Ventilation of the Cariaco Trench, a case of multiple source competition?

Det,p-5~ ,qam'c~ Voa, Y?, No. 2, pp. 203-225, tOq0. Primed in Cheat Bream.

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Ventilation of the Cariaco Trench, a case of multiple source competition? KIM J. HOLMI~N* and CLAES G. H. ROOTH*

(Received 8 August 1988;/n revisedform 15 July 1989; accepted3 August 1989) Abstra~--The joint evolution of potential temperature, salinity and tritium concentrations in the deep basin in the Cariaco Trench, over a 13 year period from late 1972 to early 1986, suggests a complex pattern of ventilation of the basin. SCRANTONet al. (1987, Deep-Sea Research, 34, 945963) found that a purely diffusive model could accommodate the observed evolution from 1973 to 1982 of concentrations of a range of hydrographic and chemical trace species, but the tritium data demand inclusion of two distinct convective ventilation sources with differently distributed depth penetration. Exploratory computations with an extension of Scranton's model, including penetrative convection effects, suggest that a single ventilation mode cannot explain the total observed evolution. The observed trends in temperature, salinity and tritium concentration can be individually matched by fitting simpler models, but jointly they demand injection of warm hypersaline shelf waters which reach the basin bottom, as well as input of Caribbean thermocline waters at the sill. While the overflow events at the sill appear not to have penetrated into the deepest basin layers in recent times, the observed bottom temperature demands at least episodic ventilation with Caribbean thermocline waters colder than 16.5°C. The apparent absence of such activity, for several decades through the mid-1980s, implies climatically persistent differences in the circulation dynamics of the southern Caribbean Sea. A theoretical discussion suggests that this may be but one example of extreme sensitivity of bottom ventilation processes in enclosed deep basins to forcing fluctuations, and that even weak geothermal heating may exert a significant influence on the stratification and ventilation statistics in such systems.

I. iNTRODUCTION DEEP isolated basins with shallow sills represent in miniature an essential principle of the global thermohaline circulation, viz. that the sinking branch of the circulation tends to be very concentrated, perhaps though split between several sites, and that the upwards return flow is much more broadly distributed if not almost homogeneous. It is well established that even very dense water sources m a y not be capable of inducing sinking all the way to the b o t t o m unless the source strength (properly measured in terms of buoyancy flux) is sufficiently large (TURNER, 1973). In a stratified environment, entrainment of fluid is capable of rapidly diluting the driving buoyancy anomaly of a convective current, causing such currents to terminate their vertical motion well before reaching the level corresponding to their initial density. T h e resulting layered intrusions are of substantial interest also in bio-geochemical applications since they can create quite complex transport paths for trace constituents in the system. L a b o r a t o r y studies with accompanying theoretical models (e.g. KILLWORTH and TURNER, 1982) provide a basic f r a m e w o r k for consideration of d e e p basin ventilation by variable convective sources, but the direct rescaling of results f r o m such studies to " Rosenstiel School of Marine and Atmospheric Science, University of Miami, 4600 Rickenbacker Canseway, Miami, FL 33149-1098, U.S.A. 203

204

K . J . H o t . q ~ and C. G. H. ROOTH

geophysically interesting situations is far from a trivial matter, mainly because of effects of the Earth's rotation. Observational tests require a basin for which the lateral advective-diffusive stirring is fast compared to the vertical exchange time scales, and with depths great enough to render interior vertical diffusion ineffective on the ventilation time scale, except in a limited upper pycnocline domain. As discussed in Section 4, a deep interior domain will then ensue which is dynamically controlled by advection and vertical stirring due to penetrative convection processes, and by in situ buoyancy sources (geothermal heating). The above criteria are fulfilled by the Cariaco Basin (also known as the Cariaco Trench; see map, Fig. 1), a marginal basin off the coast of Venezuela with a sill depth of about 150 m. It will be referred to henceforth as the CB, for brevity. Its area is ca 10~° m 2 at the sill depth. Its maximal and mean depths below the sill are about 1250 and 750 m, respectively. The waters are oxygen free from a depth of about 300 m downwards, making it an attractive site for the study of anoxic and microaerobic processes (RICHARDS and VACCAgO, 1956; S C I O N et al., 1987; the latter work will be referred to as $87 hereafter). A key point of $87 is that care must be taken in interpretation of data from long-term chemical balance studies in this basin since conditions there are subject to significant changes on decadal time scales. These indications of a transient character of the physical state of the basin lend it particular significance as a test case for our dynamic understanding of the ventilation processes. We report here on the implications of two sets of tritium (3H) observations for the basin ventilation scenario presented in $87. Although limited, this data set has characteristics that are unequivocally inconsistent with the minimal complexity in the $87 model. We suggest that an interplay of two dense water sources, viz. relatively fresh Caribbean thermocline water and hypersaline water from the Venezuelan shelf, controls the normal

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Map of the Cariaco Basin. The tritium data was taken in the central parts of both subbasins, at positions listed in Table 1.

205

Ventilation of the Cariaco Trench

state of the CB. The recent transient evolution of its deep water mass stratification is thus seen as caused by a temporary weakening of the sill overflow which allows domination of the deep ventilation by the shelf water source. Complete cessation of the sill overflow is also inconsistent with the data, however. A continual mid-depth ventilation with tritiumtagged Caribbean thermocline water is clearly implied. As the data set is much too limited to allow detailed process diagnostics, we invoke laboratory and theoretical results regarding convective ventilation to provide a constraining framework of a mechanistic model. The relevant discussion and some results of computations with a stationary multiple course ventilation model are presented in Section 4 and the Appendix, as a basis for the adoption of a bi-modal convective ventilation process in our final diagnostic picture of the system. 2. T H E D A T A IN T H E C O N T E X T OF T H E S87 M O D E L

The available tritium observations in the CB (Table 1) are from cruises in 1972 by the NOAA R.V. Discoverer, and in 1986 by University of Miami R. V. Columbus Iselin. The tritium presently in the oceans is almost exclusively due to modern nuclear technology, including weapons testing. An effective source function estimate by DttEISiGACr,ER and RoFrRER (1978) suggests only minimal new input during the period considered here. While tritium decays radioactively with a half life of 12.43 years, one can model its behavior as that of a conservative tracer by rescaling the concentrations to a reference datum according to the exponential decay law. However, special care has to be taken in Table 1. Station positions and data listings for Cariaco Basin tritium data

Depth (m)

Pot. temp.

Salinity

(*C)

(%.)

U.S./NOAA R.V. Discoverer, 1972 Station 0051; position 10*40'N, 65"28'W; date 26 Nov. 1972 0 26.83 36.540 40 24.29 36.630 80 23.26 36.740 120 19.07 36.520 200 17.71 36.360 280 17.34 36.300 340 17.17 36.270 460 16.97 36.220 580 16.87 36.200

Tritium TU81N

ETU

2.88 3.05 3.90 3.23 2.38 1.07 1.09 0.30 0.09

0.10 0.10 0.11 0.11 0.09 0.06 0.06 0.06 0.06

0.18 0.12 --0.02 0.05

0.07 0.07 0.10 0.13

0.92 0.45 0.04 0.03

0.10 0.10 0. I0 0.09

1.95 3.03

0.13 0.12

University of Miami R.V. Columbus lselin, 1986 Station 563; position 100"37'N, 65028'W; date 12 Mar. 1986 800 1000 1200 1300

16.86 16.84

36.206 36.206 36.210 36.216

Station 569; position 10°37'N, 65°31°W; date 13 Mar. 1986 500 700 900 1100

17.00 16.90 16.85 16.83

36.253 36.219 36.209 36.204

Station 572; position 10"39'N, 65"31'W; date 13 Mar. 1986 150 300

17.57

36.572 36.341

206

K . J . HOLM~ and C. G. H. ROOTH

the scaring of source terms and boundary conditions; time-independent boundary concentrations are transformed, for instance, into exponentially growing ones. Accordingly, we present the two data sets in decay-corrected (time-normalized) form, against depth in Fig. 2, and against potential temperature in Fig. 3. The unit designation TU81N signifies that the time normalization has been performed relative to 1 January 1981, using the new half-life estimate. Data, not shown here, from several Caribbean Sea stations on the same Discoverer cruise (Os-rLum~, 1984) and from the Tropical Atlantic Study phase of the Transient Tracers in the Oceans (TI'O/TAS) project (Os'rLtn~ and Gg~.L, 1987) show that through the 1970s, the normalized tritium concentration has remained essentially steady at a value of 3 TU81N in the depth (potential density) range from which sill overflows into the Cariaco Basin must be derived. $87 reports that a significant transient evolution in chemical trace constituents, as well as in temperature and salinity, was observed over essentially the same time span (19731982) as that covered by our tritium data (late 1972-1986). The observed evolution was successfully rationalized on the basis of a one-dimensional multi-layer diffusion model, in the sense that results from this model appeared to fit the observed transient evolution for the trace substances considered without invoking any advection effects. The implied cessation of intensive ventilation at the basin sill must be temporary, of course, and most likely dependent on extreme fluctuations in the external forcing conditions. A duration of such conditions for several decades is suggested by Fig. 4, which shows the evolution of bottom temperature and concentration of dissolved silica since the 1960s. Although the silica concentration exhibits a more complex pattern, the evolution of both variables suggests that the state of the basin in this time interval must have been very far from an equilibrium with respect to the current external forcing effects. 3 O0

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1200

1400

Fig. 2. Tritium concentrations vs depth, expressed in TU81N, i.e. l0 's times the mole fraction of tritium in the water, decay corrected to a virtual date of I January 1981. Also shown is the prediction of the 1986 distribution produced by our implementation of the $87 model. The effective detection limit using the University of Miami beta counting system is indicated by the dotted line.

Ventilation of the Cariaco Trench

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Fig. 3. (a) Tritium concentration vs potential temperature for the total deep water range in the Cariaco Basin. Also shown are the predictions produced by the $87 model, and by experiment VII with the model as modified by us (see Sections 5 and 6). The lightly dashed square shows area enlarged in (b). (b) Expanded plot of the deep water part of (a).

208

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Fig. 4. Long-term evolution of temperature and dissolved silica concentration in the bottom waters of the Cariaco Basin. The temperature data are plotted after Table 1 in $87, except for the final point which is from cruise CI 8602 (cf. Table 1). The silica data are from $87 for the middle area, from FANNli~Gand Pit.SON (1972) for 1968, and from CI 8602 (according to note added in proof, $87) for 1986. Note consistency in slope between the last three silica points. This will be taken as representative for the dissolution rate at the bottom, and used to estimate overflow rate at the sill required to balance input by dissolution.

As a first step, we used the $87 model code with the reported preferred parameters (including a correction to the basin hypsography reported by SCRArCrOS, 1987) to predict the observed tritium transient. As the upper boundary condition, we adopted a uniform value (3 TU81N, as suggested above) decay-corrected tritium concentration. The model predicted significant tritium concentrations at the bottom of the basin by the time the second data set was acquired, a result clearly at variance with the available data. This result is represented in Fig. 2 by the continuous line, while the initial and final observations for the period are given by the discrete symbols. While the prediction is good in the depth range from 500 to 800 m depth, substantial errors are observed both at shallower and greater depths. The former could perhaps be blamed on inadequate specification of the upper boundary condition for the tritium concentration (for further discussion of this, see Section 7). Given the successful prediction at mid-depth, the errors in the tritium concentration distribution in the deep waters must be blamed on transport processes in the model. The conclusion that the latter are somehow inadequate is readily apparent. The question now arises, whether some variations in the distribution of the model diffusivity coefficients could suffice to rectify these discrepancies, or whether essential modifications of the model are required. We have found that different aspects of the data demand such modifications in distinctly different ways, and show in the following section (3) that, in addition to the bottom water evolution problem identified above, the evolution of the joint distributions of tritium and potential temperature (and of the salinity) in the upper basin half are irreconcilable with any purely diffusive model for the interior water column. Any acceptable model structures must therefore include effects of a penetrative boundary convection regime with at least two distinct forcing modes. This

Ventilation of the Cariaco Trench

209

conclusion, together with theoretical considerations in Section 4 of a convective ventilation process with variable (multiple) sources, forms the basis for augmentation, in Section 5, of the $87 model with a lateral injection of water from a (prescribed) convective boundary process, and for a set of model integrations aimed at discovering how the available data constrain the admissible parameter ranges for several conceivable model structures. 3. THE J O I N T M I X I N G P R O B L E M FOR T R I T I U M AND T E M P E R A T U R E

We consider the general case of advective-diffusive tracer transport in a basin of depth-dependent cross section, allowing for the existence of a concentrated vertical convective flux in a narrow boundary layer. We assume for the present purpose that no significant deviation between isopycnic (isothermal) and horizontal surfaces occurs in the interior, and that all trace properties are laterally uniform there. This implies that processes of lateral homogenization are fast compared to the rate of evolution of vertical structure. WAL,N 0977) has shown that the general treatment of this type of system in a density coordinate frame leads to the same algorithmic structure as the one found here. Let the mass (volume) transport by time t across level surfaces in the interior domain be V(z), their area A ( z ) and (potential) temperature T(z). Furthermore, let C be the concentration of a tracer (decay corrected if radioactive, as discussed above), m the rate of lateral injection of water from terminating convective plumes, and 7" and C* the respective property anomalies in the waters injected from terminating plumes (the water removed from any layer by entrainment into the convective plumes is assumed to have the average basin properties). Then AT, + VTz = mT* + AzQ + (AKT:)z ,

(1)

ACt + VCz = mC* + A z F + (AKCz)z ,

(2)

where the first terms on the right-hand side in each equation are the heat and tracer input, respectively, due to injection of water from terminating convective events in the inflow boundary layer, Q is the geothermal heat flux and F is the mean tracer source intensities at the bottom interface. To derive a governing equation for the tracer concentration (C), as a function of T and t, we combine the equations after multiplying (1) term by term by - C r , and use the identity:

c,(z) = C,(r) + Cn,)T,(z). The result is Ct.r = A - t m ( C * - CrT*) + (In A ) z ( F - QCr) + K(Tz)2Crr .

(3)

(Note that in our case the question of whether the (potential) density stratification is uniquely determined by T(z) is moot as long as T is monotonic in z, and one is not attempting to parameterize K as a function of the vertical stability. Also, if the stratification is based on T alone, then neutrality of the terminating plumes requires that T* = 0, identically. In our case the sill overflow is fresher than the CB interior waters, however, so that neutrality requires T" < 0.) Now, in Fig. 3, we see that a substantial temporal increase in C is observed over most of the temperature range in the basin. This implies that the right-hand side of equation

210

K.J. Hcoa~

and C. G. H. ROOTX

(3) should be positive there. Only the second data set (from 1986) has sufficient detail to allow clear conclusions regarding the sign of Crr. Since the latter is clearly negative over the central temperature range, positive contributions from either or both of the source terms must be invoked. This is precisely what lateral injection of colder (fresher) water with higher tritium concentration than the local value would achieve, since C r is clearly positive. The complex structure at the bottom left of the graph is only marginally significant in view of the analysis uncertainty of 0.05-0.07 TU associated with the tritium data. We must rely on the tritium concentration changes (or rather on estimates of the total mass of tritium transported to the bottom waters), together with the observed evolution of the T-S correlation for the judgement of model quality in the extreme bottom waters. In the discussion section in $87, model runs are referred to which include vertical advection effects. A non-divergent vertical transport was used, which presupposes that all convective activity reaches the bottom. With reasonable choices of diffusion coefficients no compelling empirical rationale was found for the inclusion of such ventilation within the simulated period, but such ventilation is clearly necessary as a mechanism for creating the initially observed conditions. What we have shown here is that the observed tritium/temperature transient demands a lateral injection pattern distributed in depth (and with depth-dependent characteristics). This implies occurrence of continual convective processes at the basin boundary. A theoretical digression in Section 4 provides support for inclusion of penetrative boundary convection processes in transport models, and thus for our approach in the model computations presented in Section 5. 4. K I N E M A T I C A S P E C T S OF P E N E T R A T I V E C O N V E C T I V E B A S I N V E N T I L A T I O N

Idealized models BAINES and TURNER (1969; referred to as BT hereafter) introduced the idea that penetrative convective processes which entrain interior waters during the sinking process might dominate over diffusive mixing in the conditioning of the deep waters in enclosed basins. KILLWORTHand TURNER (1982; KT from now on) showed that a time-variable buoyancy flux at the source produced a wide distribution of penetration depths which could be modeled as due to an ensemble of simultaneously acting sources, coupled in their behavior only through their joint effect on the mean state. This implies that a timedependent convective source, interacting with a large enough receiving basin, is in its long-term mean effects equivalent with an ensemble of parallel sources. We extend in this section the concepts put forth in KT, with the objective of making plausible a scenario of bimodal penetration of the convective processes at the basin sill, where a small fraction only of the inflow events actually ventilate the bottom. The reader who is primarily interested in our model integration results can at this point skip to Section 5. Let a basin with depth-dependent cross section A(z) be filled with an incompressible fluid with a density finear in a conservative "'temperature", T, measured in buoyancy units, and let Q represent normalized heat fluxes, expressible in the form VT, where V is a mass (volume) flux. We consider a finite ensemble of N(z) convective plumes, defined by an index n ~< N, each characterized by a mass flux V,, and a mean temperature T,,. If we further denote the corresponding interior basin parameters by V and 7", and define a local plume heat (buoyancy) flux as = V,,(z)(r-

(4)

Ventilation of the Cariaco Trench

211

we have the, almost trivial, steady-state conservation relations (z is positive upwards) N

E

v. = v

(5)

1

'Y. Q,, = A q + KATz + 1

A T,dz,

(6)

t,

where K is an eddy diffusion coefficient for T, averaged over A, q is a uniform geothermal heat flux rate, and zb is the extreme bottom depth. A basic kinematic property of entraining convective transport is that each V,, is monotonically increasing with depth, until the termination level where in idealized models one usually assumes localized injection into the interior. The entrainment rate,-V,,.z, is thus positive definite as long as Q,, is positive. Using the delta function operator, the plume termination can thus be formally represented as the effect of a detrainment operator V,,5(Q,,). In reality, the plume termination involves fluid injection into the interior domain over some finite range of interior density (hence depth). Since the water injected from the plume has the density of the interior at the termination level, no local density change is induced. However, as shown in Fig. 5, this density neutrality will generally happen with compensating finite values of temperature and salinity anomaly at the termination point. The figure shows an idealized mixing diagram for a convective flow which originates with properties corresponding to point P. The convective plume flows through a stratified column with properties defined by the curve ABC. To terminate at the level corresponding to B, the entrainment mixing must produce a plume with properties P', corresponding to a point on the potential isopycnal t~n, which passes through B. Thus, if the average entrained water temperature and salinity correspond to a point M (in general not on the curve ABC) the degree of

8 /

c

,%

z

Fig. 5. Schematic mixing diagram of potential temperature vs salinity space for an entraining dense plume which terminates part way to the bottom. ABC denotes basin background O-S relation, P the source properties, and M the average characteristics of the entrained water. For the plume to terminate at B, the mixing point P' must lie on the potential density curve through B (dashed line). Shaded area indicates expected properties due to mixing of water with P' character into the waters surrounding layer B.

212

, K.J. HOL.,~Nand C. G. H. ROOTH

entrainment dilution of the source water is defined. Finally, when water of characteristics P' is added to the interior and partially modified by mixing at the level corresponding to B, a local distortion of the 0-S curve is induced, as indicated by the hatched area. In the idealized model case this area collapses to a spike aiong the potential isopycnal line. A physically complete model would have to account for the three-dimensional dynamics of the injection process. This process will begin as a gravitational intrusion [see M~'~NS (1976) and (1979) for mid-level and bottom intrusion dynamics] but may typically result in generation of weak geostrophic eddies like the boluses of Mediterranean water that are frequently observed in the Atlantic (McDoWELL and RossBv, 1978; Atom et al., 1988). With a smooth and stationary probability distribution of injection events, the result of this process is a vertically distributed time-dependent ventilation process which is "climatologically" smooth.. The discrete plume terminations induce diffusively damped transient property anomalies. The associated transient eddy current processes fall outside the scope of this paper. To determine the convective termination depth statistics we must have a recipe for the evolution of Q,, for an individual plume. From its definition in equation (4), we see that it depends only indirectly on the entrainment process. Because Q is defined relative to the local interior density, its evolution depends on V, the volume transport, and on the interior stratification only. Thus (7)

Q.,z = V.Tz.

Combined with equation (6), this gives AKfA.~

= V~

Q,,, - , 4 q

.

(8)

The coefficients in this equation define an adjustment scale height H,, = AK/Vn, which is inversely proportional to the monotonically increasing plume mass flux. To see more clearly what the implications of this equation are, we consider first the case of a single plume, i.e. N = 1. We have then (in steady state, i.e. with Tt = 0): Qi.z = H:I(QI

-

Aq),

(9)

where both Hi and Aq are monotonic functions of z. Thus Qt will track Aq, with an ever decreasing lag effect as the mass flux VI grows by the entrainment process. This can be intuitively understood by observing that although the plume dynamics respond directly only to the local temperature gradient, a steady-state situation demands a temperature profile which allows this close tracking to occur. This is an inevitable consequence of the requirement for buoyancy conservation within the volume below any level surface. Applied to a plume ensemble, this result explains the effective limitation of the weaker plume intrusions to a shallow ventilation depth. If we sum equations (7) and (8) over an ensemble of plumes, a form identical with equation (9) arises for the total ensemble fluxes. As for a single plume situation, the total heat (buoyancy) flux will track the geothermal input. However, for any individual member of the ensemble, the rate of change of Q,, is underestimated by equation (9). This effect is more pronounced, the smaller the total flux percentage contributed by the plume considered. Thus, the final approach to the termination (zero buoyancy flux) condition tends to be linear rather than exponential with depth, causing a well-defined termination.

213

Ventilation of the Cariaco Trench . ,. 0.0

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25 io ' ' 100% FRACTION OF PLUMES PENETRATING

Fig. 6. Distribution of depth penetration probability for entraining convective plumes with a topographically controlled geothermal heating (also a proxy for mean trend in temperature, see text)• The curve-labeled basin shapes represent total heat flux demand vs depth, the latter is controlled by the diffusive boundary layer in the uppermost 25%, and by the basin shape in the deepest 75% of the depth range• This figure should bc considered for its qualitative implications o n l y - n o attempt has been made to achieve apparent realism by parameter tuning•

That even a weak geothermal heat flux contribution may have significant effects on the ventilation processes in the deeper portions of a confined basin is illustrated in Fig. 6, which shows the result of a set of model integrations using the free plume dynamics case of Pr:TERSON(1979), i.e. with diffusive interior, but with a "geothermal" heat source added, as in equation (8). (The model equations and conditions for the computations are described in the Appendix.) The geothermal heat source, which balances only 5% of the total plume buoyancy flux in the cases presented, is taken as uniform with respect to the horizontally projected basin area. Its vertical distributibn is thus controlled by the different hypsographic curves (defined in the figure insert)• The resulting differences in penetration depth statistics stand out quite vividly. For those plumes which do not terminate within the upper convective regime, the probability of plume termination in any particular depth range is clearly related to the relative bottom exposure, i.e. to the relative contribution to the total geothermal buoyancy flux which arises there. A less obvious consequence of the plume statistics described above is that statistical fluctuations in the bottom ventilation process may be substantial• This phenomenon is reflected in the coarse step structure in the distribution function for the finite number of stead~, model plumes in Fig. 6. The effect is enhanced if the hypsographic curve is strongl) concave at the bottom, i.e• if the deepest layers contain a relatively small fraction of the basin water volume.

Implications for the Cariaco Basin diagnostics In ar,alogy with the KT model, the Cariaco Basin is not a steady-state system, but rather one where the mean properties change gradually due to the convective injection

214

K . J . H o t . q ~ and C. G. H. ROOTH i

processes. The deep layer property trends there are only weakly depth dependent. In a twist on the use made in BT (and in KT as well) of the approximately uniform trend in mean field properties, we shall take this to imply that the observed deep water warming effects are due to a vertically uniform admixture of warm salty shelf water per unit volume of water in the deep basin. The following analysis suggests that this state is due to a cessation of bottom-reaching ventilation by inflow of Caribbean water across the sill. The joint evolution of tritium concentration and T-S characteristics in the upper third of the basin is, however, inconsistent with complete cessation of inflow at the sill. A cessation of deep ventilation with retention of ventilation effects in the uppermost part of the basin is in fact an expected consequence of any significant decrease in the rate of dense water input (negative buoyancy flux). For a single source this effect is transient, but with multiple sources it could remain permanent as long as some other source with greater extreme intensity exists. 5. E X P E R I M E N T S WITH A 1 . 5 - D I M E N S I O N A L V E N T I L A T I O N M O D E L

General considerations

The contradictions between the observed tritium distributions and the prediction obtained by the basic $87 model which were identified in Section 2, and illustrated in Fig. 2, are qualitatively different above and below the topographic saddle point level (at a depth of 900 m). Taking our cue from the theoretical convective ventilation discussion in Section 4, we deviate therefore from the common assumption that the dense water influx will uniformly reach the bottom. The concept of topographic control of penetration statistics suggests to us that the contrasting requirements for convective ventilation influence can be met by invoking two distinct source mechanisms with different penetration characteristics. A basic population of deeply penetrating convection events, with source characteristics defined as hypersaline shelf waters, is assumed to be responsible for the salinity increase and, together with the geothermal heating, for the warming observed in the deep layers. The demand for tritium injection at intermediate depths is met by imposition of a second inflow source at the sill, with larger volume flux but smaller initial buoyancy anomaly, causing it to penetrate only marginally into the basin interior. Table 2 shows a tritium profile from the Grenada Basin which can be taken as indicative of the expected tritium source characteristics, because of the strong westward flow of the upper Caribbean waters (e.g. GORDON, 1967). To represent these processes in our Table 2. A tritium profile in the Grenada Basin. TTO Tropical Atlantic Study; R.V. Knott Station 8; position 11°59'N, 62"28'W; date 6 Dec. 1982 Depth (m) I0 47 I01 152 202" 403 599 798

Pot. temp.

(°C)

27.43 27.45 22.21 19.79 16.67 9.82 6.99 5.75

Salinity

(%.)

35.501 35.951 36.749 36.560 36.187 35.065 34.730 34.726

Tritium TU81N

ETU

1.91 1.92 2.55 3.02 3.28 0.90 0.24 0.06

0.09 0.08 O. I0 0.13 0.13 0.09 0.05 0.06

" Most nearly representative of a dense inflow event at the Cariaco Basin sill.

Ventilation of the Cariaco Trench

215

augmentation of the $87 model code, we have introduced a parameterized injection process. This section describes the rationale for, and the main results from a number of exploratory experiments with this model. The starting point for our model experiments is the multi-layer one-dimensional transport code described in $87. We have used the corrected basin hypsography presented by SCRANTON(1987). The depth resolution in $87 is 50 fathoms (91.4 m). The depth range from the sill to the basin bottom is thus divided into 12 layers. To this model was added a representation of lateral injections of overflow water by the termination of convective plumes. The resulting model can be characterized as 1.5-dimensional, since it involves a one-dimensionai resolved advection-diffusion prediction for the evolution of properties in the main water body in the modeled basin, coupled with a parameterized representation of the processes in the convective (lateral) boundary layer. To be complete, prescriptions for the convective boundary process require specification of source properties, of injection depth distribution, and of the rate at which the convective boundary plumes entrain interior fluid along their path to the termination depth (cf. Section 4 and the Appendix). Since our objective is not a detailed consideration of the dynamics of the convective process but rather to establish, in a diagnostic sense, the patterns of circulation necessary to rationalize the observed composition transients, we have chosen to represent explicitly in our computation only the process of external property injection. It can be justified, a posteriori, that our conclusions are robust with regard to this approximate model treatment, as indicated in Section 6. We note here only that any empirically generated parameter fits in the computations will represent an upper bound on the effective mean vertical mixing processes in the interior basin domain. The model-matching requirements established above are distinct in the deep basin waters and above the saddle point level. They can be summarized as: (a) an adequate diagnostic model must explain how warming is achieved in the deep layers without observable increase in tritium concentration, (b) in contrast, the model must accommodate a significant tritium increase in the upper deep basin which is accompanied by only a marginal temperature increase. Regarding the first point, geothermal heating effects were dismissed in $87 as requiring unreasonably large conductive heat flux values. Model runs employing diffusivities adjusted to eliminate excessive tritium penetration, but twice the geothermal heat flux used in $87 (0.044 vs 0.022 cal m -2 s' l ) failed to produce the observed salinity increase, as one might indeed have expected based on the results in $87. The only alternative obvious to us depends on the fact that near-surface tritium concentations are not significantly influenced by the evaporation processes, and not at all by sensible heat transfer. Thus, the production of warm saline shelf waters results in a water type which when injected into the deep basin can increase the temperature and salinity with only minuscule enhancement of the tritium concentration. As a matter of fact, the Caribbean surface waters have even lower tritium concentrations (as reflected in the tritium gradient reversal near the surface in Table 1) than the values observed at the levels appropriate for the sill overflow. The total injection rate for this water is optimized empirically in the model runs, based on an assumed vertical distribution of the injection rate which is proportional to the basin area at the injection depth. This produces a uniform rate of admixture of water from the shelf source per unit volume of basin water. The rationale for the latter assumption is

216

K.J. Ho~

and C. G. H. ROOTH

related to the basic model device used by BT, i.e. on recognition of the fact that the observed warming and rate of salinity increase are only weakly depth-dependent in the deep water section of the basin ($87, Figs 2 and 3). Since, in our case, the vertical property gradients are also very weak, we cannot assume with BT that interior vertical advection balances the mean rate of change of these properties. However, as noted in Section 4, the process of plume termination at zero buoyancy allows heat and salt injection at relative rates such that the net injection for buoyancy anomaly is essentially zero. With regard to the second point, our analysis of the diffusive--advective case in Section 3 shows that the observed increase in tritium concentration is fundamentally inconsistent with a purely diffusive model. A significant rate of lateral injection of tritium, at least somewhere in the depth range of 300-500 m, is required to overcome the deficit in the diffusive case. Its magnitude can be roughly estimated by observing that the available source waters at the sill have tritium concentrations close to 3 TU81N, i.e. an excess tritium concentration relative to the observations in the layer in question of 2.2-2.4 TU81N (see Table 2). Thus, to achieve the required correction of the tritium concentration by +0.5 TUS1N, approximately 25% admixture of new sill overflow water over the 13 year period in question would be sufficient. Our choice for depth distribution of the injection is for the shallow (sill) injection based on the notion that only weak buoyancy inflows are occurring at the sill, although the mass flux may be substantial, and on the observation that the measurable tritium incursion actually terminates close to the 16.9°C potential isotherm. Recognizing that the data available do not allow resolution of a detailed injection depth distribution, we have arbitrarily assigned the sill level injection process a gradually decreasing intensity in the first three model grid layers below the sill. Out of a substantial number of model runs with different parameter choices we have chosen eight for presentation here. A summary specification of these model runs is given in Table 3. The resulting tritium distributions vs depth for case numbers II, IIl, VI and VII are given in Fig. 7, together with the tritium observations from 1986. Case I (the $87 parameter set) is presented in Fig. 2 to establish its basic shortcomings. Cases I and VII Table 3. Exp.

Characteristics o f selected model tuns

Eddy diffusivities

Plume source

Notes $87 standard case

I

As in S87 (F(N2))

None

II

Constant = 0.8 cm 2 s -I

None

Ill

1/2 of $87

Shelf

See spec. A below See spec. B below

IV

$87

Sill

V

1/2 of ,587

Sill

VI

0.6 cm 2 s -t above 600 m 2.0 cm 2 s -I below 600 m

Shelf

As in case VI As in case VI

Sill Sill + shelf

VII VIII

As in A and B

Plume source specifications: A. Shelf source: potential temp. 24.0~C; salinity 3 9 . 0 ~ ; tritium 3 TUI81N.

40 m 3 $-t distributed to all levels in proportion to box volume. B. Sill source: potential temp, 17.0~C; salinity 36.25%e; tritium 3 TUSIN. 1400, 1000 and 220 m 3 s- I to levels 1, 2 and 3, respectively.

217

Ventilation of the Cariaco Trench

Z

200

~wwD21.50

ii•' \ '-S. \ '..k.

II.- 1.00

t.[Gl[t40

-

: ~s ~ '~ •", ~ "*'~ \ "..

•

,,,,,.-,,"""--"

" ° III Trlllulm 1114111 --- ¥t r r i , , . . ~141. ---VII Trllh~im IIII)11 .... O.'eq=,. L~mi,

0..50 0.0(3 ..................~ ~ q , . , , . . ~ 400 600 800 I000 200 DEPTH (m)

. . . . ,,. ..... 1200 1400

Fig. 7. Tritium distribution vs depth as predicted by several model versions (see Tables 2 and 3, and discussion in text). The observations for 1986 are also shown for comparison. Note that the prediction made using the basic $87 model was presented similarly in Fig. 2.

are also shown for comparison with the data in the tritium vs temperature format in Fig. 3. Cases V and VIII give distinct vertical profile adjustments only in the salinity fields near the bottom. They are discussed in Section 6 based on the error field characterizations in Table 4.

Summary characterization of results The impacts of different model recipes (defined in Table 3) are illustrated in Table 4 which lists, along with the observed changes, the prediction errors for tritium, temperature and salinity, averaged respectively over the uppermost and deepest four layers (denoted U and L), for the model runs listed in Table 3. The observed changes are listed Table 4. Observed changes, and errors in test run predictions for changes in Cariaco properties. Prediction periods 1973--1986 for tritium; 1973-1982 for temperature and salinity. Model parameters as defined in Table 2. Average values for model layers 1--4, U and 9-12, L. Depth ranges 230-595 and 961-1327 m, respectively Tritium TU81N

Pot. temp. (*C)

Salinity (Y.)

Case

U

L

U

L

U

L

Obs. [ II 1I! IV V VI VII VIII

1.09 -0.42 -0.10 -0.67 -0.17 -0.31 -0.31 -0.08 -0.08

0.03 O. 14 -0.02 0.02 0.19 0.02 0.02 0.03 0.04

O. 165 0.037 0.150 -0.030 -0.018 -0.093 0.089 0.013 0.025

0.07 0.008 -0.033 -0.005 0.006 -0.022 -0.005 -0.022 -0.1)05

0.037 0.001 0.022 -0.009 -0.008 -0.022 0.014 -0.022 0.003

0.010 0.001 -0.009 0.001 0.001 -0.005 0.001 -0.005 -0.001

218

K.J. H o ~

and C. G. H. Room

in the first row of the table. The resulting tritium concentration errors are shown to two significant figures, even though in terms of the measurement resolution anything below 0.05 TU is effectively zero. This is clone to facilitate judgement of how the different parameter choices influence the results. The choice of our ensemble of cases was made primarily in order to demonstrate how the need for model complexity is impressed by various aspects of the data. The exclusion of explicit treatment of the entrainment process means that a vertical recirculationinduced mixing is not accounted for, and also that the mean interior vertical velocity is underestimated. We are now in a position to consider, a posteriori, whether our main conclusions are robust with respect to these approximations. The question takes on a quite different character when the near-bottom and mid-depth transient, respectively, are considered. In the bottom water problem, we were inexorably driven to assume a shelf source as the current main agent of change. As seen in type A in Table 3, the total volume flux required is very small. Even with a substantial enhancement by entrainment it would be dominated, as a transport agent for basin properties by the adopted interior diffusivity. By the same token, interior vertical advection effects are totally insignificant for the evolution of the relative distributions of trace properties in the deep domain. In the shallow ventilation situation, the tritium data demand a pattern of sill overflow with only minimal vertical penetration before the flow reaches its limiting level. We have not attempted to tune this overflow rate but simply adopted a fixed one large enough to supply the observed tritium excess relative to the potential temperature-based diffusive mixing equilibrium. This adopted value gives an interior upwelling rate of 10 m y-t at the sill depth. Changing the magnitude of this flow rate would change the optimal mixing coefficients in the model, but a more detailed mechanistic model could not be verified without further extensive process studies. We can at this point only claim that the adopted overflow rate gives a reasonable magnitude of the effects. Our conclusion that a continual mid-depth ventilation of the basin by sill overflows must have occurred during the period covered in this study, i.e. that only the bottom ventilation from the sill had been cut off, is extremely robust, however. Note that because we had access only to limited hydrographic data from 1986, the test period considered here is 13 years for tritium observations, but 9 years (i.e. the period used for calibration of the $87 standard model case) for potential temperature and salinity. We see in Table 3 that the warming in case I is somewhat overpredicted both for the upper and lower layers; still the significant shortfall of this model case lies in the tritium predictions. Case II was run as a demonstration of the fact that the tritium data alone can be fitted within the observational precision with a purely diffusive model with constant diffusivity, K. This model fails as badly for temperature and salinity prediction, as does case I for tritium. Case III serves to demonstrate that by halving the diffusivities used in $87 (case I) and including convective ventilation by a tritium-tagged shelf water, the evolution of the deep layers can be satisfactorily modeled. As expected from the results of case I, the upper layers are poorly represented by this integration. Cases IV and V involve injection of sill overflow water composed according to type B in Table 3, as a variation on cases I and Ill. We learn from these experiments that the

Ventilation of the Cariaco Trench

219

diffusive coupling to the upper boundary plays a significant role as a tritium source for the upper layers, along with the sill overflow process. Cases VI and VII are selected from experiments done with a simplified distribution of eddy diffusivity, as examples of what can be achieved with ad hoc tuning of the model. It is at this point instructive to compare the impression of fit given by this table, and by Fig. 7, with that of the potential temperature vs tritium cross plot in Fig. 3. As in the introductory discussion, we see here that this type of cross plot is a much more sensitive test of model performance than are the depth distributions of individual properties. Finally, case VIII combines the two-tiered eddy diffusivity receipe with joint imposition of both a shelf and sill source. No effort was made to fine tune intensities since neither data quality nor model sophistication seems sufficient to lend much credence to the detailed results of such an exercise. 6. D I S C U S S I O N

Implications for the ventilation mechanics in the Cariaco Basin The data and simulation experiments described here clearly show that the process of transient water mass modification which operated in the Cariaco Basin deep water mass through the 1970s and onwards cannot be adequately reproduced in a purely diffusive model. Combining type A and B plume ventilations allowed a much improved simulation, showing that the model has sufficient response complexity to allow independent tuning of several aspects of the observed property changes, and that neither type alone suffices to cure the deficiency of a purely diffusive model. Our model results support the qualitative diagnostic conclusion in Section 3, that the recent transient regime cannot be totally devoid of sill overflow effects. However, the tritium data also constrain very strongly the estimate of to what depth the latter penetrate into the basin. The model results also support our conjecture, in Section 2, about the need to include in our ventilation model a significant injection rate of hypersaline warm shelf water which is capable of reaching the bottom. An aspect of the deep ventilation problem not touched upon in the discussion so far is the essential role played in the system by geothermal heating effects. In order to get a high enough density to allow sinking to the bottom, at a winter time shelf water temperature of 24°C (APARlaO, 1989), the shelf water mass must have a salinity which exceeds 39%,. Introduction of such water in the bottom layers of the basin in sufficient amounts to cause the observed rate of warming would lead to an excessive ratio of salinity to temperature increase, except for the additional effect of the geothermal heat flux. Moreover, it turns out that the potential density of the bottom water was in fact decreasing over the period considered here. Since the bottom water cannot be made lighter by convective effects from above, and since the tritium inventory balance precludes significant warming by diffusion from above, this implies that the geothermal heating was a major factor in the density change rate, even though it did not dominate the warming rate. Sooner or later, if this trend were to continue, the system would reach a point where inflow waters at the sill would be capable of ventilating the bottom even if the present overflow regime were maintained. A balance could be struck then between the cooling effects of the sill overflow and the warming induced by the shelf waters and the geothermal effects, but at a temperature which is higher than what apparently characterized conditions in the middle of this century.

220

K.J. H o ~

and C. G. H. Room

Figure 4 suggests that input of relatively cool Caribbean thermocline water, with its low silica content, has been weak for about 30 years. Hydrographic stations taken in the basin in the period from 1952 to 1972 (HERRERA and FEBREs-ORTEGA, 1975) SUggest a hiatus in intense overflow ventilation beginning approximately in 1963, and a large variability in conditions at 400 m. While recent trends in warming as well as in silica concentration (from 1982 to 1986) show no indication of a fall off in intensity, it appears that a hiatus in warming in the 1970s (with its implication of events of enhanced Caribbean water inflow) coincides with a brief period of decrease in dissolved silica concentration. Such conclusions must be viewed with caution though, since the data base is small and of uncertain precision. It is also obvious that the maintenance of the presently observed cool (potential temperature well below 17°C) bottom regime is possible only based on fairly frequent if episodic overflows of Caribbean upper thermocline waters across the Cariaco Basin sill. While little climate information exists which might be applicable to explain the reason for the recent transient behavior in this system, APARXCIO(1989) notes that one has observed in the region a "pronounced decreasing trend in the zonal (easterly) component of the wind stress since the 1960s". Current observations in the Straits of Florida have demonstrated strong correlations between the water transport there, hence throughout the Caribbean Basin, and the regional wind variability (e.g. SCHOTrand ZAI~rroPP, 1985). The rate of ventilation of the coastal shelf region is also much dependent on the regional wind stress. Standard parameterizations of boundary layer processes suggest that the momentum transfer is quadratic in the wind speed, while the direct wind speed effect on transfer of heat and water vapor is linear. So the prospect exists that a weakening trade wind climate could have a dual effect in shifting the preponderance of the deep water ventilation process in the Cariaco Basin towards dominance of the shelf source. Such events might be typically spaced by decades, or their frequency of occurrence may be modulated on decadal and longer time scales by climatic fluctuations, even perhaps by the very irregular statistics of hurricanes.

Some geochemical implications Of all the diverse consequences of variations in ventilation conditions in the basin, the impact on silica concentrations appears to us the most predictable, hence perhaps most useful for observation of the mixing state. This is so because the silica source estimate given in $87 can be only marginally contaminated by diffusion effects. It is therefore likely to be more stable than any other system parameter but the geothermal heat flux. The silica concentration curve in Fig. 4 indicates a growth rate for the dissolved silica concentration of approximately 1 stmol kg -t y-t. With a mean basin depth below the sill of about 900 m, this corresponds to an extremely intensive silica source of 3 x 10-~2 mol cm -2, 10 times typically quoted values (as mentioned in $87). To balance this input in the deepest layers, we can effectively draw only on the sill overflow process, since any shelf water input rate must be very much smaller in terms of mass flux. Assuming the silica concentration in the overflow water to be effectively zero [a value of <2 itmol kg -l is suggested by a cross section by MORRISONand NOWLIN(1981) from the Caribbean Basin] and diffusive silica loss to be a secondary effect, the equilibrium silica concentration, expressed in ~tmol kg -l, has the same numerical value as the basin ventilation time in years. In case of very weak ventilation, the deep concentration of silica would be diffusively limited. We can estimate the level for this case roughly as follows: Let the

Ventilation of the Cariaco Trench

221

vertical diffusivity be 10"~ m 2 s-t, and assume that the geothermal heating causes the deep water to be well mixed to within about 500 m of the sill depth. To balance the sifica source estimated above by a diffusive flux, the mean gradient would have to be 0.3 lamol kg-t, i.e. the deep water excess of silica concentration over that at sill depth would be of the order of 150 I~mol kg-t (adjusted in inverse proportion to the assumed eddy diffusivity if a different value is chosen). Interestingly, if we now estimate an equilibration time scale as the fractional rate of adjustment towards the above-estimated equilibrium, we get a time scale of about 80 years, i.e. of the same order as that sill ventilation time scale required to stabilize the silica concentration at the level observed in the early 1980s. A different perspective on the silica balance problem is provided by FANNING and PILSON (1972) in a steady-state advective-diffusive model wherein the primary rate constraint was their estimate of silica flux from the sediments. They, as well as $87, determined gradients of dissolved silica in the sedimentary pore waters, finding very similar gradient values, and concentrations of about 600 ~tmol kg -t at 0.8 m depth. The resulting silica flux estimate yielded in their model a residence time for the deep waters of 800 years. This work supports the conclusion in $87 that dissolution of settling silica debris in the water column must play an essential role in the Cariaco Basin. Another indication of a regime shift in vertical distribution somewhere around the saddle point between the two deep sub-basins (around 900 m depth) comes from a study by DEUSER (1973) of the total dissolved inorganic carbon (DIC) distribution as observed in 1971. Not only did the DIC show a monotonic increase to about 20% above the surface values at a depth of about 800 m, but a distinct change in the trend in isotopic composition also appeared at that level. Observations like these lend some additional credence to our application of the idea of bimodai penetration distribution for the ventilation events, which we derived from plume dynamics. The implications of this study for biogeochemical process studies in the upper part of the chemocline (the region of rapid transition in chemical conditions) in the Cariaco Basin could thus be substantial. In particular, the incursion of oxygen-containing waters could provide micro-structure in redox potentials which may persist for substantial distances into the interior if globular eddy structures are formed. SCRAr,rroN (1988) finds circumstantial evidence for such effects in an attempt to model the methane balances in the upper half of the deep basin. 7. F I N A L R E M A R K S

We emphasize again that the stated objective of $87 was tO produce the simplest model capable of rationalizing the set of observations used in that study. It is the introduction of the tritium data into the problem that forces us to greater model complexity although we adhere to the same objective. The power of the tracer constraints in this situation is due to the fact that we are dealing with sharply distinct source properties, and the system topology creates distinct and relatively simple response regimes. A similarly powerful impact of joint analysis of multiple transient components was demonstrated by J~NrONS (1980) with regard to 3H and 3He in the Sargasso Sea. Another important basis for the tractability of this problem is that the observed trends are large and distinct in different parts of the system, so that the overall system structure could be resolved even without very detailed information about the specific characteristics of the sources.

222

K..L Hot~.N and C. G. H. ROOTH

Because of these factors in combination, we could successfully separate and determine the relative contributions of forcing processes and response models in the following simple pattern: Vertical diffusion causes increases in temperature, salinity and tritium activity. Sill overflow causes cooling, salinity decrease and tritium increase. Winter shelf water input causes warming, salinity increase, and marginal tritium increase. Geothermal effects cause heating alone. While the tritium distribution observed in 1972 constrains quite effectively the possible scenarios for ventilation events after the mid-1960s, a severe limitation on this work is the assumption that only variations in the overflow processes are involved in the transient modification of the basin, and above all that forcing conditions while changing over longer time scales can in fact be considered stationary over the forcing period. As one expands the perspective to include modeling other tracers (we have in particular considered silica and the inorganic sulfur compounds), one quickly runs into inconsistencies that seem to require even greater model complexity for their resolution. Consider, for instance, the joint transport problem for tritium and dissolved silica: Caribbean tritium data from the early 1970s (OsTLUNU, 1984) suggest that the tritium content at the silica minimum was between 3 and 4 TU81N at this time. Thus, to avoid injection of measurable tritium amounts of the order of 0.05 TU81N, at most around 1% of the deep water could be "new" sill water, leading to no more than 1% relative dilution of the silica concentration. This leads to some serious problems about our understanding of the system evolution prior to 1970. The drop in dissolved silica concentration as well as the hiatus in warming apparent in Fig. 4 appears to demand sill overflow effects which would have introduced measurable tritium amounts if they happenened as late as around 1970. Whether this discrepancy is due to noisy data, to unaccounted for variations in forcing conditions, or simply to deficiencies in the model concept is a problem which is not likely to be solved based on current information. With regard to the scientific opportunities for future exchange studies in the Cariaco Basin, we have barely begun to tap the potential of this basin as a test bed for models of convective basin ventilation. The possibility that the present transient state may represent a response to a long-term climate drift provides additional impetus to the continuation of process studies in the Cariaco Basin through the foreseeable future. Given the substantial changes on decadal time scales discussed here, repeated observations of the state of the Cariaco Trench deep basin would therefore seem warranted on perhaps a semi-decadal time scale. It may be possible in the near future to plan specific response studies for the evolution of the chemical stratification in the Cariaco Basin, since climate-oriented ocean observing programs such as the international World Ocean Circulation Experiment (WOCE), and the U . S . N . O . A . A . Subtropical Atlantic Climate Studies (STACS) may provide advance warnings of ventilation regime transitions by observing circulation changes in the Caribbean. The results presented here have implications for paleoclimatic diagnostics in this basin since changes in the basin-wide baroclinicity in the upper layers of the Caribbean Sea are likely to be the main cause of the inferred ventilation rate anomalies. While further work will be necessary to sort out the relative significance of the large-scale circulation climatology and the local wind structure along the southern border of the Caribbean Basin, we can conclude that significant information on Atlantic-wide rather than just local climate history is likely to be preserved in the bottom sediments of the Cariaco Basin.

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223

Acknowledgements---Tritium analyses were performed at the University of Miami Tritium Laboratory by Dr G. Ostlund, who also provided helpful discussion of the manuscript. The data for 1972 derive from samples which were collected by N O A A AOML on the R.V. Discoverer, those from 1986 were collected on a geochemistry cruise on the R.V. Columbus Iselin, Dr Oliver Zafiriou of WHOI chief scientist. Permission by the Repubfic of Venezuela for this scientific expedition to the Cariaco Basin is gratefully noted. The start of this study was much simplified by the fact that Dr Mary Scranton has made her original transport computation program available to the community at large. The early tritium data used derives from work supported at the University of Miami Tritium Laboratory by the NSF under grants GA18241, OCE75-14368 and OCE-8117845, and the crucial 1986 analyses were supported by U.S. Office of Naval Research contract N 00014-87-J-II16. KJH acknowledges support by the Swedish Natural Sciences Research Council under a post-doctoral stipend no. GPD 9286-100. CGR was mainly supported by internal research developments funds at the University of Miami, but acknowledges the importance of several NSF grants for tracer studies, most recently no. OCE 8609383. REFERENCES APARICIO R. (1988) Meteorological and oceanographic conditions along the southern boundary of the Caribbean Sea, 1951-1986. In: Implications of climatic changes in the wider Caribbean region. A report of the Committee of Experts. Regional Coordination Unit, Caribbean Environmental Program, UNEP (OCA)/CAR WG.1/NF 3 August 1988, Ch. 2.5, pp. 65--81. ARMI L., D. HEnERT, N. OAKEY, J. PRICE, P. RICHARDSON,T. ROSSeYand B. RUDDtCK(1988) The history and decay of a Mediterranean salt lens. Nature, 33, 649--651. BAINES W. D. and J. S. TURNER (1969) Turbulent buoyant convection from a source in a confined region. Journal of Fluid Mechanics, 37, 51-80. DEUSER W. G. (1973) Cariaco Trench: oxidation of organic matter and residence time of anoxic water. Nature, 242, 601--603. DREISIGACKER E. and W. ROETtlER (1978) Tritium and Sr-90 in North Atlantic surface water. Earth and Planetary Science Letters, 38, 301-312. FANNING K. A. and M. E. Q. PILSON (1972) A model for the anoxic zone in the Cariaco Trench. Deep-Sea Research, 19, 847-863. GORDON A. (1967) Circulation of the Caribbean Sea. Journal of Geophysical Research, 72, 6207--6223. GRIVTmIS R. W. (1986) Gravity currents in rotating systems. Annual Review of Fluid Mechanics, 18, 59-89. IIERRERA L. E. and G. Ft~BRt~s-OR'rEGA(1975) Proccsos dc surgcncia y dc renovation dc aguas en la Fosa dc Cariaco, Mar Caribe. Boletino de lnstituto Oceanographico, Universidad Oriente, Cumana, Venezuela, 14. 31--44. JI~NKINSW. J. (1980) Tritium and ~[-[c in the Sargasso Sea. Journal of Marine Research, 38, 533-569. Kn.WORTII P. D. and J. S. TURNER 0982) Plumes with time variable buoyancy in a confined region. Geophysical and Astrophysical Fluid Dynamics, 20, 265--294. MANINS P. C. (1976) Mixed-region collapse in a stratified fluid. Journal of Fluid Mechanics, 77, 177-183. MANINS P. C. (1979) Turbulent buoyant convection from a source in a confined region. Journal of Fluid Mechanics, 79, 765-78l. McDowI.:LL S. E. and H. T. Rossuv (1978) Mediterranean water: an intensive mcsoscale eddy off the Bahamas. Science, 202, 1085-1087. MORRISON J. M. and W. D. NOWUN, Jr (1982) General distribution of water masses within the Eastern Caribbean Sea during the winter of 1972 and fall of 1973. Journal of Geophysical Research, 81, 4207-4229. OSTLUND H. G. (1984) NAGS TRITIUM: North Atlantic Gyre Studies and Associated Projects, Tritium Laboratory Data Report No. 13. University of Miami, Rosenstiel School of Marine and Atmospheric Science, Miami, FL 33149, 324 pp. (unpublished manuscript). OSl"LUNDH. G. and C. GRALL (1987) Transient tracers in the ocean: North Atlantic tritium and radiocarbon. Tritium Laboratory Data Report No. 16. University of Miami, Rosensticl School of Marine and Atmospheric Science, Miami, FL 33149, 277 pp. (unpublished manuscript, data disk available from the author). OSLUND H. G., M. RINKEL and C. G. H. ROOTH (1969) Tritium in the equatorial Atlantic current system. Journal of Geophysical Research, 74, 4535--4543. Pt:'rERSON H. (1979) A steady thermohaline convection model. Ph.D. dissertation, University of Miami. Technical report TR 79-4, Rosenstiel School of Marine and Atmospheric Science, 160 pp. (unpublished manuscript). RICHARDSF. A. and R. VA¢C^RO (1956) The Cariaco Trench, an anaerobic basin in the Caribbean Sea. DeepSea Research, 3, 214-228. SCRANTONM. 1. (1987) Errata note. Deep-Sea Research, 34, 1653. SCRANTONM. I. (1988) Temporal variations in the methane content of the Cariaco Trench. Deep-Sea Research, 35, 1511-1523. SCRANTONM. I., F. L. SA't'LES,M. P. BACONand P. G. BREWER(1987) Temporal changes in the hydrography and chemistry of the Cariaco Trench. Deep-Sea Research, 34,945-963.

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ScHoyr F. and R. M. ~ r t , (1985) Florida Current: seasonal and interannual variability. Sc/ence, 227, 308-311. Tuit~g J. S. (1973) Buoyancy effec~/nflu/ds. Cambridge University Press, Cambridge, U.K., 367 pp. WALING. (1977) A theoretical framework for the description of estuaries. TeUus, 29, 128-136. Wr~ss R. F., J. L. BuzJ..Lvrr~,R. H. GAMMONand M. J. W ~ (1985) Atmospheric chlorofluoromethanes in the deep equatorial Atlantic. Nature, 314, 6/)8--610.

APPENDIX Description o f the convective plume ensemble used to produce Fig. 6

The model as used in this paper used free plume dynamics following TURNER (1973) and PETERSON (1979), closing the interior problem by invoking a combination of buoyancy input by geothermal heating (proportional to the gradient of basin area with depth) and of buoyancy diffusion with a prescribed constant diffusivity. The key to free plume dynamics is that the plume buoyancy must either accelerate entrained fluid, or the mass of the plume itself. In this respect the case. treated here is an unrealistic representation of convection along boundaries in rotating systems, where the Coriolis effect acting on contour-following flows plays a significant role, and the primary instability mechanisms on intensive currents are likely to be of the character of unstable waves (GRIFFrrHS, 1986). Still, it is felt that because much of the basic interaction between plume and interior buoyancy fluxes is kinematic in nature (as discussed in the main text, Section 4) the formalism for the plume dynamics used here is not crucial for the qualitative nature of the results. It has the advantage of allowing a direct comparison with the BAINES and TURNER (1969), PETERSON (1979) and KILLWORTHand TURNER (1982) cases. We assume self-similar plume dynamics, in the Boussinesq approximation, and define a local buoyancy anomaly for a plume as the difference between its specific buoyancy and that in the interior. Let the plume characteristics at any level be defined by a scale velocity, v, a linear dimension, l, and a density anomaly, b, relative to the interior buoyancy function which we shall call b ' . We now define new flux-oriented variables: a2vl2 = V, the volume flux; a2v2[z --- M, the momentum flux; and a3bvl2 = B, the local relative buoyancy flux, respectively, for an individual plume. Let the entrainment coefficient be E, such that V Z = Ely, then conservation of volume, momentum and buoyancy can be expressed by the following three equations: Vz = C t E M Irz"

(At)

MMz = C2BV

(A2)

B: .m -C3Vb~.

(A3)

ttere the coefficients are parameters which depend on assumptions about the self-similar structure adopted for the plumes, i.e. they are basically shape factors which can be absorbed into the variable scaling without loss of generality with regard to the forms of solutions available for the system. To close the system, whether dealing with a single plume or an ensemble in steady state, we use the condition of stationarity of the interior buoyancy distribution b*. Note that for realistic computations, where heat and salt are conservative quantities while buoyancy is not, budget equations for both must be carried, and the vertical stability function bz* be explicitly computed from the equation of state. If we now, as in the main text, identify the buoyancy flux with the heat flux, Q, and b* with the interior temperature, T, suitably scaled, equations (A 1, A2, A3) together with equation (6) form a system which can be integrated from the top downwards, given an upper boundary value for T, and for all the individual plume parameters. To produce Fig. 5, this was done with an implicit stepping scheme, using a 400 level vertical grid. Forty plume categories were specified, and the initial buoyancy flux was taken as proportional to the index number for the category. An additional degree of freedom is available, in that each category can be taken to represent several identical plumes, i.e. the frequency distribution of occurrence of each plume category must also be specified. For the example shown in Fig. 5, this was chosen as uniform.

Ventilation of the Cariaco Trench

225

The buoyancy flux balance is for slowly evolving mean density distributions easily generalized to accommodate mean density trends. This fact is central to the approaches of BAnqES and TURNER (1969) and of KIt~WORTH and TURNER (1982) and is approximately applicable independently to the deep water distribution of salinity and temperature in our case. This realization formed the basis for our parameterization of the shelf water input rate against depth as proportional to the local basin area. Finally, a comment on the complication of the buoyancy flux normalization for plumes with finite initial volume transport. The concept of a point source of pure buoyancy input is of course totally unphysical. A realizable plume source will have a finite volume of mass transport, as well as a characteristic initial buoyancy anomaly--the product of which defines the initial buoyancy flux. The appropriate reference density is that which is externally imposed at the upper basin boundary, since the deep interior basin density is in fact a dependent parameter of the problem. (There is thus an important distinction between the problem of analysing an individual plume event with a specified interior basin environment, and the problem of the long-term stationary state of the ventilation process.) In our case, the two ventilation types (A and B in the footnote to Table 3) specify a mean input rate of shelf water of less than 2% of the average input rate of the assumed sill source. This was done because we could a priori estimate the required input rates for these water types. Physical reasonableness was assured by assuming an initial potential density which would allow penetration of the sill source without dilution only about half way to the bottom of the basin. If, as suggested in the final discussion section, the shelf source is highly seasonal, maybe active only 10% of the year, then its mass flux intensity when active would be of order 20% of the sill source. Furthermore, a more diluted initial buoyancy flux will by equation (A3) (or equations 6-9 in Section 4) undergo a faster relative diminution since its decay rate is proportional to the volume flux. It is thus quite reasonable, physically, that a smaller mass flux with greater initial density anomaly could dominate the competition to reach the basin bottom.