climate models. J. Phys. Oceanogr.,14, 666–673.
Cox, M. D., 1987: Isopycnal diffusion in a z-coordinate ocean model. Ocean Model.,74, 1–5.
Cummins, P. F., G. Holloway, and A. E. Gargett, 1990: Sensitivity of the GFDL ocean general circulation model to a parameterization of vertical diffusion. J. Phys. Oceanogr.,20, 817–830.
Danabasoglu, G., and J. C. McWilliams, 1995: Sensitivity of the global ocean circulation to a parameterization of mesoscale transports. J. Climate,8, 2967–2987.
Duffy, P. D., K. Caldeira, J. Selvaggi, and M. I. Hoffert, 1997: Effects of subgrid-scale mixing parameterizations on simulated distributions of natural 14C, temperature, and salinity in a three-dimensional ocean general circulation model. J. Phys. Oceanogr.,27, 498–523.
England, M. H., 1993: Representing global-scale water masses in ocean general circulation models. J. Phys. Oceanogr.,23, 1523–1552.
Federov, K. N., 1988: Layer thicknesses and effective diffusivities in “diffusive” thermohaline convection in the ocean. Small-Scale Turbulence and Mixing in the Ocean, J. C. J. Nihoul and B. M. Jamart, Eds., Elsevier, 471–479.
Gargett, A. E., 1984: Vertical eddy diffusivity in the ocean interior. J. Mar. Res.,46, 359–393.
——, 1986: Small-scale parameterization in large-scale ocean models. Advanced Physical Oceanographic Numerical Modelling, J. J. O’Brien, Ed., Elsevier, 154–163.
——, 1988: Reynolds number effects on turbulence in the presence of stable stratification. Small-Scale Turbulence and Mixing in the Ocean, J. C. J. Nihoul and B. M. Jamart, Eds., Elsevier, 517–528.
——, and R. Schmitt, 1982: Observations of salt fingers in the central waters of the eastern North Pacific. J. Geophys. Res.,87, 8017–8029.
——, and G. Holloway, 1992: Sensitivity of the GFDL ocean model to different diffusivities for heat and salt. J. Phys. Oceanogr.,22, 1158–1177.
Gent, P. R., and J. C. McWilliams, 1990: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr.,20, 150–155.
Hellerman, S., and M. Rosenstein, 1983: Normal monthly wind stress over the world ocean with error estimates. J. Phys. Oceanogr.,13, 1093–1104.
Hirst, A. C., and W. Cai, 1994: Sensitivity of a world ocean GCM to changes in subsurface mixing parameterization. J. Phys. Oceanogr.,24, 1256–1279.
Kelley, D. E., 1984: Effective diffusivities within oceanic thermohaline staircases. J. Geophys. Res.,89, 10 484–10 488.
——, 1988: Explaining effective diffusivities within diffusive oceanic staircases. Small-Scale Turbulence and Mixing in the Ocean, J. C. J. Nihoul and B. M. Jamart, Eds., Elsevier, 481–502.
——, 1990: Fluxes through diffusive staircases: A new formulation. J. Geophys. Res.,95, 3365–3371.
Large, W. G., J. C. McWilliams, and S. C. Doney, 1994: Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization. Rev. Geophys.,32, 363–403.
Levitus, S., 1982: Climatological atlas of the World Ocean. NOAA Prof. Paper No. 13, U.S. Govt. Printing Office, Washington, D.C., 173 pp.
McDougall, T. J., and J. R. Taylor, 1984: Flux measurements across a finger interface at low values of the stability ratio. J. Mar. Res.,42, 1–14.
Muench, R. D., H. J. S. Fernando, and G. R. Stegun, 1990: Temperature and salinity staircases in the northwestern Weddell Sea. J. Phys. Oceanogr.,20, 295–306.
Pacanowski, R. C., 1995: MOM 2 documentation user’s guide and reference manual, Version 1.0. Geophysical Fluid Dynamics Laboratory Ocean Tech. Rep. 3, 232 pp.
Padman, L., and T. M. Dillon, 1987: Vertical heat fluxes through the Beaufort Sea thermohaline staircase. J. Geophys. Res.,92, 10 779–10 806.
——, and ——, 1988: On the horizontal extent of the Canada Basin thermohaline steps. J. Phys. Oceanogr.,20, 1458–1462.
Polzin, K. L., J. M. Toole, J. R. Ledwell, and R. W. Schmitt, 1997: Spatial variability of turbulent mixing in the abyssal ocean. Science,276, 93–96.
Redi, M. H., 1982: Oceanic isopycnal mixing by coordinate rotation. J. Phys. Oceanogr.,12, 1154–1158.
Robitaille, D. Y., and A. J. Weaver, 1995: Validation of sub-grid-scale mixing schemes using CFCs in a global ocean model. Geophys. Res. Lett.,22, 2917–2920.
Schmitt, R. W., 1981: Form of the temperature–salinity relationship in the central water: Evidence for double-diffusive mixing. J. Phys. Oceanogr.,11, 1015–1026.
——, 1988: Mixing in a thermohaline staircase. Small-Scale Turbulence and Mixing in the Ocean, J. C. J. Nihoul and B. M. Jamart, Eds., Elsevier, 435–452.
——, 1994: Double diffusion in oceanography. Annu. Rev. Fluid Mech.,26, 255–285.
——, H. Perkins, J. D. Boyd, and M. C. Stalcup, 1987: C-SALT: An investigation of the thermohaline staircase in the western tropical North Atlantic. Deep-Sea Res.,34, 1655–1665.
Toggweiler, J. R., and B. Samuels, 1995: Effect of sea ice on salinity of Antarctic bottom waters. J. Phys. Oceanogr.,25, 1980–1997.
Turner, J. S., 1968: The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech.,33, 639–656.
Weaver, A. J., and T. M. C. Hughes, 1996: On the incompatibility of ocean and atmosphere models and the need for flux adjustments. Climate Dyn.,12, 141–171.
Zhang, J., R. W. Schmitt, and R. X. Huang, 1998: Sensitivity of GFDL Modular Ocean Model to the parameterization of double-diffusive processes. J. Phys. Oceanogr.,28, 589–605.
(a) Diapycnal diffusivities
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
(a) Diapycnal diffusivities
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
(a) Diapycnal diffusivities
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Occurrence of double diffusion, as diagnosed by Rρ, in annual-mean forced runs I, Id (K∗ = 10 cm2 s−1), and annual-mean climatology, at 180 m (a–c), 700 m, (d–f), and 2420 m (g–i).
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Occurrence of double diffusion, as diagnosed by Rρ, in annual-mean forced runs I, Id (K∗ = 10 cm2 s−1), and annual-mean climatology, at 180 m (a–c), 700 m, (d–f), and 2420 m (g–i).
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Occurrence of double diffusion, as diagnosed by Rρ, in annual-mean forced runs I, Id (K∗ = 10 cm2 s−1), and annual-mean climatology, at 180 m (a–c), 700 m, (d–f), and 2420 m (g–i).
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
(Continued)
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
(Continued)
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
(Continued)
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
(Continued)
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
(Continued)
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
(Continued)
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Volume census of Rρ for run I (thin solid lines), run Id (thick solid lines), and annual-mean climatology (dashed lines) at (a) all depths, (b) 0–277 m, (c) 227–1167 m, and (d) below 1167 m.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Volume census of Rρ for run I (thin solid lines), run Id (thick solid lines), and annual-mean climatology (dashed lines) at (a) all depths, (b) 0–277 m, (c) 227–1167 m, and (d) below 1167 m.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Volume census of Rρ for run I (thin solid lines), run Id (thick solid lines), and annual-mean climatology (dashed lines) at (a) all depths, (b) 0–277 m, (c) 227–1167 m, and (d) below 1167 m.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Horizontal-mean temperature (a) and salinity (b) for runs I (thin solid curves) and Id with K∗ = 10 cm2 s−1 (thick solid curves). The dashed curves indicate annual-mean Levitus (1982) climatology.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Horizontal-mean temperature (a) and salinity (b) for runs I (thin solid curves) and Id with K∗ = 10 cm2 s−1 (thick solid curves). The dashed curves indicate annual-mean Levitus (1982) climatology.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Horizontal-mean temperature (a) and salinity (b) for runs I (thin solid curves) and Id with K∗ = 10 cm2 s−1 (thick solid curves). The dashed curves indicate annual-mean Levitus (1982) climatology.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Salinity difference fields: (a) run I − annual-mean climatology at 67 m, (b) run Id − I at 67 m, (c) run I − climatology at 227 m, (d) run Id − I at 227 m, (e) run I − climatology. at 832 m, (f) run Id − I at 832 m, (g) run I − climatology at 2732 m, and (h) run Id − I at 2732 m.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Salinity difference fields: (a) run I − annual-mean climatology at 67 m, (b) run Id − I at 67 m, (c) run I − climatology at 227 m, (d) run Id − I at 227 m, (e) run I − climatology. at 832 m, (f) run Id − I at 832 m, (g) run I − climatology at 2732 m, and (h) run Id − I at 2732 m.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Salinity difference fields: (a) run I − annual-mean climatology at 67 m, (b) run Id − I at 67 m, (c) run I − climatology at 227 m, (d) run Id − I at 227 m, (e) run I − climatology. at 832 m, (f) run Id − I at 832 m, (g) run I − climatology at 2732 m, and (h) run Id − I at 2732 m.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
(Continued)
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
(Continued)
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
(Continued)
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Correlation between the run I − climatology and run Id − I difference fields versus depth (K∗ = 10 cm2 s−1 in run Id). Negative correlations indicate a tendency for double-diffusive mixing to correct the temperature and salinity errors in run I.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Correlation between the run I − climatology and run Id − I difference fields versus depth (K∗ = 10 cm2 s−1 in run Id). Negative correlations indicate a tendency for double-diffusive mixing to correct the temperature and salinity errors in run I.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Correlation between the run I − climatology and run Id − I difference fields versus depth (K∗ = 10 cm2 s−1 in run Id). Negative correlations indicate a tendency for double-diffusive mixing to correct the temperature and salinity errors in run I.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Salinity difference fields: (a) run Id1 − I at 67 m, (b) run Id1 − I at 227 m, (c) run Id1 − I at 832 m, and (d) run Id1 − I at 2732 m. Note that the range of the color bar is half that in Fig. 5.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Salinity difference fields: (a) run Id1 − I at 67 m, (b) run Id1 − I at 227 m, (c) run Id1 − I at 832 m, and (d) run Id1 − I at 2732 m. Note that the range of the color bar is half that in Fig. 5.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Salinity difference fields: (a) run Id1 − I at 67 m, (b) run Id1 − I at 227 m, (c) run Id1 − I at 832 m, and (d) run Id1 − I at 2732 m. Note that the range of the color bar is half that in Fig. 5.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Correlation between the run I − climatology and run Id1 − I difference fields versus depth (K∗ = 1 cm2 s−1 in run Id1). Negative correlations indicate a tendency for double-diffusive mixing to correct the temperature and salinity errors in run I.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Correlation between the run I − climatology and run Id1 − I difference fields versus depth (K∗ = 1 cm2 s−1 in run Id1). Negative correlations indicate a tendency for double-diffusive mixing to correct the temperature and salinity errors in run I.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Correlation between the run I − climatology and run Id1 − I difference fields versus depth (K∗ = 1 cm2 s−1 in run Id1). Negative correlations indicate a tendency for double-diffusive mixing to correct the temperature and salinity errors in run I.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Occurrence of double diffusion, as diagnosed by Rρ, in runs II and IId (K∗ = 10 cm2 s−1) and annual-mean climatology, at 700 m (a–c), and 2420 m (d–f).
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Occurrence of double diffusion, as diagnosed by Rρ, in runs II and IId (K∗ = 10 cm2 s−1) and annual-mean climatology, at 700 m (a–c), and 2420 m (d–f).
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Occurrence of double diffusion, as diagnosed by Rρ, in runs II and IId (K∗ = 10 cm2 s−1) and annual-mean climatology, at 700 m (a–c), and 2420 m (d–f).
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
(Continued)
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
(Continued)
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
(Continued)
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Volume census of annual-mean Rρ for run II (thin solid lines), run IId (thick solid lines), and climatology (dashed lines), at (a) all depths, (b) 0–277 m, (c) 227–1167 m, and (d) below 1167 m.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Volume census of annual-mean Rρ for run II (thin solid lines), run IId (thick solid lines), and climatology (dashed lines), at (a) all depths, (b) 0–277 m, (c) 227–1167 m, and (d) below 1167 m.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Volume census of annual-mean Rρ for run II (thin solid lines), run IId (thick solid lines), and climatology (dashed lines), at (a) all depths, (b) 0–277 m, (c) 227–1167 m, and (d) below 1167 m.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Horizontal- and annual-mean temperature (a) and salinity (b) for seasonally forced runs II (thin solid curves) and IId with K∗ = 10 cm2 s−1 (thick solid curves). The dashed curves indicate annual-mean Levitus (1982) climatology.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Horizontal- and annual-mean temperature (a) and salinity (b) for seasonally forced runs II (thin solid curves) and IId with K∗ = 10 cm2 s−1 (thick solid curves). The dashed curves indicate annual-mean Levitus (1982) climatology.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Horizontal- and annual-mean temperature (a) and salinity (b) for seasonally forced runs II (thin solid curves) and IId with K∗ = 10 cm2 s−1 (thick solid curves). The dashed curves indicate annual-mean Levitus (1982) climatology.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Correlation between annual-mean run II − climatology and run IId − II difference fields versus depth (K∗ = 10 cm2 s−1 in run IId). Negative correlations indicate a tendency for double-diffusive mixing to correct the temperature and salinity errors in run II.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Correlation between annual-mean run II − climatology and run IId − II difference fields versus depth (K∗ = 10 cm2 s−1 in run IId). Negative correlations indicate a tendency for double-diffusive mixing to correct the temperature and salinity errors in run II.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Correlation between annual-mean run II − climatology and run IId − II difference fields versus depth (K∗ = 10 cm2 s−1 in run IId). Negative correlations indicate a tendency for double-diffusive mixing to correct the temperature and salinity errors in run II.
Citation: Journal of Physical Oceanography 29, 6; 10.1175/1520-0485(1999)029<1124:AGOMWD>2.0.CO;2
Summary of model runs.
Circulation characteristics and volumetric mean diapycnal diffusivities of model runs. ACC refers to barotropic transport by the Antarctic Circumpolar Current across Drake Passage, and NADW and AABW to North Atlantic Deep Water and Antarctic Bottom Water formation rates, as deduced from maxima in the meridional overturning streamfunctions. All transports are in Sv.
Comparison between results of ZSH97, GH92, and present study.
