1982 OCEAN SUBDUCTION show that hardly any commercial enhancement Finney B, Gregory-Eaves I, Sweetman J, Douglas MSV program can be regarded as clearly successful. and Smol JP (2000) Impacts of climatic change and Model simulations suggest, however, that stock- Rshing on PaciRc salmon over the past 300 years. enhancement may be possible if releases can be Science 290: 795}799. made that match closely the current ecological Giske J and Salvanes AGV (1999) A model for enhance- and environmental conditions. However, this ment potentials in open ecosystems. In: Howell BR, Moksness E and Svasand T (eds) Stock Enhancement requires improvements of assessment methods of and Sea Ranching. Blackwell Fishing, News Books. these factors beyond present knowledge. Marine Howell BR, Moksness E and Svasand T (1999) Stock systems tend to have strong nonlinear dynamics, Enhancement and Sea Ranching. Blackwell Fishing, and unless one is able to predict these dynamics News Books. over a relevant time horizon, release efforts are Kareiva P, Marvier M and McClure M (2000) Recovery not likely to increase the abundance of the target and management options for spring/summer chinnook population. salmon in the Columbia River basin. Science 290: 977}979. Mills D (1989) Ecology and Management of Atlantic See also Salmon. London: Chapman & Hall. Ricker WE (1981) Changes in the average size and Mariculture, Environmental, Economic and Social average age of PaciRc salmon. Canadian Journal of Impacts of. Salmonid Farming. Salmon Fisheries: Fisheries and Aquatic Science 38: 1636}1656. Atlantic; Paci\c. Salmonids. Salvanes AGV, Aksnes DL, FossaJH and Giske J (1995) Simulated carrying capacities of Rsh in Norwegian Further Reading fjords. Fisheries Oceanography 4(1): 17}32. Salvanes AGV, Aksnes DL and Giske J (1992) Ecosystem Asplin L, Salvanes AGV and Kristoffersen JB (1999) model for evaluating potential cod production in Non-local wind-driven fjord}coast advection and its a west Norwegian fjord. Marine Ecology Progress potential effect on pelagic organisms and Rsh recruit- Series 90: 9}22. ment. Fisheries Oceanography 8: 255}263. Salvanes AGV and Balino B (1998) Production and Rtness Blaxter JHS (2000) The enhancement of marine Rsh in a fjord cod population: an ecological and evolution- stocks. Advances in Marine Biology 38: 2}54. ary approach. Fisheries Research 37: 143}161. Coleman F, Travis J and Thistle AB (1998) Marine Stock Shelbourne JE (1964) The artiRcial propagation of marine Enhancement: A New Perspective. Bulletin of Marine Rsh. Advances in Marine Biology 2: 1}76. Science 62. Svasand T, Kristiansen TS, Pedersen T et al. (2000) The Danielssen DS, Howell BR and Moksness E (1994) An biological and economical basis of cod stock enhance- International Symposium on Sea Ranching of Cod and ment. Fish and Fisheries 1: 173}205. other Marine Fish Species. Aquaculture and Fisheries Thorpe JE (1980) Salmon Ranching. London: Academic Management 25(Suppl. 1). Press.
OCEAN SUBDUCTION
R. G. Williams, University of Liverpool, lithosphere slides beneath a more buoyant plate and Liverpool, UK into the hotter part of the mantle. Ventilation connects the atmosphere and ocean Copyright ^ 2001 Academic Press interior through the transfer of Suid from the doi:10.1006/rwos.2001.0109 surface mixed layer into the ocean interior. Water masses are formed in the surface mixed layer Introduction and acquire their characteristics through the ex- change of heat, moisture, and dissolved gases Ocean subduction involves the transfer of Suid from with the atmosphere. When the water masses are the mixed layer into the stratiRed thermocline transferred beneath the mixed layer, they are (Figure 1). The upper ocean is ventilated principally shielded from the atmosphere and only subsequently through the subduction process, while the deep modify their properties by mixing in the ocean ocean is ventilated through open-ocean convection interior. Hence, the ventilation process helps and cascading down coastal boundaries. The term to determine the relatively long memory of the ‘ocean subduction’ makes the geologicial analogy of ocean interior, compared with the surface mixed a subduction zone where a rigid plate of the Earth’s layer. OCEAN SUBDUCTION 1983
we Subduction Process Ekman layer The subduction process involves the seasonal cycle Mixed of the mixed layer (Figure 2). The mixed layer is layer vertically homogenous through the action of convec- S tive overturning and turbulent mixing. At the end of winter, the mixed layer is at its maximum density and thickness, and overlies the main thermocline Thermocline (where there is a strong vertical temperature gradi- ent). During spring and summer, the surface warm- ing forms a seasonal thermocline, which is capped Figure 1 A schematic diagram showing isopycnals in the thermocline outcropping into a vertically homogeneous mixed by a thin, wind-stirred, mixed layer. During autumn layer. The subduction rate, S, measures the rate at which the and winter, the cooling of the surface ocean leads stratified thermocline is ventilated through the vertical and hori- to a buoyancy loss and convective overturning. The zontal transfer of fluid from the mixed layer. In comparison, the mixed layer thickens and entrains Suid from the wind-induced, Ekman pumping, we, measures the vertical flux underlying thermocline until the cooling phase pumped down from the surface Ekman layer. (Reproduced with permission from Marshall et al. (1993).) ceases at the end of winter. Fluid is subducted from the mixed layer into the thermocline during the warming in spring and sum- Subduction occurs throughout the ocean over mer, whereas Suid is entrained into the mixed layer recirculating wind-driven gyres within ocean basins from the thermocline during the cooling in autumn (with horizontal scales of several thousand kilo- and winter. Whether there is annual subduction of meters), across frontal zones and convective, over- Suid into the thermocline depends on the buoyancy turning chimneys (on horizontal scales of several input into a water column. If there is a buoyancy hundred to tens of kilometers). The reverse of the input over an annual cycle (as depicted in Figure 2), subduction process leads to the transfer of Suid the mixed layer at the end of winter becomes lighter from the main thermocline into the seasonal bound- and thinner than at the end of the previous winter. ary layer, which affects the properties of the mixed In this case, Suid is subducted into the main or layer and air}sea interaction. permanent thermocline over the annual cycle.
Time
March, year 1September March, year 2 Mixed layer Mixed layer thickness
Seasonal thermocline
Depth
(March, year 2) Main/permanent m thermocline τ Sann year
m (March, year 1)
Figure 2 A schematic diagram illustrating the seasonal cycle of the mixed layer following the movement of a water column. The mixed layer thins in spring and summer, and thickens again in autumn and winter. If there is an overall buoyancy input, the end of winter mixed layer becomes lighter and thinner from one year to the next (as depicted here). Consequently, fluid is subducted irreversibly from the mixed layer into the main or permanent thermocline. The mixed layer thickness is marked by the thick dashed line, isopycnals m outcropping at the end of winter into the mixed layer by the full lines, and the isopycnal identifying the base of the seasonal thermocline by the short dashed line. The annual subduction rate, Sann , determines the vertical spacing between the isopycnals subducted from the mixed layer in March for consecutive years 1 and 2 (year is one year). 1984 OCEAN SUBDUCTION
Conversely, if there is a buoyancy loss over an (A) annual cycle, the mixed layer at the end of winter September outcrop becomes denser and thicker than at the end of the y previous winter. In this case, there is annual transfer of Suid from the main thermocline into the seasonal x boundary layer (deRned by the maximum thickness of the winter mixed layer).
\ Seasonal Recti cation March outcrop The subduction process leads to an asymmetrical coupling between the mixed layer and main thermo- (B) cline. For example, the temperature and salinity relation in the main thermocline is observed to March position September position match that of the winter mixed layer, rather than z of isopycnal of isopycnal the annual average of the mixed layer. This biased y coupling is due to the seasonal cycle of the mixed layer. Isopycnals in the mixed layer (density out- crops) migrate poleward in the heating seasons and Seasonal Main boundary retreat equatorward in the cooling seasons. This thermocline seasonal displacement of density outcrops is much Interface S greater than the movement of uid particles over an Figure 3 A schematic diagram illustrating the seasonal rectifi- annual cycle. Consequently, Suid subducted from cation of subduction for (A) a plan view at the sea surface and the mixed layer in summer is reentrained into the (B) a meridional section. Over the cooling season in the North- mixed layer during the subsequent cooling seasons ern Hemisphere, the outcrop of a density surface migrates (Figure 3) (through the equatorial migration of equatorward from September to March (denoted by dashed and full lines). Consider a fluid parcel (circle) subducted from the density outcrops and winter thickening of the mixed vertically homogeneous mixed layer and advected equatorwards layer). Fluid only succeeds in being permanently along this density surface. If the fluid parcel is advected past subducted into the main thermocline over a short the March outcrop during the year, then it is subducted in to window, one to two months long, at the end of the main thermocline (the upper extent of which is shown by winter when the density outcrops are at the the dotted line), otherwise it is eventually entrained into the mixed layer. (Reproduced with permission from Williams et al. equatorial end of their cycle. Hence, there is a sea- (1995).) sonal rectiRcation in the transfer of water-mass properties from the mixed layer into the ocean in- terior. Idealized tracer experiments suggest that the De\nitions of Subduction Rate seasonal rectiRcation still occurs even in the pres- ence of a vibrant, time-varying circulation. The instantaneous subduction rate, S, the volume Sux from the mixed layer into the stratiRed thermo- Formation of Mode Waters cline is given by eqn [1]. There are local maxima in the subduction and R ventilation processes leading to the formation of "! h! ! ,! !Dbh S wb ub. h wb [1] characteristic ‘mode’ waters, which are apparent in Rt Dt a volumetric census of the temperature and salinity characteristics of the ocean. These mode waters S is deRned as positive when Suid is transferred into consist of large volumes of weakly stratiRed Suid the thermocline (Figure 4); h is the thickness of the with nearly vertically homogeneous properties. For mixed layer, wb and ub are the vertical velocity and example, strong buoyancy loss to the atmosphere horizontal velocity vector, respectively, at the base ,R R # over the Gulf Stream leads to the formation of of the mixed layer, and Db /Dt / t ub. is the 183C mode water within the mixed layer, which Lagrangian rate of change following the horizontal is subducted following a buoyancy input along the Sow at the base of the mixed layer. The subduction anticyclonic circulation south of the Gulf Stream. rate is deRned as the volume Sux per unit horizontal Signals of mode water formation over the North area in [1] relative to the base of the instantaneous Atlantic are revealed in diagnostics of water-mass mixed layer. Hence, S includes a contribution from formation from surface buoyancy Suxes, which are the change in thickness of the mixed layer, as well shown later in Figure 11. as from the vertical and horizontal movement of OCEAN SUBDUCTION 1985
t stratiRcation (and a large vertical spacing between subducted isopycnals).
Gyre-scale Subduction Subduction occurs over ocean basins predominantly through the gyre-scale circulation. The surface h(t ) Dh wind-stress drives anticyclonic and cyclonic recircu- ∆t Dt lations, referred to as subtropical and subpolar gyres, respectively, within a basin. The wind forcing S(t) ∆t induces downwelling of surface Suid over the sub- ∆ b t tropical gyre and upwelling over the subpolar gyre. The gyre-scale subduction rate deRned in eqn [2] depends on both the vertical and horizontal circula- tions together with the thickness of the end of Figure 4 A schematic diagram showing a particle being winter mixed layer. subducted from the time-varying base of the mixed layer into the thermocline. The vertical distance between the particle and Subduction Rate over the North Atlantic the mixed layer, S(t) t, is the sum of the vertical displacement The North Atlantic is the most actively ventilated of the particle,!wb t, and the shallowing of the mixed layer following the particle,!(Dh/Dt ) t; where h is the thickness of oceanic basin. The wind-induced downwelling \1 the mixed layer, wb is the vertical velocity and t is a time reaches magnitudes of 25}50 m y over the interval. (Reproduced with permission from Marshall et al. North Atlantic (Figure 5A), which is charac- (1993).) teristic of most basins. However, the annual sub- duction rate is signiRcantly enhanced over the vertical transfer through the lateral transfer Suid particles. Equivalently, S in eqn [1] can be across the sloping base of the mixed layer. evaluated from the vertical velocity and the Lagran- The surface buoyancy loss to the atmosphere leads gian change in mixed-layer thickness following the to the winter mixed layer thickening poleward, horizontal circulation. from typically 50 m in the subtropics (e.g., at 203N) The subduction into the main thermocline is to 500 m or more in the subpolar gyre (e.g., at physically more important than that into the 503N). seasonal thermocline, since water-mass proper- Over the subtropical gyre, the annual subduc- ties become shielded from the atmosphere for tion rate reaches between 50 m y\1 and 100 m y\1 longer timescales within the main thermocline. (Figure 5B). South of the Gulf Stream, there is The annual rate of subduction into the main a band of high subduction rates that are controlled S thermocline, Sann, is evaluated from the volume ux by the lateral transfer. Elsewhere, the vertical and per unit horizontal area passing through a control horizontal transfers are comparable over the sub- surface H that overlies the main thermocline tropical gyre. (eqn [2]). Over the subpolar gyre, Suid is generally transfer- red from the main thermocline into the seasonal "! ! Sann wH uH . H [2] boundary layer. Fluid is eventually returned from the seasonal boundary layer and into the in- wH and uH are the vertical velocity and horizontal terior through deep convection events or through velocity vector at the depth H. The control surface subduction along the western boundary of the is deRned by the base of the seasonal thermocline subpolar gyre. The negative subduction rates given by the maximum thickness of the winter reach several 100 m y\1 over the North Atlantic mixed layer (Figure 1). (Figure 5B), which is controlled by the lateral
Alternatively, Sann may be evaluated directly from transfer rather than the vertical transfer. This nega- S in eqn [1] using a Lagrangian integration follow- tive subduction leads to water-mass properties of ing the movement of a water column over an annual the main thermocline being transferred or inducted cycle. For example, for the mixed-layer cycle shown into the downstream winter mixed layer. This in Figure 2, Sann controls the vertical spacing be- induction process is particularly important for the tween isopycnals subducted at the end of consecut- biogeochemistry in transferring inorganic nutrients ive winters. Hence, a high rate of subduction leads from the thermocline into the winter mixed layer. to the formation of a mode water with a weak These nutrients are entrained into the euphotic zone 1986 OCEAN SUBDUCTION
_ 50 W W ˚ W W W E ˚ ˚ ˚ ˚ ˚ 60 50 ˚ _ 80 60 40 20 0 20 _ 25 70˚N 100 70˚N 0 60˚N 60˚N 50˚N 50˚N 25 40 50 40˚N 3 1 40˚N ˚N 3 2 30˚N 4 30 N 5 ˚ 6 20 N 20 N ˚ 7 ˚ 10 N 10 N 20 50 ˚ ˚ 80˚W60˚W40˚W20˚W0˚ 0 0 0˚ ˚ _ 25 (A) 100 W80W60W40W20W200 E 25 _ 50 ˚ ˚ ˚ ˚ ˚ ˚ ˚ (A)
W W ˚ W W W E ˚ ˚ ˚ ˚ ˚ 80 20 ˚ 60 _ 100 60 40 0 20 050 200 70 N 70 N _ ˚ ˚ 100 60˚N 60˚N _ 0 _ 50 50 N 200 0 ˚ 50˚N 2 40˚N 40˚N 40 100 50 N _ 100 30 N 8 ˚ ˚ 10 30˚N 20˚N 20 N 8 ˚ 10˚N 10˚N 20 50 0˚ 0˚ 0 _0 (B) 100 W80W60W40W20W200 E 50 50 ˚ ˚ ˚ ˚ ˚ ˚ ˚ _100 Figure 6 Observations of the tritium}helium age (years) on " " 80 40 0 potential density surfaces F 26.5 (A) and F 26.75 (B) in the North Atlantic. These surfaces are ventilated from the north (B) W ˚ east and the tritium}helium age increases following the anticyc- Figure 5 Diagnostics for (A) wind-driven Ekman downwelling lonic circulation of the subtropical gyre. (Reproduced with per- velocity (contours every 25 m y\1) and (B) annual subduction mission from Jenkins WJ (1988) The use of anthropogenic rate into the main thermocline of the North Atlantic (contours tritium and helium-3 to study subtropical gyre ventilation and every 50 m y\1). The annual subduction rate is evaluated circulation. Philosophical Transactions of the Royal Society of London A 325, 43}61.) from SH"!wH!uH. H with the interface H defined from the mixed-layer thickness at the end of winter, uH evalu- ated from a density climatology using thermal-wind balance, and wH derived from the wind-stress climatology and linear density surfaces reveals the general ventilation of the vorticity balance. The subduction rate represents the volume subtropical gyre from the north east and gradual flux per unit horizontal area which ventilates the stratified aging following the anticyclonic circulation (Figure thermocline. (Reproduced with permission from Marshall et al. 6). The invasion of transient tracers into the main (1993).) thermocline provides an integrated measure of ventilation including the contribution of the time- and enable high values of biological production to mean circulation and the rectiRed contribution occur. of eddies. For example, the rate of ventilation inferred from the tracer age distribution is two to Evidence from Transient Tracers three times greater than the rate of wind-induced Characteristic signals of subduction and ventilation (Ekman) downwelling, which is possibly consis- are provided by distributions of transient tracers, tent with the gyre-scale subduction rate diagnostics such as tritium and CFCs (chloroSurocarbons), over in Figure 5. However, the rate of ventilation the ocean interior. Quantitative information on inferred from inSux of tracers also includes a dif- the ventilation process is provided when the transi- fusive contribution, which differs for different ent tracers have a known source function and life- tracers, making a more exact comparison with the time. For example, in the North Atlantic, the subduction rate based on volume Suxes difRcult tritium}helium age distribution along potential to achieve. OCEAN SUBDUCTION 1987
Subduction and the Main W Thermocline 90˚ 80˚ 70˚ 60˚ 50˚ 40˚ 30˚ 20˚ 10˚ 0˚ 65˚ Formation of the Main Thermocline 60˚ Throughout the ocean there is a persistent thermo- cline separating the mixed layer and the weakly stratiRed deep ocean. In ideal thermocline theory, 50˚ the subduction process forms an upper thermocline over the subtropical gyre. The wind-driven circula- 200 200 N 200 tion drives downwelling over a subtropical gyre, 40˚ 100 S which leads to uid being subducted from the mixed 40 layer into the adiabatic interior of the ocean * see 30˚ 10 20 30 the seminal work of Luyten et al. (1983) listed in 40 the Further Reading section. 20˚ The thermocline is an advective feature formed 30 through the circulation tilting the horizontal con- 20 20 10˚ 40 trast in surface density over the subtropical gyre 0 1 _1 into the vertical. The subducted thermocline extends (A) 0˚ cm s over the mixed-layer density range within the sub- tropical gyre. However, observations reveal that the 65˚ thermocline also extends over denser isopycnals that do not outcrop within the subtropical gyre. Thermo- 60˚ cline models incorporating diffusion suggest that this denser thermocline may be formed through the vertical convergence of downwelling of subtropical 50 Suid and upwelling of denser Suid originating from ˚ 100 outside the subtropical gyre, such as from the sub- 50 30 50 polar gyre or Southern Ocean. N 40 ˚ 20 10 15 Dynamical Tracer Distributions 30˚ 10 The subduction process helps to determine the stratiRcation within the main thermocline, and 20˚ hence the distribution of a dynamic tracer, the 10 10 potential vorticity. Fluid parcels conserve potential 10˚ 5 vorticity for adiabatic, inviscid Sow. Potential 0 1 cm s_1 vorticity depends on the absolute spin of the (B) 0˚ Suid and stratiRcation. A large-scale estimate of potential vorticity is provided by eqn [3] where Figure 7 Diagnosed distribution of a dynamic tracer, potential vorticity Q (10\11 m\1 s\1), over the North Atlantic. (A) Between f"2 sin is the Coriolis parameter or planetary " the potential density F 26.3 and 26.5 surfaces, the Q vorticity, is the Earth’s angular velocity, is the contours appear to be closed in the north-west Atlantic, or latitude, is a potential density and is a reference to be open and thread back to the winter outcrop (shaded area) " density. in the north-east Atlantic. (B) Between the F 26.5 and 27.0 surfaces, the Q field appears to be relatively homo- geneous south of the winter outcrop over most of the subtropical f R Q"! [3] gyre. (Reproduced with permission from McDowell et al. Rz (1982).)
Climatological maps of large-scale potential vortic- ity over the main thermocline reveal different regions of nearly uniform Q (Figure 7B). The regimes consisting of open, closed, or blocked blocked contours run zonally from coast to coast Q contours along potential density surfaces (Figure and are usually associated with weak meridional 7). The open Q contours thread from the stratiRed Sow unless directly forced. The open Q contours interior to the mixed-layer outcrop at the end of dominate for lighter surfaces, whereas the closed winter (Figure 7A). Conversely, closed Q contours or blocked Q contours dominate for denser do not intersect the mixed layer and usually contain surfaces. 1988 OCEAN SUBDUCTION
Competing Paradigms: Gyre-scale Subduction versus Eddy Stirring 40 Different hypotheses involving gyre-scale subduction or eddy stirring have been invoked to explain these 0.15 contrasting tracer distributions seen in the data. 0.13 Open tracer contours (such as in Figure 7A) are 30 usually associated with gyre-scale subduction. Fluid is subducted from the end of winter mixed layer Latitude (degree) and, when the Sow is adiabatic and inviscid, stream- 0.20 lines become coincident with Q contours in the 0.25 thermocline. A thermocline model example is shown 20 in Figure 8, where Q along potential density sur- 0.30 0.50 faces in the thermocline is determined by subduction 0.30 _ _ _ _ _ from the overlying mixed layer. The isopleths of 60 50 40 30 20 Q reveal the anticyclonic circulation of the subtropi- (A) Longitude (degree) cal gyre. The Q contrast in the thermocline can become small given realistic end of winter mixed- layer variations. In an ideal thermocline model, each potential density surface can be separated into a 40 ventilated zone, which divides unventilated regions of a western pool and an eastern shadow zone. The unventilated zones are not directly connected by the 0.13 time-mean streamlines to the overlying mixed layer, although they may still be indirectly ventilated 30 through mixing acting along the coastal boundaries. Latitude (degree) The ventilated zone extends over most of the sub- tropical gyre for light potential density surfaces, but contracts eastwards for denser surfaces. 20 0.15 0.18 Nearly uniform tracer distributions (such as in 0.15 0.10 Figure 7B) are instead usually associated with stirring by mesoscale eddies. The eddy stirring can _60 _50 _40 _30 _20 homogenize conserved tracers within closed stream- (B) Longitude (degree) lines. An eddy-resolving model example is shown in Figure 8 An ideal thermocline model solution for the dynamic Figure 9 for a pair of wind-driven gyres. Advection \9 \1 \1 " tracer, potential vorticity Q (10 m s ), along (A) F 26.4 by the gyre circulation leads to tracer contours and " surface and (B) the F 26.75 surface. Fluid is subducted streamlines becoming nearly coincident and closed across the density outcrop in the mixed layer (thick dashed line) over much of the interior domain. Eddy stirring into the stratified thermocline within a ventilated zone (between transfers tracer down-gradient within these closed the thin dashed lines). Streamlines are coincident with the contours, which forms extensive regions of nearly potential vorticity contours in the adiabatic interior. Given appro- priate mixed-layer variations, the subducted potential vorticity uniform tracer. This interpretation is supported can become nearly uniform, as obtained in (B). These model through observations of nearly uniform distributions solutions are for an imposed anticyclonic wind forcing and of tritium, as well as potential vorticity, along a mixed layer, which becomes thicker to the north and denser to weakly ventilated potential density surfaces within the north and east. (Reproduced with permission from Williams the wind-driven gyres of the North PaciRc and (1991).) North Atlantic. Gyre-scale subduction and eddy stirring are not and Soat trajectories suggest that the implied Peclet mutually exclusive processes, and can occur simulta- number (a nondimensional measure of advection/ neously and modify each other (as revealed in diffusion) is typically less than 10. This value is general circulation model experiments). Ventilation much smaller than the high value expected from helps control the input of tracer and the tracer nondiffusive, ideal thermocline models. Hence, eddy contrast along the winter outcrop of the potential diffusion appears to be signiRcant along potential density surface, while eddies act to smear out sub- density surfaces throughout a basin and is parti- ducted mode waters and tracer contrasts in the cularly important in regions of weak background ocean interior. Diagnostics from transient tracers Sow. OCEAN SUBDUCTION 1989
120 The Relationship between Subduction, 120 Potential Vorticity and Buoyancy Forcing 120 100 Local, kinematic connection The relationship 100 100 between subduction rate, the mixed-layer evolution, and underlying potential vorticity is illustrated here.
100 For a particle subducted from the mixed layer into the underlying thermocline (with a continuous match in potential density as depicted in Figure 2), the subduction rate [1] and potential vorticity [3] are kinematically related as in eqn [4].
f D Q"! b m [4] S Dt 80
80 where Db m/Dt is the Lagrangian change in mixed- 80 80 layer potential density, m, following the velocity
80 ub at the base of the mixed layer, which is usually (A) taken to be a geostrophic streamline. Hence, Q in the thermocline is diagnostically related to the evolution of the mixed-layer density following the horizontal Sow and the subduction rate * see Figure 8 for an example of the resulting Q solution
100 100 for an ideal thermocline model of a subtropical 100 100 100 gyre. Alternatively, eqn [4] can be rearranged to high- 100 light how subduction occurs only when the mixed- 100
100 layer density becomes lighter following a geo- strophic streamline (eqn [5]).
f D S"! b m [5] Q Dt
' ( where S 0 occurs when Db m /Dt 0. This rela- tion reSects how subduction relies on Suid being capped by a lighter mixed layer and hence transfer- red into the thermocline (Figure 2). For gyre-scale subduction, the required buoyancy input can be pro- (B) vided by an annual average of a surface buoyancy Figure 9 An eddy-resolving, three-layer model solution for the Sux or a convergent Ekman Sux of buoyancy; the dynamic tracer, potential vorticity, for a double wind-driven gyre latter contribution dominates in climatological diag- over a rectangular basin: plan views of (A) climatological mean nostics over the subtropical gyre of the North Atlan- and (B) instantaneous potential vorticity for the intermediate layer. The wind forcing drives a pair of wind gyres antisymmetri- tic (as implied from buoyancy diagnostics associated cally about the middle latitude, which are unstable, generating with Figure 5). a vigorous mesoscale eddy circulation. The eddy stirring leads However, these kinematic relations [4] and [5] to the time-averaged potential vorticity (in (A)) becoming nearly cease to be useful in a time-averaged limit in the uniform within the circulating gyres, while outside the gyres presence of an active eddy circulation owing to there is a poleward increase arising from the meridional gradient R R in planetary vorticity. The instantaneous potential vorticity (in the dif culty in de ning an appropriate stream- (B)) shows nearly perfect homogenization within the pair of line. The Lagrangian change in mixed layer density, gyres. At the edges of the gyre, the eddy activity is apparent Db m/Dt, might even vanish following the through the winding up of potential vorticity contours. An experi- time-mean geostrophic streamline and provide a ment by W. Holland. (Reproduced from Rhines PB and Young misleading result from [5]. Instead, the role of the WR (1982) Homogenization of potential vorticity in planetary gyres. Journal of Fluid Mechanics 122: 347}367, with per- time-varying circulation in subduction and an integ- mission from Cambridge University Press.) rated view of the buoyancy forcing need to be considered. 1990 OCEAN SUBDUCTION
Integral connection An integral view of the STMW SPMW )
1 10 ventilation process may be obtained by considering _ s the conversion of water masses within a basin or 3 m
6 5 restricted domain (Figure 10). Buoyancy Suxes at M the sea surface and diffusive Suxes within the ocean lead to water masses being transformed from one 0 density class to another. The convergence of this ME diapycnal volume Sux, or water-mass transforma- _5 tion, deRnes the rate of water-mass formation Mass source (10 26.0 26.4 26.8 27.2 27.6 28.0 _ within a particular density class. In the limit of no Density (kg m 3) diffusive Suxes within the ocean, the rate of water- Figure 11 Diagnosed water-mass formation (106 m3 s\1) mass formation rate is equivalent to the area-integ- versus density (kg m\3) evaluated from climatological surface rated subduction rate over the particular density buoyancy fluxes (full line) and from Ekman pumping (dashed class into the main thermocline (Figure 10); this line) over the North Atlantic. The left-hand peak is centered near the density of subtropical mode water (STMW) and the right- connection is exploited for the later example of hand peak spans subpolar mode water (SPMW) and Labrador a convective chimney in Figure 13. Sea Water densities. (Reproduced with permission from Speer The contribution of surface buoyancy Suxes to K and Tziperman E (1992). Rates of water mass formation the rate of water-mass formation has been estimated in the North Atlantic. Journal of Physical Oceanography 22: from climatological air}sea Suxes. While there are 93}104.) signiRcant errors in the air}sea Suxes, the diagnos- tics reveal how the buoyancy forcing and subduc- and diffusing the downstream properties of sub- tion process leads to the preferential formation of ducted Suid. Eddies lead to an effective stirring of distinct mode waters in the North Atlantic (Figure water-mass properties along isopycnals. This pro- 11), rather than creating similar rates of formation cess can lead to subducted mode waters becoming for all densities. rapidly smeared out, such that the downstream water-mass properties reSect an average of the up- Role of Eddies and Fronts stream characteristics determined in the mixed layer at the end of winter. Mesoscale eddies can directly assist in the subduc- tion process through modifying the subduction rate Eddy-induced Transport and Subduction Eddies provide a volume Sux and transport of Buoyancy tracers, which can modify the subduction rate. The fluxes eddy-driven transport, u z, is given by the tem- poral correlation in velocity and thickness of an isopycnal layer, z; the overbar represents a time Transformation average over several eddy lifetimes and the primes Diffusive represent a deviation from the time average. An fluxes example of an eddy-driven transport is shown in Figure 12A, where the oscillating velocity leads to an eddy-driven transport through the volume Sux in Control surface Subduction the thick ‘blobs’ of Suid being greater than the return Sux in the thin ‘blobs’ of Suid. An eddy- induced transport velocity or ‘bolus’ velocity within Figure 10 A schematic diagram of the upper ocean showing an isopycnic layer is deRned by uH"u z/ z. The the sea surface, two outcropping isopycnals, and a fixed control eddy ‘bolus’ velocity is particularly large in regions surface across which subduction is monitored. Buoyancy fluxes of baroclinic instability, where the transport is at the sea surface and diffusive fluxes in the interior transform S water masses from one density class to another. If there are no generated through the attening of isopycnals diffusive fluxes in the interior, the convergence of the trans- (Figure 12B). formation flux controls the subduction flux across the control Evaluating the instantaneous subduction rate [1] surface (which is chosen to be the interface between the base in the presence of eddies is difRcult, since time- of the end of winter mixed layer and the main thermocline). averaged correlations in velocity with mixed-layer (Reproduced from Marshall J, Jamous D and Nilsson J (1999) Reconciling thermodynamic and dynamic methods of computa- thickness and velocity with mixed-layer outcrop tion of water-mass transformation rates. Deep-Sea Research area are required. However, the subduction rate I 46: 545}572. ^ 1999, with permission from Elsevier Science.) into the main thermocline and across the control OCEAN SUBDUCTION 1991
inates over the eddy ‘bolus’ contribution, since the wind forcing drives an anticyclonic circulation v ∆z across contours of mixed-layer thickness. However, the eddy contribution to subduction becomes crucial throughout the Southern Ocean, as well as (A) across separated boundary currents and inter-gyre boundaries.
Subduction Associated with Fronts and Convective Chimneys ∗ Subduction and ventilation occurs over Rne scales v associated with narrow fronts and convective chim- neys, as well as over the larger-scale circulation. Secondary circulations develop across a front fol- lowing the instability of the front and acceleration of the along stream Sow. Frontal modeling studies demonstrate how this secondary circulation leads to frontal-scale subduction, which injects low stratiR- ∗ cation into the thermocline. Observational studies z v have identiRed upwelling and downwelling zones on either side of a narrow front (10 km wide) with vertical velocities reaching 40 m d\1, which is (B) y much greater than the background, wind-driven, Figure 12 A schematic diagram illustrating the concept of downwelling velocity. Indirect support for frontal- the eddy rectified transport and ‘bolus’ velocity. (A) The time- scale subduction is also provided by separate averaged meridional volume flux in an undulating layer, v z" observations of bands of short-lived chlorophyll v z#v z, depends on advection by the time-mean meridional penetrating downward for several hundreds of me- velocity v and the time-averaged correlations in the temporal ters into the stratiRed thermocline on the horizontal deviations in velocity v and thickness of an isopycnal layer z. scale of 10 km; this frontal-scale process is also The time-averaged volume flux is directed to the right as drawn R here, since v'0 correlates with large layer thickness, while identi ed as being important in the atmosphere in v'0 correlates with small layer thickness. (B) The slumping of transferring ozone-rich, stratospheric air into the isopycnals in baroclinic instability induces a secondary circula- troposphere tion in which the bolus velocity, vH"v z/ z, is poleward in An example of Rne-scale subduction associated the upper layer and equatorward in the lower layer. Eddy-driven with a convective chimney is shown in Figure 13. subduction is likely to occur in baroclinic zones where there are strongly inclined isopycnals. (Reproduced with permission from Buoyancy loss to the atmosphere drives the conver- Lee M-M, Marshall DP and Williams RG (1997) On the eddy sion of light to dense water within the mixed layer transfer of tracers: advective or diffusive? Journal of Marine and the concomitant thickening of the mixed layer. Research 55, 483}505.) Baroclinic instability of the chimney leads to an eddy-driven transport, which Suxes light Suid into the chimney at the surface and, in turn, subducts surface, H, can be evaluated, in principle, by includ- denser Suid into the thermocline. Hence, the eddy- ing the eddy-induced ‘bolus’ velocity in eqn [2] to driven transport enables recently ventilated dense give eqn [6]. waters to disperse away from a convective chimney. The eddy-driven inSux of light Suid partly offsets S "!(w #wH)!(u #uH). H [6] ann H H the buoyancy loss to the atmosphere and can inhibit further mixed-layer deepening over the center of the The vertical eddy-transport contribution, wH, is ob- chimney. tained from uH through continuity. Hence, the an- nual subduction rate includes contributions from the time-mean and time-varying circulation. The eddy Conclusions contribution to subduction is expected to be large wherever the bolus velocity is signiRcant, such as in The subduction process controls the rate at baroclinic zones with strongly sloping isopycnals. which the upper thermocline is ventilated, as well Over a subtropical gyre, the subduction contribu- as determining the water-mass structure and stratiR- tion from the time-mean circulation probably dom- cation of the upper ocean. Subduction leads to an 1992 OCEAN SUBDUCTION
of the mixed layer and the difRculty in estimating _2 100 W m _ B in the eddy transport contributions. An additional _ (B in + Beddy) challenge is to determine the role that subduction 0 plays in climate variability, particularly how sub- duction communicates atmospheric variability to the _ B eddy ocean interior.
_ 27.80 1.5 Sv Glossary _0.1 Sv S 0.1 Sv Ventilation The transfer of uid from the mixed 0.2 Sv layer into the ocean interior. 2500m Subduction The transfer of Suid from the mixed 27.85 0.3 Sv layer into the stratiRed thermocline. ∗ 0.4 Sv u 0.4 Sv Subduction rate The volume Sux per unit horizontal 0.2 Sv area passing from the mixed layer into the strat- iRed thermocline. 27.90 Thermocline A region of enhanced vertical tem- 200km perature gradient over the upper 1 km of the ocean. Figure 13 A model solution for the eddy-driven subduction Seasonal boundary layer A region over which the rate and volume fluxes into and out of a convective chimney mixed layer and seasonal thermocline occur. (shaded) with isopycnals depicted by solid lines. Baroclinic R instability of the chimney leads to an eddy-driven circulation. The base of the seasonal boundary layer is de ned There is entrainment of warm, buoyant fluid over the upper by the maximum thickness of the winter mixed kilometer with subduction of cold, dense fluid at greater depths layer. I the net subduction of deep water is 1.6 Sv (1 Sv" Potential vorticity A dynamical tracer, conserved by 6 3 \1 10 m s ). The subduction rate is determined by the buoyancy Suid in adiabatic and inviscid Sow, which is de- forcing, B #B , where B is the surface buoyancy loss to in eddy in termined by the absolute spin of the Suid and the the atmosphere and Beddy is the eddy flux of buoyancy within the mixed layer. (Reproduced with permission from Marshall DP stratiRcation. (1997).) Sverdrup 1Sv"106 m3 s\1. asymmetrical coupling between the mixed layer and See also ocean interior. Fluid is transferred into the perma- Deep Convection. Ekman Transport and Pumping. nent thermocline in late winter and early spring, Mesoscale Eddies. Open Ocean Convection. Over- rather than throughout the year. This transfer ]ows and Cascades. Thermohaline Circulation. of Suid into the permanent thermocline helps to Upper Ocean Mixing Processes. Upper Ocean determine the relatively long memory of the Vertical Structure. Water Types and Water ocean interior, compared with that of the surface Masses. Wind and Buoyancy-forced Upper Ocean. mixed layer. Conversely, the reverse of the sub- Wind Driven Circulation. duction process is also important. The induction of thermocline Suid into the seasonal boundary layer affects the downstream water-mass properties of Further Reading the mixed layer, and hence alters the air}sea Cox MD (1985) An eddy-resolving model of the venti- interaction and biogeochemistry. For example, lated thermocline. Journal of Physical Oceanography, biological production is enhanced wherever 15: 1312}1324. nutrients are vertically and laterally Suxed from Cushman-Roisin B (1987) Dynamics of the Oceanic the thermocline into the mixed layer and the Surface Mixed-Layer. Hawaii Institute of Geophysical euphotic zone. Special Publications, Muller P and Henderson D (eds), } Subduction can occur over a range of scales pp. 181 196. Jenkins WJ (1987) 3H and 3He in the Beta triangle: extending over fronts, meoscale eddies, and gyres. observations of gyre ventilation and oxygen util- A major challenge is to identify the relative import- ization rates. Journal of Physical Oceanography ance of the frontal, eddy, and gyre contributions to 17: 763}783. subduction. Reliable estimates of subduction rate Luyten JR, Pedlosky J and Stommel H (1983) The venti- are difRcult to achieve owing to the spatial and lated thermocline. Journal of Physical Oceanography temporal variability in the circulation and thickness 13: 292}309. OCEAN THERMAL ENERGY CONVERSION (OTEC) 1993
Marshall DP (1997) Subduction of water masses in an Rhines PB and Schopp R (1991) The wind-driven circula- eddying ocean. Journal of Marine Research 55: tion: quasi-geostrophic simulations and theory for non- 201}222. symmetric winds. Journal of Physical Oceanography Marshall JC, Nurser AJG and Williams RG (1993). 21: 1438}1469. Inferring the subduction rate and period over the Samelson RM and Vallis GK (1997) Large-scale circula- North Atlantic. Journal of Physical Oceanography tion with small diapycnal diffusion: the two-thermo- 23: 1315}1329. cline limit. Journal of Marine Research 55: 223}275. McDowell S, Rhines PB and Keffer T (1982) North Atlan- Stommel H (1979) Determination of watermass properties tic potential vorticity and its relation to the general of water pumped down from the Ekman layer to the circulation. Journal of Physical Oceanography 12: geostrophic Sow below. Proceedings of the National 1417}1436. Academy of Sciences of the USA 76: 3051}3055. Pedlosky J (1996) Ocean Circulation Theory. New York: Williams RG (1991) The role of the mixed layer in setting Springer. the potential vorticity of the main thermocline. Journal Pollard RT and Regier LA (1992) Vorticity and vertical of Physical Oceanography 21: 1803}1814. circulation at an ocean front. Journal of Physical Williams RG, Spall MA and Marshall JC (1995) Does Oceanography 22: 609}625. Stommel’s mixed-layer ‘Demon’ work? Journal of Price JF (2001) Subduction. In: Ocean Circulation and Physical Oceanography 25: 3089}3102. Climate: Observing and Modelling the Global Ocean, Woods JD and Barkmann W (1986) A Lagrangian mixed G. Siedler, J. Church and J. Gould (eds), Academic layer model of Atlantic 183C water formation. Nature Press, pp. 357d371. 319: 574}576.
OCEAN THERMAL ENERGY CONVERSION (OTEC)
S. M. Masutani and P. K. Takahashi, are very high because large pipelines and heat ex- University of Hawaii at Manoa, Honolulu, HI, USA changers are needed to produce relatively modest R Copyright ^ 2001 Academic Press amounts of electricity. These high xed costs dom- inate the economics of OTEC to the extent that it doi:10.1006/rwos.2001.0031 currently cannot compete with conventional power systems, except in limited niche markets. Consider- Ocean thermal energy conversion (OTEC) generates able effort has been expended over the past two electricity indirectly from solar energy by harnessing decades to develop OTEC by-products, such as fresh the temperature difference between the sun-warmed water, air conditioning, and mariculture, that could surface of tropical oceans and the colder deep offset the cost penalty of electricity generation. waters. A signiRcant fraction of solar radiation inci- dent on the ocean is retained by seawater in tropical State of the Technology regions, resulting in average year-round surface tem- peratures of about 283C. Deep, cold water, mean- OTEC power systems operate as cyclic heat engines. while, forms at higher latitudes and descends to They receive thermal energy through heat transfer Sow along the seaSoor toward the equator. The from surface sea water warmed by the sun, and warm surface layer, which extends to depths of transform a portion of this energy to electrical about 100}200m, is separated from the deep cold power. The Second Law of Thermodynamics pre- water by a thermocline. The temperature difference, cludes the complete conversion of thermal energy in T, between the surface and thousand-meter depth to electricity. A portion of the heat extracted from ranges from 10 to 253C, with larger differences the warm sea water must be rejected to a colder occurring in equatorial and tropical waters, as de- thermal sink. The thermal sink employed by OTEC picted in Figure 1. T establishes the limits of the systems is sea water drawn from the ocean depths performance of OTEC power cycles; the rule-of- by means of a submerged pipeline. A steady-state thumb is that a differential of about 203C is neces- control volume energy analysis yields the result that sary to sustain viable operation of an OTEC facility. net electrical power produced by the engine must Since OTEC exploits renewable solar energy, equal the difference between the rates of heat trans- recurring costs to generate electrical power are fer from the warm surface water and to the cold minimal. However, the Rxed or capital costs of deep water. The limiting (i.e., maximum) theoretical OTEC systems per kilowatt of generating capacity Carnot energy conversion efRciency of a cyclic heat