Journalof MarineResearch, 58, 547–569, 2000

Recipe forBanda Sea water byJorina M. Waworuntu 1,RanaA. Fine 1,DonaldB. Olson 1 andArnold L. Gordon 2

ABSTRACT Waterfrom the western PaciŽ c owsthrough the Indonesian Seas following different pathways andis modiŽed by various processes to form the uniquely characterized isohaline Banda Sea W ater. Theprocesses contributing to the isohaline structure are studied using data from three ARLINDO cruisesin 1993, 1994, and 1996. An inverse-model analysis using salinity and CFC-11data is applied toaverticalsection along the main path of  ow,from the Makassar Strait to the Flores Sea and Banda Sea.The model reproduces the seasonal and interannual variability of the through ow andshows reversalsof owinthevertical structure. The model solutions suggest strong baroclinic  owsduring thesoutheast monsoon of 1993 and 1996 and a small,more barotropic  owduring the northwest monsoonof 1994. The isohaline structure can be accounted for by isopycnal mixing of different sourcewaters and by vertical exchanges, which are signiŽ cant in this region. A downward ux equivalentto a downwellingvelocity of 5 3 102 7 m/sisestimated for the section. The total balance alsosuggests that seasonally and possibly interannually variable back ushing of water from the BandaSea into the Straits contribute to the isohaline structure of BandaSea water.

1.Introduction TheIndonesian Seas are the tropical link between the PaciŽ c Oceanand the Indian Oceanand are part of the global thermohaline circulation (Gordon, 1986). The circulation andtransport through the Indonesian Seas have a largeannual variation due to thestrong monsoonalchange in the wind pattern in this area. The through ow has the maximum transportduring the south monsoon (northern summer), andthe  owreachesits minimum inthe north monsoon (northern winter) (e.g., Wyrtki, 1987; Murray and Arief, 1988; Meyers et al., 1996;Molcard et al., 1996).The change in the circulation pattern and volumeof thethrough ow mustaffect the different processes that occur in theIndonesian Seas.Dynamics of interaction with coastlines and shelves invigorate processes like upwelling,downwelling, and internal wave action. Changesin the owpatternand transport variability in turn produce changes in water massesand properties. During different monsoon seasons, waters from differentsources owto the Indonesian Seas, and the result can be seen in the variation of salinity, temperature,and other tracers from thesurface down to the lower thermocline. Local

1.Rosenstiel School of Marine and Atmospheric Science, Universityof Miami,4600 Rickenbacker Causeway, Miami,Florida, 33149, U.S.A. email:jwaw4296@ corp.newmont.com 2.Lamont Doherty Earth Observatory, Columbia University, Palisades, New York,10964, U.S.A. 547 548 Journalof MarineResearch [58, 4

Figure1. Station locations during Arlindo Mixing 93 cruise (6 August– 12 September 1993), Arlindo Mixing94 cruise (26 January– 28 February 1994), and Arlindo Circulation cruise (18 Novem- ber–15 December 1996). processessuch as precipitation,tidal mixing and coastal upwelling also contribute to these changes.Historical and recent data show the seasonal as well as interannual changes in the waterproperties in theIndonesian Seas (e.g., Wyrtki, 1961; Boely et al., 1990;Zijlstra et al., 1990;Gordon and Fine, 1996; Ilahude and Gordon, 1996). Thesource of the through ow waters dependson the nonlinear properties of the MindanaoCurrent and South Equatorial Current retro ection at thePaciŽ c entranceto the IndonesianSeas and the tropical PaciŽ c windŽ elds(Nof, 1996;W ajsowicz,2000) (Fig. 1). Thereare two main pathways of thethrough ow inthe Indonesian Seas, the western route andthe eastern route. The primary is water that  owsthrough the western route which is mostlyfrom theNorth PaciŽ c. It owsthrough Makassar Strait, Flores Sea, and BandaSea beforeexiting to theIndian Ocean via Timor Sea and Ombai Strait (Fine, 1985; FŽ eld and Gordon,1992; Fieux et al., 1994,1996; Gordon et al., 1994;Bingham and Lukas, 1995; Ilahudeand Gordon, 1996; Gordon and Fine, 1996). Part of this water also exits to the IndianOcean through Lombok Strait (Murray and Arief, 1988).Prior toentering the Banda Sea,water that takes the eastern route (east of SulawesiIsland) is mostlyfrom theSouth PaciŽc (VanAken et al., 1988;Gordon, 1995; Ilahude and Gordon,1996; Gordon and Fine, 1996;Hautala et al., 1996).It  owsvia Halmahera and Seram Seato the Banda Sea and 2000] Waworuntuet al.: Recipe for Banda Sea water 549

TimorSea. There is probably also a mixtureof water coming from theNorth PaciŽ c throughthe eastern route via the Maluku Sea. Most studies neglect the through ow from thewestern PaciŽ c throughthe South China Sea, Karimata Strait and Java Sea because of theshallowness of theshelf (mean depth of JavaSea is around40 m). Thereis also some evidenceof owfrom theIndian Ocean into the Banda Sea through the Straits of Lesser SundaIslands. This  owfrom theIndian Ocean is mostly conŽ ned to the surface layer duringboreal winter (Michida and Y oritaka,1996). As thewater  owsthrough the Indonesian sills and straits, the extremely complex topographyand the combination of active monsoonal changes and higher frequency forcingin the low latitude region contribute to momentum transfer and water mass transformationthroughout the water column. Different studies show a largerange of verticaldiffusivity estimates for thedifferent basins in Indonesia. Gordon (1986) uses a 2 4 highvalue of verticaldiffusivity ( Kz . 3 3 10 m/s) withinthe Indonesian thermocline toaccount for themodiŽ cation of the North PaciŽ c thermoclinetemperature-salinity structure.FŽ eld and Gordon (1992), using a simpleadvection-diffusion model for average 2 4 basinproŽ les, estimate a lowerlimit of vertical diffusivity, Kz at 1 3 10 m/s, for transformationof PaciŽ c waters intoIndonesian water .Thesevertical diffusivities are greaterthan those typically estimated for theinterior ocean (e.g., Gargett, 1984; Ledwell andWatson,1991; T oole et al., 1994). Hautala et al. (1996)examine isopycnal advection and mixing between North and South PaciŽc lowlatitude western boundary current sources to form BandaSea water. Three regimesare apparent in their analysis. The surface and upper thermocline layers, down to s u 5 25.8,required vertical mixing of surfaceprecipitation and runoff. V erticalmixing is alsoapparent below s u 5 27.0.In the lower thermocline purely isopycnal spreading gives a simplevariation in the ratio of sources toward a largerSouth PaciŽ c contributionwith depth. Besidesa largerange of transportand diffusivity estimates, little is knownabout vertical distributionof  owand mixing in the Indonesian Seas. Changes in the direction of the currentssuggest that the  owishighlybaroclinic. Change in direction and strength of the windforce the change in thesurface Ekman  ows,moving surface water toward opposite directions.The build up of wateralong the boundaries change the pressure gradient across theshallowsills surrounding this area and presumably force the baroclinic  owthroughout thewholeregion. V erticalmotion could also play an important role in the waterdistribution andtransformation in this region. Lack of sufficient direct and long-term measurements makeit difficult to get a completepicture of circulation and processes in the region, especiallythe vertical distribution of the circulation. Inthis paper we willdiscuss some new observations from theArlindoMixing cruises in 1993and 1994 (AM93, AM94) onboard KALBarunaJaya I andArlindoCirculation 1996 cruise(AC96) onboard KALBarunaJaya IV . Wewilldescribe an inverse analysis for quantifyingthe mixing and advection parameters along the pathways of thethrough ow 550 Journalof MarineResearch [58, 4 thatform BandaSea water .Thisanalysis makes use of Arlindotemperature, salinity and CFC-11data. As moretracer data become available, different techniques are developed to quantifythe velocityŽ eldand mixing parameters from thetracer distribution. One of theŽ rst attempts toobtain velocities from tracerdistributions was doneby Fiadeiro and V eronis(1984). Lee andV eronis(1989) show that velocities and mixing coefficients can be obtainedfrom an inversionof perfect tracer data, but inversion of imperfectdata leads to substantialerrors. Hogg(1987) obtains the  owŽ eldsand diffusivities on two isopycnal surfaces from temperature,oxygen and potential vorticity distribution of Levitus Atlas data (Levitus, 1982). Oneway to solvethis problem is byusingdifferent tracer distributions, with at least one transienttracer .Wunch(1987, 1988) studies the transient tracer inverse as a problemin controltheory and the regularization aspect of using transient tracers. Jenkins (1998) combines 3H-3He agewith salinity, oxygen, and geostrophy to computeisopycnal diffusivi- ties,oxygen consumption rates, and absolute velocities for theNorth Atlantic subduction area.Mc Intoshand V eronis(1993) show that an underdetermined tracer inverse problem canbe solvedby spatialsmoothing and cross validation. Here aninversemethod similar to thatof McIntosh and V eronis(1993) is used to quantify the advective and diffusive processesin the eastern Indonesian Seas.

2.Observations a. Data Atotalof 103hydrographic stations were occupiedduring AM93 cruise from 6August to12 September 1993 in the Southeast Monsoon (SEM). TheAM94 cruise from 26 Januaryto 28 February1994 during the Northwest Monsoon (NWM) hasa similarstation distribution(station 104– 209). Cruise AC96, including 37 hydrographic stations into the easternBanda Sea were occupiedfrom 18November to 15December1996 (Fig. 1). TheCTDdatawere collectedby Lamont Doherty Earth Observatory (LDEO) groupand resultsfrom AM93and AM94 have been reported before (Gordon and Fine, 1996; Ilahude andGordon, 1996; Mele et al., 1996).Chloro ourocarbon-11 (CFC-11) was measured duringthe three cruises by the University of Miami.The CFC analyseswere donevia a custombuilt extraction system and gas chromatograph similar to Bullister and W eiss (1988).The average analytical blanks for CFC-11for theAM93,AM94, and AC96 cruises are0.001, 0.029, and 0.001 pmol/ kg,respectively. The high blank levels especially at the beginningof AM94are due to high CFC concentrations in the laboratory air where the sampleswere analyzed.The average bottle blanks for CFC-11for theAM93, AM94, and AC96cruises are 0.009, 0.060, and 0.002 pmol/ kg,respectively. Improvements in the analyticalsystem and lower concentrations of CFC in the laboratory air during AC96 cruiseincreased the quality of CFC measurementssigniŽ cantly. The precision of theCFC analyseswas estimatedby drawing duplicate samples from thesame Niskin bottle. For 2000] Waworuntuet al.: Recipe for Banda Sea water 551

Figure2. (a) T/ Sdiagramfor stations in SulawesiSea, Northern Makassar Strait, Seram Sea, and BandaSea during AM93. Shown also are the NCEP/ NCAR Reanalysisdaily average surface wind duringAM93, provided through the NOAA ClimateDiagnostic Center (ftp.cdc.noaa.gov). (b) Sameas (a)for AM94, with additional T/ Sdiagramfor stations in southern Makassar Strait and HalmaheraSea. (c). Station groups used for the T/ Sdiagramsin (a) and (b). measurementof CFC-11greater than 0.1 pmol/ kg,the averaged concentration-difference betweenduplicates in theeight to twenty replicates are 3.48%, 3.32%, and 0.32% for the AM93,AM94, and AC96cruises, respectively. b.Observed properties and circulation based on AM93,AM94, and AC96 data TheBanda Sea water is uniquein itsalmost isohaline water column at around 34.5 from thethermocline down to the bottom (see for exampleGordon, 1986; FŽ eld and Gordon, 1992;Gordon et al., 1994;Gordon and Fine, 1996; Ilahude and Gordon, 1996; Fieux et al., 1996).Observations of water masses in the Banda Sea during the three Arlindo cruises showthe same thermocline isohaline structure in the Banda Sea (Fig. 2). Lower salinity wateris observed at the Banda surface especially during AM93 in the SEM. At the intermediatedepths the temperature-salinity (T/ S)characteristicsmatch the Antarctic IntermediateW aterand so must come from theSouth PaciŽ c. 552 Journalof MarineResearch [58, 4 i.Upper layer . Allaround Indonesia, the upperlayer tracer distribution changes seasonally andinterannually (Figs. 2, 3and5). During AM93 (SEM), NorthPaciŽ c SubtropicalW ater (NPSW) salinitymaximum of 34.75 is observed at about 150 m depthin the Makassar

Strait (s u 5 24.5).This maximum is observed into the Flores Sea with diminished intensity.It is not apparent in the Banda Sea. During AM94 (NWM), verylow surface salinityis foundin thesouthern Makassar Strait. The low salinity signal penetrates to over 100m depth.At thistime, a veryweak salinity maximum (34.6) is observedin FloresSea at 150 m.

TheT/Scurvesin the Makassar Strait between s u 5 23 and s u 5 25.5during NWM lack theNPSW salinitymaxima and are similar to theBanda Sea T/ Scurvesduring SEM. There arefour possible explanations for thislack of salinitymaxima. (1) Qiu et al. (2000)state thatthe salinity maxima input to the Indonesian Seas displays strong variability at intraseasonaltime scales, resulting from eddyformations at the Mindanao retro ection. Gordonand Fine (1996) suggest that relaxation of thethrough ow during NWM allows moreattenuation of thesalinity maximum signal in the Makassar Strait. (2) Ilahudeand Gordon(1996) suspect a southwarddrift of SuluSea water wipes out the NPSW salinity maximacausing a localizedsalinity minimum. (3) Upwellingin the frontal boundary betweenthe out ow ofMakassarStrait and current from theFlores Sea can contribute to theproperties of waterin the south Makassar Strait as well (Ilahude, 1970; Hughes, 1982). (4) Here abackushing of modiŽ ed Banda Sea W aterinto the Makassar Strait is offered as anotherpossible explanation. The term back ushing as used here does not distinguish betweenhorizontal advection and diffusion processes. Theback ushing possibility is best addressed by using a transienttracer that can differentiatetemporal changes. In 1993 (SEM), asubsurfaceCFC-11 maximum is observedjust above the salinity maximum core at about 100 m ( s u 5 24.5)(Fig. 5). CFC-11concentration is up to 1.8 pmol/ kgat this depth, north of Dewakang sill in the MakassarStrait and decreases to about 1.4 pmol/ kgin the Banda Sea at the same level. DuringNWM, theCFC-11 distribution follows the trend of salinityin the upper 150 m, the subsurfacemaxima in the Makassar Strait is not observed; however, a weakCFC-11 maximumwith concentration of 1.7 pmol/ kgis observedin the Flores Sea at 100 m depth. Byexaminingthe salinity distribution alone, one may conclude that the salinity maxima in thethermocline is destroyed by vertical mixing of fresh waterat the surface. Localized CFCmimimaabove the Flores maximum suggest that it cannot be a resultof mixingdown ofsurfacewater that is high in CFC. The strong stratiŽ cation suppresses such mixing. Thesalinity distributions during AC96 are similar to AM93 with the exception of a lowersurface salinity in the beginning of NWM,anda deeperthermocline by about50 m comparedwith AM93 and AM94 (Fig. 5). The latter may be aclueto interannual variations (FŽ eld et al., 2000).In 1996, a morecontinuous subsurface CFC maximum is observed from thenorthernmost station in the Makassar Strait to Flores Sea at about150 m depth. Theconcentration is 1.9pmol/ kgin Makassar Strait and decreases to 1.7 pmol/ kgin the westernBanda Sea. Higher CFC-11 concentrations compared to the previous cruises are 2000] Waworuntuet al.: Recipe for Banda Sea water 553 expectedin the subsurface waters becauseof the increase in the atmospheric input function.CFC-11 concentrations in theatmosphere increased until year 1993 and decrease slightlyafter 1993 (W alker et al., 2000).W aterbelow 50 minthis region, during AM93, AM94,and AC96, has been ventilated prior to 1993and, therefore, increases in CFC-11 concentrationwith time. Changes in the circulation pattern and ventilation rate due to seasonaland interannual variability can also alter the CFC concentration.Later, the inverse analysisresults will show that part of theincrease is dueto thechange in thecirculation. Freshwater in ux atthe surface is an important contributor to theT/ Sstructure.Fresh water increasesthe stability of the upper layers. The major sources of fresh water areriver runofffrom islandsplus precipitation over the ocean. Maximum fresh waterin ow occurs duringthe NWM, whenthe wind brings the warm moistair from theSouth China Sea. In theNWM, thereis a sea-surfacesalinity minimum in the Southern Makassar Strait, possiblyadvected from theJava Sea. The surface salinity minimum in BandaSea during themonth of AM93 cruise is suspectedto be advectedto the east from theprevious NWM season.Other possible sources of fresh waterin the upper Banda Sea are river out ows from IrianJaya (New Guinea;Wyrtki, 1961; Zijlstra et al., 1990).In the SEM, thesurface temperatureof theBandaSea is about4° C coolerthan in the NWM. Thesurface cooling is expectedto be the result of upwelling and local evaporative cooling processes when the windis blowingfrom thesoutheast bringing dry air . ii.Mid and lower thermocline. Themid and lower thermocline layers have a lessvariable tracerdistribution. The North PaciŽ c IntermediateW ater(NPIW) salinityminimum is clearlyobserved in the Makassar Strait at s u 5 26.5with salinity 34.45 during all three cruises(Figs. 2 and5). The NPIW salinityminimum around 300 m isapermanentfeature inboth monsoon seasons. This suggests that the mid-depth circulation Ž eldis more constant.The salinity minimum can be traceddownstream to Flores Sea and all the way to theBanda Sea with diminished intensity. Theincrease in salinity at the NPIW levelalong the path from MakassarStrait to the Floresand Banda Seas can alternatively occur from verticalmixing or as a productof isopycnalmixing between the low salinityNPIW waterwith a saltierwater of SouthPaciŽ c origin.The latter conclusion is drawnfrom theHautala et al. (1996)mixing analysis, where purelyisopycnal mixing between North and South PaciŽ c thermoclinewater can produce theobserved Banda Sea water .Here CFC’s areused to constrainthe problem. Inthe upper layer, CFC-11 partial pressure age isyoungerin thenorthern Makassar, ages increasein theFlores and Banda Seas (Fig. 3). Along the sectionin themiddle of theBanda Sea,above 500 m, CFC-11 ages increase from southto northduring AM93. CFC agesin theSouthern Banda Sea suggest that it is more recently ventilated and that the central BandaSea main thermocline is ventilated by owfrom theFlores Sea. However, the trend changesbelow 400 m, where younger ages of CFC-11are observed in the Seram Seaand northernBanda Sea, as compared with the Flores Sea and Makassar Strait. Figure 4 shows 554 Journalof MarineResearch [58, 4

Figure3. CFC-11 derived ages on s u surfacesalong different sections in the Indonesian Seas during AM93,AM94, and AC96. theCFC-11 proŽ les in the northern Makassar Strait, Banda Sea, and Seram Seaduring AC96.Below the subsurface maximum, the CFC-11 concentrations in the northern MakassarStrait decrease rapidly to near blank levels. In the Banda Sea the CFC-11 proŽ le hasno subsurfacemaxima, and the concentration decreases less with depth. BandaSea lower thermocline and intermediate water is in uenced by South PaciŽ c waterentering above the sills at the eastern entrance to the Banda Sea. The deepest sill connectingthe PaciŽ c andthe Banda Sea is the Lifamatola sill (1950 m) at126° 57 8 E, 1° 498 S,betweenSulu Archipelago and Obi Island (Fig. 1). The Halmahera Sea sill depth isaround 500 m. Seram Seawater is characterized by saltylower thermocline water that canonly be derived from theSouth PaciŽ c. In 1993 the salinity maximum is 34.7at 250 m depth (s u 5 26.0)at station 41. A morepronounced intrusion of SouthPaciŽ c Subtropical Wateris found during the AM94 in the Halmahera and Seram Seas.The intrusion is characterizedby a salinitymaximum located on s u 5 26.0,with salinity up to 34.9 (Ilahudeand Gordon, 1996). CFC-11 proŽ les in theBanda Sea are similar to theproŽ les in Seram Sea.The scatter in thedata at thelow concentrations makes it difficult to determine thetrend of the CFC-11 age along the eastern route (Fig. 3). It is possible that some recirculationoccurs between the Seram Seaand the Banda Sea at this level. 2000] Waworuntuet al.: Recipe for Banda Sea water 555

Figure4. CFC-11 proŽ les in the Makassar Strait (station 1-6), Seram Sea (station 22, 24– 26) and BandaSea (station 27– 37) during AC96 cruise. iii.Intermediate water . Belowthe Dewakang sill depth (550 m), attheend of Makassar Strait(118° 48 8 E, 5° 248 S), theCFC-11 concentrations are low ,butstillshow a cleartrend betweenbasins. In Makassar Strait, north of thesill, CFC-11 concentrations are near blank levelat 1000 m andbelow .Thepresence of this old water suggestsa blocked ow.At depthsaround 1000 m, the Banda Sea has deŽ nitely higher concentrations than the Makassarwater at the same depth. At thisdepth the Seram Seahas slightly higher CFC-11 556 Journalof MarineResearch [58, 4 concentrationsas compared to the Banda Sea (Fig. 4). At theseintermediate depths the concentrationsdecrease from BandaSea to the west (Flores Sea). The relatively high CFC-11below 500 m inthe FloresSea in the AM94 data set have been discounted here due toblank problems at thebeginning of thecruise. BothT/ SandCFC proŽ les suggest the possibility of someback ushing of waterfrom theBanda Sea to Seram Sea,Flores Sea and Makassar Strait. There is also exchange with theJava Sea for thetop 50 m.These observations described in thissection agree with the patternof circulationillustrated by Wyrtki(1961) and V anBennekom(1988).

3.An inversemodel for the passageto the BandaSea Thetracer distribution at a pointis aresultof theadvection and mixing history prior to theobservation. The result is also subject to the different boundary conditions for each individualtracer .Theobserved tracer distributions re ect the dynamics integrated over time.If asystemis stationary and there are enough linearly independent tracers, it is possibleto obtain an optimal solution for thecirculation Ž eldand mixing parameters that canproduce the observed tracer Ž eld.In most cases, there are not enough observations, or theinformation in thetracer Ž eldsare not linearly independent, leading to an underdeter- minedproblem. The Arlindo program provides sufficient data for amulti-tracerinverse analysisfor theregion. Thedomain of interestis atwo-dimensionalvertical section along the  owpathfrom MakassarStrait to Flores Sea and Banda Sea (Fig. 5), for 1993,1994, and 1996. It is assumedthat these Straits and Seas act as a channeland the  owand tracer Ž eldsare uniformacross the channel. The 2-D channelassumption does not ignore the input for the BandaSea from theeastern channel. In fact, the model solutions show that there is ow from theeast in the lower thermocline during AM93 and AC96. The sections are gridded into200 km binsin horizontaldirection and by50m invertical direction. By excluding the top50 mofthe water column, the Java Sea in uence and the surface exchange is minimized.The region below 650 m isnot evaluated because the tracer Ž eldis almost uniformthere. When tracer gradients are parallel in a region,or gradientsdisappear, the problembecomes degenerate and solutions are indeterminate (McIntosh and V eronis, 1993).The model uses open boundary conditions. The top, bottom, northern and southern boundaryconditions allow varying streamfunctions, so that exchanges with regions outsidethe domain are determined by thesolutions of themodel only. A quasi-steadystate isassumed for thetracer distributions for eachcruise in turn. The tracers used in the calculationsare salinity and CFC-11 age. The information contained in the potential temperaturesis usedin the CFC-11 age calculation. Thesteady advective-diffusive equation for conservativetracer C canbe written as

2 v.= C 1 = .(K= C ) 5 0. (1) 2000] Waworuntuet al.: Recipe for Banda Sea water 557

Figure5. Model input tracer distribution. The contour lines for salinity are every 0.05, for u every 1°C, andfor CFC-11 every 0.1 pmol/ kg,but the color shadings are irregular. The white dashed linesare sigma-theta contours. The map shows the location of the vertical section along the MakassarStrait, Flores Sea, to theBanda Sea.

Asteadyadvective-diffusive equation for anideal tracer age T becomes

2 v.= T 1 = .(K= T ) 1 1 5 0 (2) wherefactor one comes from alinearincrease in age with time. Here thecalculation is posedin terms of the two-dimensional streamfunction w , where u 5 2 ­ w /­ z and w 5

­ w /­ x.Verticaldiffusivity Kz isassumed uniform throughout the channel. There is no horizontaldiffusivity in the model. The terms chosen to balance the advective-diffusive equationare similar to the ones used by FŽ eld and Gordon (1992), where advection is balancedby verticaldiffusion. FŽ eld and Gordon (1992) use a movingreference frame, so theadvection term appears as the local rate of changein tracer concentration. For an m 3 n grid(see Fig.6), there are ( m 1 1)(n 1 1)unknownsfor w . For k tracers therewill be k 3 m 3 n equations,in this case k 5 2(salinityand CFC-11 age). For the casewhere vertical diffusivity is equalto zero, the inhomogeneous terms needed to solve theinverse problems come from thetransient tracer, in this case the CFC-11 age. Ineach grid, tracer concentrations are evaluated at the center of thegrid and streamfunc- tion w atthecorners. The discrete form oftheadvective-diffusive equations in the inverse 558 Journalof MarineResearch [58, 4

Figure6. Grid used in the inverse calculation. Ci,j isthe tracer, w isthe velocity streamfunction. calculationis:

1 2[(Ci1 1, j 2 Ci, j1 1)C ij 1 (Ci, j2 1 2 Ci1 1, j)C i, j2 1

(Ci, j1 1 2 Ci2 1, j)C i2 1, j 1 (Ci2 1, j 2 Ci,j2 1)C i2 1, j2 1] (3)

5 (Ci, j1 1 1 Ci, j2 1 2 2Ci, j)K* 1 tij where

C 5 w /(D xD z) 2 K* 5 Kz/(D z) and tij equalszero for conservativetracers and minus one for ageequations. Over theentire grid,the difference equation can be writtenin matrix form as

Ax 5 b (4) where A is a (mnk 1 1) by (m 1 1)(n 1 1)coefficient matrix, x isthe unknown vector of C and b isa vectorof zeros and minus ones plus the diffusive terms. The one additional equationaugmented on theset of the tracer equations is for thearbitrary constant for the streamfunction.This system of equations contains two kinds of errors, errors inthe coefficientsthat come from measurementerror, anderrors inthemodel. Tosolve this system of linearequations, the technique similar to thatof McIntoshand Veronis(1993) is used.This inverse method seeks the optimal solution for theadvective- diffusivetracer problem by spatialsmoothing and cross validation. 2000] Waworuntuet al.: Recipe for Banda Sea water 559 a.Smoothing Thistechnique solves the system of equations Ax 5 b bybalancing the solution smoothness,based on spatialderivatives of the solution, and the residual in the advective- diffusiveequation. A penaltyfunction, P,isformedas a weightedlinear combination of roughnessand the residual equation e 5 Ax 2 b.

Á Á P 5 x Wx x 1 e Wee. (5)

Wx isaroughnessmatrix containing semi-norm operators and weights for thestreamfunc- tion.

Wx 5 µWw . (6)

Ww isaderivativeoperator .Whenoperated on the solution Ž eldit gives the measure of roughness.A smoothsolution is obtained by minimizing the second derivatives (second orderseminorm) for streamfunction. We istheerror covariancematrix. In the calculation, a noncorrelated,uniformly weighted covariance matrix is used. It is adiagonalmatrix with diagonalelements that are inversely proportional to the relative measurement error for salinity (ws)andCFC-11 age ( wa). Thenumerical values of ws and wa areunimportant, it isonlythe size of We relative to Ww thatis important,and the relative size is controlled by thesmoothing parameter µ .TheCFC measurementsduring AC96 are improved signiŽ - cantlycompared to the AM93 and AM94. In the calculation, different error weights, wa, areapplied. For AC96 wa 5 1 year, and wa 5 10years for AC93and AC94. For salinity ws 5 0.001for allthree observations. These weights are relative weights to theerror inthe streamfunctions.The optimal solution (smooth solution consistent with observation) is obtainedby minimizing P asa functionof µ parameters. b.Cross validation Toestimateµ ,aparameterestimation technique known as the generalized cross- validationtechnique is used. The idea is to withholdone equation, solve the M 2 1 problem, andcompare the withheld datum with the value predicted from thereduced problem (McIntoshand V eronis,1993). A crossvalidation function V is formed.

2 1 Á M e Wee V(µ) 5 (7) 2 1 2 [M trace(I2 Rb)]

2 g where Rb 5 AA and

2 g Á 2 1 Á A 5 [A We A 1 Wx ] A We

2 g 2 g Rb iscalled the dataresolution matrix. A isthe generalizedmatrix inverse and x 5 A b. Theentire minimization process is done by minimizing this single function V. The minimizationprocedure used is the simplex minimization routine fmins in MATLAB. 560 Journalof MarineResearch [58, 4

Figure7. Ratio of theoutput horizontal velocity u at distance 5 100km anddepth 5 300 m to the

inputvertical diffusivity Kz. c.Model results Theinversecalculations were carriedout over a rangeof verticaldiffusivity coefficients,

Kz.Figure7 showsthe ratio between the horizontal velocity, u,atdistance 5 100 km and depth 5 300m tothe input vertical diffusivity. Although this Ž gureonly shows the value from onepoint in thesection, the pattern is thesame throughout the entire grid. A linear relationbetween velocity and vertical diffusivity is obtained when Kz islarger than 2 5 2 2 5 2 10 m /s. When Kz issmaller than 10 m /s, u/Kz isinversely proportional to Kz. This behaviorcan be explained as follows.When Kz islarge,the factor one in the age equation becomesnegligible. The balance between the terms in the advective-diffusive equation is thenbetween the advective term and the vertical diffusion term. When Kz issmall, the balanceis between the horizontal advection and the vertical advection. A velocity- diffusivityratio ( u/Kz)thatis inverselyproportional to Kz, shows that u staysconstant even though Kz decreases.This gives the limit of advection in theabsence of diffusion. In other 2 5 2 words,the solution for u remainsthe same for anydiffusivity below Kz 5 10 m /s. Figures8 and9 showthe solutions of theinverse model for twoextreme cases. The Ž rst oneis for anodiffusivitycase ( Kz 5 0),and the second Ž gureshows the solution for alarge 2 3 2 verticaldiffusivity case ( Kz 5 10 m /s). Table1 summarizesthe parameters used and the smoothingparameter of the optimalsolution for eachcase. The nodiffusivitycase gives an unrealisticsmall advection and is shown mainly for comparison.The vertical diffusivity 102 3 m2/sischosento give the solution in the range of observedhorizontal velocities. The surfacecurrents based on ship drift data in theMakassarStrait are of theorder of afew tens cm/s(Mariano et al., 1995).Other diffusivities larger than 10 2 5 m2/swillgive very similar velocityproŽ les, scaled with the mixing coefficient used, as explained above. The dashed lineson the velocity proŽ les are the residuals between the optimal solution and the observedtracer coefficient multiplied by the generalized inverse matrix. The solution x 5 A2 gb isequal to a vectorof streamfunctionon everygrid. The streamfunction residual is 2000] Waworuntuet al.: Recipe for Banda Sea water 561

Figure8. (a) Horizontal velocity u forAM93, AM94, and AC96 sections from Makassar Strait to

FloresSea. Output from inverse calculation with no verticaldiffusivity ( Kz 5 0).The dashed lines arethe corresponding residual horizontal velocity. (b) V erticalvelocity w forAM93, AM94 and AC96sections from Makassar Strait to Flores Sea. Output from inverse calculation with no

verticaldiffusivity ( Kz 5 0).The dashed lines are the corresponding residual vertical velocity (positiveupward).

2 g calculatedas xe 5 A e where e 5 Ax 2 b istheresidual. Horizontal and vertical velocity residualsare then obtained from xe.Exceptfor theno diffusion case in AC96, all the residualsare small compared with the optimal solution. Thesolution of theinverse calculation is limitedsomewhat because of thenature of the minimizationprocess. The model minimizes the residuals, and the residuals are minimum when Kz issmall.Therefore the transport tends to be smallfor agivenvalue of diffusivity.

Ina differentexperiment where Kz istakenas an unknown variable, the optimal solution givesunrealistically small u and Kz.

4.Discussion Resultsfrom theinverse calculation are limited by the accuracy in the data and the assumptionsof themodel. The model assumes steady state conditions, while the data are takenfrom threesynoptic cruises. This condition may apply assuming that the circulation adjustmenttime to monsoon change is short, which is generally the case in monsoon 562 Journalof MarineResearch [58, 4

Figure9. (a) Horizontal velocity u forAM93, AM94, and AC96 sections from Makassar Strait to

FloresSea. Output from inverse calculation with uniform vertical diffusivity coefficient Kz 5 102 3 m2/s.The dashed lines are the corresponding residual horizontal velocity. (b) V ertical velocity w forAM93,AM94 and AC96sections from Makassar Strait to Flores Sea. Output from 2 3 2 inversecalculation with uniform vertical diffusivity coefficient Kz 5 10 m /s.The dashed lines arethe corresponding residual vertical velocity (positive upward). regionsin the world (Ray, 1984; Savidge et al., 1990; Liu et al., 1992).The  ushingtime of theMakassar Strait depends on theadvective velocity. Examples of advective velocities in theMakassar Strait are given by surfacedrifters. The surface drifter data are compiled by theDrifting Buoy Data Assembly Center (DAC), AtlanticOceanographic and Meteorology Laboratory(AOML), NOAA, Miami.Four out of Ž vesurface drifters found in the MakassarStrait entered from theSulawesi Sea between February and May, but none of thementered during the Arlindo cruises. These drifter velocities reach up to1 m/s.At these velocities,it takesonly 16 daysto carrywater and tracers as far as1400km. The velocity is expectedto belowerin the intermediate water .At velocitieson theorder of a few tensof centimetersper second, the  ushingtime can increase to on order two to three months. Becausethe  ushingtime is less than the semi annual period, the quasi steady state assumptionis still, however, applicable.

Themodel does not allow Kz tovary spatially. The impacts of this assumption are lessenedbecause the model domain does not include the top mixed layer or the bottom frictionlayer. This suppresses the effect of varying Kz dueto turbulencein thesurface and 2000] Waworuntuet al.: Recipe for Banda Sea water 563

Table1. Input parameters and smoothingparameters µ 5 em forno diffusionand large diffusion case. µisobtained by minimizingthe generalized cross validation function V.Shownalso are the mean optimal u and w foreach case. ws and wa arethe weights for errorin salinity and age coefficients, respectively.

Kv Mean u Mean w (m2/s) ws wa m* V (µ) (102 2 m/s) (102 7 m/s) AM93 0 102 3 10 1.929 1.144 0.046 2 3.55 AM94 0 102 3 10 2.615 1.297 2 0.019 2 2.90 AC96 0 102 3 1 2.304 4.699 2 0.006 2 5.28 AM93 102 3 102 3 10 2 0.350 5709 7.91 57.9 AM94 102 3 102 3 10 2.480 10841 1.25 74.4 AC96 102 3 102 3 1 0.037 23536 6.62 32.5

*(µ 5 em) bottomlayer .Verticalmixing above rough bottoms and sills indeed can be larger (e.g.,

Polzin et al., 1996,1997; V anBennekom et al., 1988).Adding these spatially varying Kz termsin themodel will change the solutions, but having more unknown terms in the system ofequations will make the system more underdetermined, and a solutionmight not be obtainedat all. Somedynamical terms like horizontal diffusion are not represented in themodel. Since horizontaladvection is the only horizontal process represented in the model, it hasto be interpretedas a combinationof allprocesses that carry or distributetracers horizontally.

Likewise,in the case where Kz 5 0,vertical advection is the only way to distribute the tracersvertically. Assuming a channel-likegeometry means that the velocity Ž eldin the modelsolutions also has to compensate for owsacross channel that might occur in reality, suchas theLombok out ow andJava Sea exchange. Theerrors inthedata are accounted for inthe error covariancematrix that contains the weightsfor measurementerrors for CFC-11and salinity. With these weights, the size of the residualequation turned out tobe relativelysmall compared with the optimalsolution. This showsthat, despite the assumptions in the model, the simple dynamics chosen can reproducethe observed tracer Ž eldswith relatively small error . Theoptimal solutions of the inverse calculation suggest that strong baroclinic  ows occurduring AM93 and AC96. On the other hand, a smalland more barotropic  owisthe optimalsolution obtained for thetracer distribution in AM94. The general  owis southwardand eastward, and sometimes accompanied by a reversalin  ow.These ow patternsin thethermocline have different directions as comparedwith the surface currents thatusually follow the local wind direction (Figs. 2 and10). During SEM, the surface currentin theFlores Sea is westward, but the solutions for AM93and AC96show a strong eastward owin the upper thermocline. During NWM, thesurface current is eastward, whilethe AM94model gives a weakeastward  owinthe upper thermocline. Thereare two possible explanations for thedifference between the observed surface circulationand the solutions given by the model for subsurface ows.First, tracer 564 Journalof MarineResearch [58, 4 distributionsre ect the circulation prior to observation. The model result may re ect the circulationduring the opposite season of themeasurement. This could explain the opposite owinthethermocline as comparedwith the surface current and wind direction. Amorelikely explanation for thedifference between observed surface circulation and modelsubsurface  owsis that the  owsin the deeper thermocline are not directly driven bythelocal wind. During SEM, upwellingoccurs in theArafura andthe eastern Banda Sea. Thewestward- owing surface current induces coastal upwelling along the eastern bound- ary.The upwelled water is suppliedby the thermocline, and so strengthens the eastward owinthe thermocline, as observedin thesolutions for AM93and AC96.During NWM, thesurface circulation in the eastern Banda Sea is downwelling favorable, pushing the waterwestward in the lower thermocline. A westward owfrom theBanda Sea to the FloresSea is required for theAM94 solution (Fig. 10). Recent current meter data in the MakassarStrait indicates that for theboreal winter the surface layer is movingopposite to thethermocline  ow(Gordon et al., 1999).It is interestingto note that the solutions for the NWM verticalvelocities show weakest downwelling in the no diffusivitycase or strongest upwellingin the large diffusivity case (Table 1), supporting the type of circulation describedabove. Flowto the west is alsopart of thesolution for AC96in the lower thermocline and is morepronounced when the vertical mixing is small.A secondarydownwelling cell may occurbelow the upwelling cell during SEM. Theidea that the  owtotheeast in theupper thermoclineis driving a secondarycell with a reversalin  owinthelower thermocline is suggestedin Gordon et al. (1994).Here itisshown that the reverse  owcan extend to the upperthermocline, like in the AM94 case, and vary seasonally and interannually. Theback ushing of waterfrom theBanda Sea to theMakassar Strait through the Flores Seacould contribute to the similarity observed in the T/ Scurvein the Makassar Strait duringAM94 as comparedto the Banda Sea. The salinity minimum in the Flores Sea is clearlycoming from theNorth PaciŽ c IntermediateW ater,which  owsthrough the MakassarStrait. The water below NPIW couldhave more variable sources. Lower thermoclinewater in the Flores Sea is affected by sources from theeast, through the passageseast of Sulawesi. Higher CFC-11 concentrations in the deep Banda Sea than what arefound at the comparable depths in the Makassar Strait suggest a SouthPaciŽ c component.The exact route and ratio of North and South PaciŽ c sourcesis undetermined. Consideringthe longer residence time of water in the Banda Sea (FŽ eld and Gordon, 1992),a modiŽed Banda Sea water, that is amixtureof NorthPaciŽ c, South PaciŽ c and BandaSea water from previousseasons, appears to be  ushedback into the Makassar Straitfrom timeto time.Recent observations of currentmeter data in the Makassar Strait from December1996 to July 1998 show some evidence of reversal of the  owin the currentmeter at 350 m anddeeper (Gordon et al., 1998;Gordon and Susanto, 1999). The currentmeter at 240 m doesnot show a owreversal.A shorterrecord of ADCP data(1 December1997– 9 March1997) from thesame location shows a maximumsouthward  ow near110 m depth,and a variablenorthward and southward  owinthetop 60 m(Gordon et 2000] Waworuntuet al.: Recipe for Banda Sea water 565

Figure10. Schematic diagram of thecirculation in the Flores Sea and Banda Sea during NWM and SEM. Thevertical cross-section (right panel) runs from west to eastin the JavaSea to Flores Sea to theeastern Banda Sea. The Makassar Strait input is shown as acrossor dotsymbolizing owinto orout of theStrait. The velocity proŽ le (left panel) is a proŽle approximately in theFlores Sea or westernBanda Sea. This would correspond to thevelocities at theend of themodel domain. The modelresults indicate that the absolute velocities depend on the diffusivity chosen, and for this reason the u axisorigin (vertical line on thevelocity proŽ le) does not necessarily lie at thezero velocity.The scale of thediagram is exaggerated to illustrate the seasonal circulation at the surface andin the thermocline. al., 1999).Thus, although from theproperty distributions and model an advective or diffusiveback ushing cannot be distinguished,the current meter data are consistent with anadvectiveback ushing process. Thechanges in the owcharacterare caused by thechanges in thepressure Ž eldalong thechannel. The pressure changes because of thechange in the local wind direction and intensity,and the changes in the remote pressure Ž eld.The solutions suggest that the changesvary with depth. The exact mechanism of how and why these changes occur cannotbe determined by aninverse model. A diagnosticor processstudy is neededto infer 566 Journalof MarineResearch [58, 4 theforcing and their responses. The seasonal  owvariabilitygiven by themodel solution supportsthe observation that the through ow isminimum during the northwest monsoon season.In the large diffusivity case, the horizontal velocity for theAM94(NWM) isabout 15%to 20% of the velocity in the AM93 (SEM) andAC96 (end of SEM). Interannual variabilitymay play an important role in thevariability of the ow.Thethree observations were indifferent ENSO phases,the 1993 and 1994 cruises occur during a prolongedEl Nin˜operiod,and the 1996 cruise was ina LaNin ˜aperiod.The solutions show a relatively stronger owtothe east in the upper thermocline during AC96 as comparedwith AM93. Thissupports the argument that during a LaNin ˜aphase,the build up of thewarmpool in thewestern PaciŽ c willstrengthen the throughow (Gordon et al., 1999).While the pattern ofthecirculation in the Indonesian Seas is stronglydependent on the local forcing and the distributionof boundaries,the strengthof thethroughow seemsto bemore closely related tothe pressure difference between the remote PaciŽ c andthe Indian Ocean. Themodel solutions show that the upper thermocline eastward  owin 1996 is also accompaniedby areverse owtothe west in the lower thermocline. The strengthening of thepressure gradient in the lower thermocline between the PaciŽ c Oceanand the IndonesianSeas during a LaNin ˜aphasecould increase the  owinthe deeper thermocline throughthe eastern passages. Since the sill depths in theeastern passages are much deeper thanthe Makassar Strait sill depth, an increase in the pressure gradient in the lower thermoclinewill increase the through ow from theeastern passages. Meanvertical velocities of thesolutions range from 2 5 3 102 7 m/s to 74 3 102 7 m/s. Althoughthe values are not unrealistic, the pattern depends on the size of the vertical diffusivitychosen. In the case where vertical diffusivity is small, the downward vertical advectionis needed to satisfy the advective-diffusive balance, and when Kz islarge, the optimalvertical velocity is mostly upward in the upper thermocline. Whichever process actuallyoccurs, whether it is large vertical mixing or downward advection, the model resultssuggest a generallydownward  uxinthisarea. V erticalexchange is an important processthat carries the heat and tracers downward. Downward movement in one place mustbe accompanied by upwelling somewhere else. Upwelling brings cooler and nutrient-richwater to the surface. A meandownward velocity of 0.5 3 102 6 m/swillcarry about 42 W/m2 ofheat over a 20°C temperaturegradient from thesurface to the lower thermocline. Thisstudy shows a markedchange in thethrough ow volumeand character seasonally andinterannually. The inverse model is also able to estimate the horizontal and vertical exchangeprocesses that produce the observed water massesand are important to the local weatherpatterns and productivity.

Acknowledgments. JMWwouldlike to thank Drs. A. Marianoand C. Thackerfor valuable discussionson the inverse method. RAF acknowledgessupport by National Science Foundation grantsOCE 9302936and 9529847. The research of ALG isfunded by NSF: OCE 9529648and the Officeof Naval Research: N00014-98-1-0270. DBO issupportedby JPL/NASA: 960606and NSF: OCE 9314447.W eacknowledgeKevin Sullivan and Kevin Maillet of RSMAS, andMuswerry 2000] Waworuntuet al.: Recipe for Banda Sea water 567

Muchtarand Suseno of LIPI forthe CFC analysis.Gratitude is extendedto Dr. A. GaniIlahude of LIPI andDr. Indroyono Soesilo of BPPT fororganizing and promoting the ARLINDO jointproject. Wethank the captain and crews of BarunaJaya I and IV forproviding professional support for our scientiŽc mission.

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Received: 3July,1999; revised: 3 May, 2000.