JUNE 2000 ZHANG AND SCHMITT 1223
The Impact of Salt Fingering on the Thermohaline Circulation under Mixed Boundary Conditions*
JUBAO ZHANG AND RAYMOND W. S CHMITT Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts
(Manuscript received 29 December 1998, in ®nal form 28 June 1999)
ABSTRACT The impact of salt ®ngers on the thermohaline circulation in a single hemisphere basin under mixed boundary conditions is investigated through scaling analysis and numerical experiments. By assuming that the internal density ratio is determined by the surface horizontal density ratio, the effect of a double-diffusive parameterization
on the vertical diffusivity of density (K) is estimated. Salt ®ngers reduce the magnitude of K, with the extent of the reduction dependent on the magnitude of the density ratio. The reduced diapycnal mixing leads to a diminished thermohaline circulation and modi®es the stability criteria for the thermal/haline mode transition under mixed boundary conditions. Quasi-equilibrium numerical experiments with the GFDL Modular Ocean Model produce results consistent with the scaling analysis in the reduction of the magnitude of the thermohaline circulation and the change in the critical freshwater forcing required for the existence of the stable thermal mode. Sensitivity experiments are also conducted on the variables in the salt ®nger parameterization and found to be consistent with the scaling analysis. These results indicate that salt ®ngers make the thermohaline circulation more susceptible to transition to the haline mode (haline catastrophe), so should not be ignored in long-term climate prediction models.
1. Introduction more realistic ``natural'' boundary conditions suggested by Huang (1993), which include the effects of the mass The impact of the upper boundary conditions on the ¯ux due to freshwater. It is often suggested that the thermohaline circulation with uniform vertical mixing climate variability during the transition from the last has been studied extensively (Stommel 1961; Bryan glacial to the present interglacial period was due to such 1986; Weaver and Hughes 1992; Huang 1995; Zhang multiple equilibria. That is, Keigwin et al. (1991) have 1998; Zhang et al. 1999). ``Relaxation'' boundary con- presented paleoceanographic evidence that during the ditions have been widely used in climate simulations; Younger Dryas cold event (about 11 000 to 10 000 years these by design force sea surface temperatures and sa- before present), North Atlantic Deep Water production linities very close to observations. Such boundary con- was substantially reduced or even eliminated. This tends ditions lead to a stable thermohaline circulation. While to support the suggestion of Broecker et al. (1985) that this approach may be appropriate for temperature, it is the ``conveyor belt'' circulation is extremely sensitive not physically justi®ed for salinity since surface water to high-latitude surface freshwater ¯uxes. Moreover, ¯uxes are insensitive to sea surface salinity. Instead, a models of future climate changes due to greenhouse virtual salt ¯ux boundary condition or freshwater ¯ux warming also support such sensitivity since warming is boundary condition (Huang 1993) should be used. With projected to enhance the hydrologic cycle, especially such mixed boundary conditions, the thermohaline cir- over the high-latitude regions where bottom water forms culation displays multiple equilibria and variability on (Manabe and Stouffer 1994). different timescales (Stommel 1961; Weaver and However, equally important to the surface boundary Hughes 1992). Similar variability is observed under the conditions are the ocean's internal mechanisms for maintaining the thermohaline circulation. In particular, it has long been recognized that diapycnal mixing plays * Woods Hole Oceanographic Institution Contribution Number an essential role in warming the cold deep water and 9971. causing it to upwell (Bryan 1987). In fact, it is the rate limiting mechanism controlling the intensity of the ther- mohaline circulation. Depending on boundary condi- Corresponding author address: Dr. Raymond W. Schmitt, Dept. of Physical Oceanography, WHOI, MS #21, Woods Hole, MA 02543- tions, the strength of the meridional overturning cell 1541. depends on the diffusivity K to the ⅔ (relaxation bound- E-mail: [email protected] ary conditions) or ½ (¯ux boundary conditions) power
᭧ 2000 American Meteorological Society
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(Zhang et al. 1999). Recent microstructure measure- merical experiments in the Geophysical Fluid Dynamics ments and tracer release experiments have revealed that, Laboratory Modular Ocean Model (GFDL MOM2) are away from rough topography, turbulent vertical mixing implemented and analyzed. A summary follows in sec- is generally very weak (Ledwell et al. 1993; Polzin et tion 5. al. 1997). This raises the issue of the potential impor- tance of the double-diffusive mixing processes, which 2. Parameterization of salt ®ngering act directly on the strong T±S gradients of the ther- mocline. Moreover, the main thermocline of the eastern Salt ®ngers can form when warmer, saltier water over- subtropical Atlantic has revealed evidence for a signif- lies colder, fresher water such that icant contribution of salt ®ngers to the vertical disper- T Ͼ 0, S Ͼ 0, 1 Ͻ R Ͻ k /k , (1) sion of tracer (St. Laurent and Schmitt 1999). Since z z t s comparable hydrographic conditions exist in all of the where R ϭ ␣Tz/Sz is the density ratio (␣ and  are subtropical gyres, it is of interest to establish the sen- the expansion coef®cients of heat and salt, respectively) sitivity of the thermohaline circulation to the differential and kt and ks are the molecular diffusivities of heat and transports of heat and salt due to salt ®ngers. salt (Stern 1960). The ratio of the heat and salt molecular Gargett and Holloway (1992) investigated this issue diffusivities is about 100, so even a very weak desta- by imposing uniformly different diffusivities for heat bilizing salinity gradient can induce salt ®ngering. The and salt in a general circulation model. They found dra- instability appears as narrow columns of up- and down- matic differences in the circulation under relaxation going ¯uid, exchanging heat laterally and allowing the boundary conditions. Indeed, the changes were so rad- downward transport of saltier water. ical that they could be taken as evidence of the inef- The evidence for the role of salt ®ngers in ocean fectiveness of double diffusion. More modest changes mixing has been reviewed by Schmitt (1994, 1998). The in the circulation were found in the study of Zhang et occurrence of ``steppy'' ®nestructure at density ratios al. (1998). They used a more realistic parameterization less than 1.7, as well as extensive microstructure mea- scheme for the double-diffusive mixing, which em- surements from a variety of instruments, support the ployed a differential mixing rate dependent on the rel- hypothesis that salt ®ngers play a signi®cant role in ative intensity of the heat and salt gradients. This study ocean mixing when the unstable salinity gradient is suf- again used relaxation boundary conditions, which does ®ciently strong. The latest evidence comes from micro- not admit the multiple equilibria states of the thermo- structure measurements made as part of the North At- haline circulation important for climate. Recent work lantic Tracer Release Experiment (Ledwell et al. 1993). by Gargett and Ferron (1996) investigated the effects St. Laurent and Schmitt (1999) found distinct evidence of differential vertical diffusion of T and S in a box in the relative amplitudes of thermal and kinetic energy model of thermohaline circulation. They found that, dissipation that the heat and salt are mixed vertically at when KT ± KS (where KS and KT are the diapycnal eddy different rates and that the diffusivity increases as the diffusivities for salinity and temperature), the model ex- density ratio approaches 1, in a manner consistent with hibits extended ranges of multiple equilibria, a different salt ®ngering. This strong evidence for a density-ratio- mode transition near present-day values of freshwater dependent diffusivity leads us to invoke a salt ®nger forcing magnitude, and the possibility of quasiperiodic parameterization similar to that of Schmitt (1981), oscillatory states. though lowered in amplitude to re¯ect knowledge In this paper, we will investigate the behavior of an gained from microstructure observations during C- ocean basin forced with mixed boundary conditions SALT (Schmitt 1988) and NATRE. (i.e., a virtual salt ¯ux condition for salinity with tem- As in Zhang et al. (1998), salt ®ngering is parame- perature relaxed to prescribed values) when double-dif- terized as follows: fusive processes modify the diapycnal exchanges of heat K* and salt. It is a successor to the studies of Zhang et al. K ϭϩKϱ, (2) S 1 (R /R )n (1998), who studied the effects of double diffusion un- ϩ c der relaxation boundary conditions, and Zhang et al. 0.7K* (1999), who established the general parameter depen- K ϭϩKϱ, (3) T R [1 ϩ (R /R )]n dence of the thermohaline circulation on hydrologic c boundary conditions and the turbulent diapycnal mixing where K ϱ is the assumed constant diapycnal diffusivity rate. We use the same tools of scaling analysis and nu- due to other mixing processes unrelated to double dif- merical modeling in this study. fusion, such as internal wave breaking; Rc is the critical The organization of the paper is as follows. In section density ratio above which the diapycnal mixing due to 2, we brie¯y give the parameterization of the salt ®n- salt ®ngering drops dramatically. A value of 0.7 is used gering process. Its in¯uence on the diapycnal diffusivity for the heat/salt buoyancy ¯ux ratio due to salt ®ngers. of density and the magnitude of the thermohaline cir- Here K* is the maximum salinity diapycnal diffusivity culation under mixed boundary conditions is addressed due to salt ®ngers. The exponent n is an index to control with a scaling analysis in section 3. In section 4, nu- the reduction of KT, KS with increasing R.
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24 Also, following Zhang et al. (1998), we apply an gK L M4 ϭ |␣⌬TM Ϫ SEL2|, (7) additional constraint that salt ®ngers can occur only if f the magnitude of the vertical temperature gradient is larger than a critical value where g is the gravitational acceleration, and f is the Coriolis parameter. Assuming that K is constant as con- |Tz| Ͼ Tz,c. (4) ventionally used, ZSH investigated the existence of mul- The variables in the above parameterization have the tiple equilibria in the thermohaline circulation and the values sensitivity of the circulation to hydrologic forcing and the magnitude of the vertical mixing. The primary focus K* ϭ 2.0 cm2 sϪ1 , Kϱ ϭ 0.5 cm2 sϪ1 , R ϭ 1.6, c of the present work is to extend this analysis to consider Ϫ4 Ϫ1 the effects on the circulation induced by changes in K n ϭ 6, Tz,c ϭ 2.5 ϫ 10 ЊCm . (5) due to salt ®ngers. The diffusivities obtained from this parameterization are comparable to the common values used in OGCMs. Somewhat smaller values could be argued for in a ®ner b. Diapycnal diffusivity of density resolution model, which would yield comparable ¯uxes The sinking limb of the thermohaline circulation is with stronger gradients. However, we feel these diffu- driven by buoyancy losses at the air±sea interface; the sivities are plausible and desirable for computational return limb involves a balance between upward buoy- ef®ciency in a coarse resolution model, which cannot ancy advection and downward buoyancy diffusion in simulate the ®nestructure in the ocean. In any case, sen- the ocean interior. However, in the GFDL MOM2, den- sitivity studies are performed to investigate the depen- sity is a diagnostic variable; thus the diapycnal eddy dence of the results on the speci®c parameter values. diffusivity of density, K, does not appear in the model explicitly. Instead, K is de®ned diagnostically as a func- 3. Scaling analysis tion of the density ratio, assuming a locally linear equa- tion of state applies to the mixing between adjacent a. Basic elements layers. An expression equivalent to that given in Eq. (5) Zhang et al. (1999, ZSH hereafter) have provided an of Gargett and Holloway (1992) is readily obtained: examination of the dependence of the thermohaline cir- RK TSϪ K culation on vertical mixing rate and upper boundary K ϭ , (8) conditions. The vertical diffusivity in that work was kept R Ϫ 1 equal for heat and salt in order to develop intuition about where KT, KS are given in (3). This expression re¯ects the response of the system to conventional turbulent the fact that, while salt ®ngers provide positive diffu- mixing. The main focus was on determining the rela- sivities for heat and salt, they produce a negative dif- tionship between hydrologic forcing, which can disrupt fusivity for density when acting alone. The overall K the thermohaline circulation, and the diapycnal mixing, will be Ͼ0 if turbulence is strong compared to the ®n- which, by its action on the available density gradients, gers. is its fundamental driver. In the following analysis we examine the impact of the unequal heat and salt dif- fusivities produced by double diffusion. The reader c. Density ratio would be well served by reference to ZSH, for, in the The density ratio is the key parameter in the study of interest of brevity, we refrain from reproducing the com- double diffusion and here we give a simple argument plete scale analysis. However, discussion of a few es- to estimate its interior value based on the surface bound- sential points will be useful. ary conditions. In the present-day ocean, water tends to The ZSH scale analysis was applied to an ocean basin be warm and salty in the subtropical regions, and cold with horizontal dimensions L ϫ L, overall depth H, and and fresh in the polar regions. Thus, the distributions the thermocline depth (or depth scale in motion) D. The of heat and salt oppose one another in terms of their basin is forced with a north±south temperature differ- effect on density. Due to these horizontal differences, ence ⌬T and low-latitude evaporation (with amplitude the strati®cation forms as water convects and sinks in E) is balanced by high-latitude precipitation. This gen- the polar regions and then spreads at depth throughout erates a north±south salinity difference the ocean for the thermal mode. Salt-driven convective SED sinking at low latitudes with higher latitude upwelling ⌬S ϭ , (6) would characterize a ``haline'' mode, which can be con- K ducive to the ``diffusive±convective'' form of double where S is the basin-averaged salinity. Furthermore, diffusion. With the more normal upper boundary forcing from the incompressibility condition, the thermal wind for T and S the thermal mode dominates. This produces relation, and the vertical advection±diffusion buoyancy a strati®cation favorable for salt ®ngers, since cold balance, the magnitude of the thermohaline circulation, freshwater sinks in the polar regions and spreads equa- M, is determined by the following quartic equation: torward, and thus for most of the thermocline, warm,
Unauthenticated | Downloaded 10/01/21 10:28 PM UTC 1226 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 30 salty water overlies cold, fresh deep water. Therefore, phenomenon ``¯ushing'' associated with the haline we assume that the vertical density ratio can be ap- mode. Thus, here we concentrate on consideration of proximated by the horizontal density ratio at the surface, the effects of salt ®ngers on the stable thermal mode. which is given by the north±south temperature and sa- linity differences. This is analogous to the Iselin (1939) d. Stable thermal mode (R Ͼ 1) hypothesis concerning the relation between the winter surface and thermocline T±S relations. Under mixed Here we solve (13) with K given in (8). From ZSH, boundary conditions, the north±south salinity difference we know that the existence of the thermal mode depends is expected to be inversely proportional to the magnitude on the relative contribution of diapycnal mixing and of the meridional overturning rate, thus the interior den- freshwater forcing. Thus, here we need to investigate sity ratio will depend on the strength of the meridional not only how the magnitude of the stable thermal mode overturning and be obtained as part of the solution, depends on the the parameterization of salt ®ngers, but also how the critical freshwater ¯ux that determines the T T ␣⌬TK ␣ z ␣⌬ existence of the thermal mode is impacted by the above R ϭϳ ϭ . (9) Sz ⌬S SED parameterization. Also, we wish to determine how the Note that the north±south salinity difference ⌬S is variables in (2) and (3) can change the above depen- derived in ZSH. They ®nd that the existence of the dence. multiple equilibria of the thermohaline circulation is The asymptotic solutions for the dependence of the governed by the equation meridional overturning circulation on the freshwater forcing are plotted in Fig. 1. Constant diapycnal dif- R4 ϭ F|R Ϫ 1|, (10) where fusivity (CDD) represents the scaling results without considering double-diffusive effects (as in ZSH), and 24 gK (␣⌬T) other curves show the impact of different salt ®ngering F ϭ . (11) fL23 E (S ) 3 parameterizations. The variables for the salt ®ngers are the same as in (5) unless speci®ed here. It is obvious ZSH showed that when K ϭ const, as in the con- that the salt ®ngering parameterization leads to a re- ventional parameterization for vertical mixing process- duction in the critical freshwater ¯ux allowing the ex- es, the existence of the thermal mode is controlled by istence of the stable thermal mode. This is consistent a criterion when F Ͼ 256/27, one stable thermal mode, with the analysis in ZSH since the upper limit (critical one unstable thermal mode, and one stable haline mode 2/3 value) of freshwater forcing depends onK . With the are possible; when F Ͻ 256/27, only one stable haline introduction of salt ®ngers, the vertical diffusivity of mode can exist. density is reduced and we expect a reduction in the In contrast with the conventional constant vertical critical freshwater forcing. From Fig. 1, we also see the diffusivity case, F now becomes a function of R since sensitivity to the variables in the parameterization of K ϭ K(R) when salt ®ngering processes are included. salt ®ngers the critical freshwater forcing decreases with To simplify the argument, we introduce a new parameter, increased maximum diffusivity due to ®ngers K*, larger g(Kϱ)(24␣⌬T) critical density ratio Rc, or smaller exponent index n. FCDD ϭ ; (12) Another impact of salt ®ngering on the stability of fL23 E (S ) 3 the thermal mode is the dependence on the strength of then the scaling relation (10) becomes freshwater forcing. When the freshwater forcing is rel- atively weak, the salt ®ngering hardly makes any dif- R4 ϭ F (K /K ϱ)2|R Ϫ 1|, (13) CDD ference compared with the CDD case. When the fresh- where K is de®ned in (8). Since in the parameterization water forcing is suf®ciently strong, the salt ®ngering of double-diffusive mixing K is strongly dependent on parameterization starts to decrease the magnitude of the the density ratio R, the order of Eq. (13) becomes high- thermal mode, and the difference becomes larger with er than four and thus no analytical solution can be ob- increasing freshwater forcing until the thermal mode tained. To solve this equation, we have two options: 1) breaks down when the critical freshwater forcing is solve the equation numerically and then eliminate all reached. This is because the density ratio is part of the unphysical solutions or 2) solve the above equation as- solution we are pursuing, and not a given external con- ymptotically, that is, we start to solve the equation with stant as it is under relaxation boundary conditions. The ϱ K ϭ K , and we will have three possible solutions. For magnitude of the density ratio decreases with increasing the stable thermal mode, we use the parameterization freshwater forcing. Given the strong dependence of the of salt ®ngers and will have a diagnosed K; then we intensity of salt ®ngering upon density ratio, we infer use this diffusivity to solve the stable thermal solution that for low freshwater forcing, since the density ratio of (13) and iterate the above processes until the solution is very high, salt ®ngering makes a negligible contri- converges. bution to the vertical mixing. As a result, solutions re- As discussed in ZSH, the unstable thermal mode is main nearly identical with the constant diffusivity so- not observed in numerical models and there is a special lution.
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FIG. 1. Sensitivity of the existence of the stable thermal mode on the freshwater forcing to the following variables in the parameterization of salt ®ngers under mixed boundary conditions: (a) the maximum double-diffusive diffusivity
K*, (b) critical density ratio Rc, and (c) exponent index n.
4. Numerical experiments will be discussed next. To be consistent with the scaling analysis in the last section and to focus on the buoyancy- a. Model con®guration driven ocean circulation, a wind stress is not applied. Here we use the GFDL Modular Ocean Model (K. For the salinity, the following e Ϫ p pro®le is used Bryan 1969; Pacanowski 1995) in a con®guration sim- in the virtual salt ¯ux condition for salinity ilar to Zhang et al. (1998) except for the inclusion of the new implementation of the Gent and McWilliams ϪW cos(10 Ϫ 20)/cos(), Ͻ 20 e Ϫ p ϭ 0 (1990, hereafter GM90) isopycnal mixing scheme pro- ϪW cos(5.5 ϩ 70)/cos(), Ͼ 20 posed by Grif®es et al. (1998). They showed that the Ά 0 original GM90 parameterization code is numerically un- (15) stable in some regions. They re®ned the GM90 param- This e Ϫ p pro®le is plotted in Fig. 2, together with eterization to satisfy the following two constraints (i) the zonally averaged e Ϫ p data from Schmitt et al. downgradient orientation of the diffusive ¯uxes along (1989). Note that the e Ϫ p from Schmitt et al. (1989) the neutral surface direction (ii) zero isoneutral diffusive is modi®ed so that the total e Ϫ p in the model region ¯ux of local potential density. 0Њ±60Њ N is zero. We can see that the ®t function given Temperature is relaxed to the following linear merid- Ϫ1 in (15) with W 0 ϭ 0.6 m yr roughly follows the me- ional pro®le: ridional variation of the climatological data. Two types of experiments are performed under T ϭ T 0(1 Ϫ / N), (14) ``mixed'' boundary conditions: one type with constant where T 0 ϭ 25ЊC, is latitude, and N is the most diapycnal diffusivity (CDD) northern grid latitude. A virtual salt ¯ux condition is 2 Ϫ1 used for salinity. The pro®le of the freshwater forcing KT ϭ KS ϭ 0.5 cm s , (16)
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FIG. 2. Fit function and climatology of the zonally averaged e Ϫ p distribution in the North Atlantic. and another type with the double-diffusive parameter- we also included the scaling results in this ®gure, with ization (DDP) (3), implemented with variables given as parameters as in (5). ␣ ϭ 2.0 ϫ 10Ϫ4 KϪ1 ,  ϭ 8.0 ϫ 10Ϫ4 psuϪ1 , b. Quasi-equilibrium experiments ⌬T ϭ 20 K, S ϭ 35 psu, f ϭ 1.0 ϫ 10Ϫ4 sϪ1 , The above scaling results and the work of ZSH show L ϭ 6.0 ϫ 1062 m, g ϭ 9.8 m sϪ1 , and (17) that under mixed boundary conditions the existence of E ϭ 1.5W0 (18) multiple equilibria in the thermohaline circulation de- pends on the relative contributions of the freshwater to represent the average of the maximum evaporation forcing and diapycnal diffusivity. Since the double-dif- in the subtropical region and the maximum precipitation fusive processes can change the diapycnal diffusivity, in the polar region. we expect that the critical freshwater forcing will be From Fig. 3, we can see that with the implementation affected. In the following experiments we vary the of the DDP, the critical freshwater forcing that desta- freshwater forcing very slowly so that the model is al- bilizes the thermal mode decreases, in agreement with ways in a quasi-equilibrium state. the scaling analysis (heavy lines). This implies that the size of freshwater ¯ux that leads to the cessation of the thermal mode is smaller with double-diffusive processes 1) TWO CONTROL EXPERIMENTS acting than in the conventional mixing case. When the Two experiments are performed, with the diapycnal freshwater forcing is relatively weak (E Ͻ 0.2 m yrϪ1), diffusivities given in (16) and (3)±(5), respectively. We the two experiments are almost identical. This is con- ®rst run the model to an equilibrium with no freshwater ®rmed by the scaling analysis, which demonstrates that Ϫ1 forcing (W0 ϭ 0myr ). From there we increased W 0 the density ratio in the ocean depends on the strength very slowly (0.05 m yrϪ1 per thousand years). Due to of the freshwater forcing. When the freshwater ¯ux is the slow rate of change of the forcing, the model remains weak, the density ratio is relatively high. The double- in a quasi-equilibrium state and we can track the re- diffusive ¯uxes only become signi®cant when the den- sponse of the model to the different (though effectively sity ratio is small. As a result, the mixing due to double steady) freshwater forcings, with the thermal forcing diffusion can be neglected for weak freshwater forcing ®xed. The results are plotted in Fig. 3. In comparison, and the circulation is nearly identical to run CDD. In
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FIG. 3. Change of the stable thermal mode with the freshwater forcing. Heavy lines represent the result from scaling analysis and the thin lines the result from quasi-equilibrium numerical experiments. the quasi-equilibrium experiments when E Ͼ 0.2 m yrϪ1, circulation was small. If such an effect occurs it would the meridional overturning in run DDP is smaller than hasten the collapse, so may be dif®cult to observe. run CDD, and the difference increases with larger fresh- water forcing. At about E ϭ 0.33 m yrϪ1, the thermal 2) PARAMETER SENSITIVITY EXPERIMENTS mode cannot survive in run DDP. In the CDD run, the thermal mode circulation rate drops dramatically at Given the present uncertainties in the salt ®ngering about E ϭ 0.40 m yrϪ1. The scaling predicted critical parameterization, it is important to examine the sensi- values of about E ϭ 0.3 and 0.42 m yrϪ1 for the above tivity of the model to the parameterization variables. In two experiments. The two numerical experiments are the last section, the parameter sensitivity was examined consistent with the scaling analysis results. It is clear through scaling analysis; here we will investigate it that the impacts of double-diffusive processes depend through quasi-equilibrium numerical experiments. on the strength of the freshwater forcing. Three experiments are implemented to compare with Zhang et al. (1998) found that there is a self-rein- run DDP in the last section (here we name it DDPCN forcing aspect to the salt ®ngers in the case with relax- the control experiment). The experiments and the cor- ation boundary conditions so that, when the double dif- responding variables are listed in Table 1. From this fusion is active, the density ratio decreases further. In table, we can see that each experiment differs from contrast, these solutions display little evidence for such DDPCN only in one variable. effects. This may be because, for these mixed boundary The numerical simulation results are plotted in Fig. condition runs, the range of R where the double dif- 4. For comparison, the results from scaling analysis are fusion is active before the collapse of the thermohaline also plotted in Fig. 4 (heavy lines). Again, the quasi- equilibrium numerical experiments are consistent with the scaling analysis. In run DDPK1, with the maximum TABLE 1. Parameter sensitivity experiments. diapycnal diffusivity due to salt ®ngers set to be half 2 Ϫ1 ϱ 2 Ϫ1 Experiment K* (cm s ) Rc nK(cm s ) of that in run DDPCN, the impact of salt ®ngers is DDPCN 2.0 1.6 6 0.5 substantially reduced. The critical freshwater forcing DDPK1 1.0 1.6 6 0.5 that stops the thermal mode is increased (though it is DDPR2 2.0 2.0 6 0.5 still larger than that in run CDD of the last section). In DDPn2 2.0 1.6 2 0.5 run DDPR2 and DDPn2, the critical density ratio and
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FIG. 4. Sensitivity of quasi-equilibrium experiments to the variables in the parameterization of salt ®ngering. The heavy lines are results from scaling analysis and the thin lines from numerical experiments. exponent index are increased and reduced, respectively, salt ®ngers on the stability of the thermohaline circu- compared to run DDPCN. Salt ®ngering in these runs lation in a single hemisphere ocean forced with mixed has a larger effect for the same density ratio distribution, boundary conditions. A scale analysis showed that a which can explain the reduction in the critical freshwater reduction in the critical freshwater ¯ux capable of de- forcing, consistent with the scaling analysis of section 3. stabilizing the thermal mode was to be expected with the incorporation of double diffusion. This was found to be due to the decrease in the net diffusivity of density 5. Summary caused by the salt ®ngers. Numerical simulations with The stability of the oceanic thermohaline circulation quasi-equilibrium experiments (with slowly changing is an issue of great interest, as paleoceanographic data freshwater forcing) and individual experiments (with indicate that it has displayed great variability in the past, ®xed freshwater forcing) were also performed. with dramatic consequences for climate (Keigwin et al. The quasi-equilibrium experiments show that double 1991). The hydrologic cycle is often identi®ed as the diffusion lowers the critical freshwater ¯ux capable of primary source of instability, as its affect on seawater destabilizing the stable thermal mode, consistent with density is counter to that of the meridional distribution the scaling analysis. For weak freshwater forcing re- of heating and cooling (Broecker et al. 1985; Huang gimes, the magnitude of the thermohaline circulation is 1994; Rahmstorf 1995). A number of studies have fo- nearly identical for both runs CDD and DDP.Only when cused on the stability of oceanic models forced with the freshwater forcing is close to the critical value does ``mixed'' boundary conditions (where SST temperature the magnitude of the thermohaline circulation in run is relaxed to prescribed values and a virtual salt ¯ux is DDP become signi®cantly smaller than in run CDD. used for salinity), which admit multiple equilibria in the The limited parameter range where the density ratio realized solutions. In Zhang et al. (1999) it was shown became small was a surprise to us, as low density ratios that a critical relationship exists between the magnitude are quite common in the subtropical gyres (Schmitt of the freshwater forcing and the diapycnal diffusivity 1990). This may indicate that a full wind-driven cir- such that, when the ¯ux exceeds a critical value, the culation is necessary to properly simulate the density normal thermal mode is no longer obtained and a haline ratio distribution in the real ocean. In addition, these mode dominates. results suggest that the present thermohaline circulation In this study, we have investigated the in¯uence of may be closer to destabilization than would be the case
Unauthenticated | Downloaded 10/01/21 10:28 PM UTC JUNE 2000 ZHANG AND SCHMITT 1231 without the in¯uence of salt ®ngers. The apparent im- Deglacial meltwater discharge, North Atlantic deep circulation, portance of the double-diffusive processes to the ther- and abrupt climate change. J. Geophys. Res., 96, 16 811±16 826. Ledwell, J. R., A. J. Watson, and C. S. Law, 1993: Evidence for slow mohaline circulation, and its sensitivity to the variables mixing across the pycnocline from an open-ocean tracer-release in the diffusivity parameterization, suggests that a much experiment. Nature, 364, 701±703. better knowledge of such mixing processes in the real Manabe, S., and R. J. Stouffer, 1994: Multiple-century response of ocean is required. a coupled ocean±atmosphere model to an increase of atmospheric carbon dioxide. J. Climate, 7, 5±23. Pacanowski, R. C., 1995: MOM2 documentation, user's guide and Acknowledgments. We are grateful to Rui Xin Huang reference manual. GFDL Ocean Group Tech. 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