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    JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 92, NO. C12, PAGES 12,941-12,946, NOVEMBER 15, 1987

    Indonesian Through Flow and the Associated PressureGradient

    KLAUS WYRTKI

    Department of Oceanographyand Hawaii Institute of Geophysics,University of Hawaii, Honolulu

    The flow of water from the western Pacific to the eastern Indian Ocean through the Indonesian

    archipelago is governed by a strong pressure gradient. Dynamic height computations determine the

    average sea level difference as 16 cm and show that most of the pressuregradient is contained in the

    upper 200 m. Sea level data from Davao in the Philippines and from Darwin in Australia are used to

    determine he annual signal and the interannual variations of the pressuregradient for the years 1966 to

    1985. The annual signal has a maximum during the southeast monsoon in July and August and a

    minimum in January and February. Interannual variations are not related to the Southern Oscillation

    becausesea level is low at both stations during E1 Nifio events,and thus there is little influence on the

    sea evel dift•rence. The mechanismof the through flow is discussed, ut a determination of its numerical

    value will have to await direct measurements.A comparison of the sea evel difference with results rom a

    numerical model by Kindle shows satisfactory agreement. t is concluded that the variability of the

    through flow can be monitored by sea evel measurements.

    INTRODUCTION

    The prevailing trade winds over the tropical oceans cause

    an increase of sea level on the western sides of the oceans and

    a lowering on its easternsides.Consequently,a pressuregradi-

    ent must exist between the western Pacific and the eastern

    Indian Ocean across he Indonesian waters, as was recognized

    by Wyrtki'[1961]. This pressuregradient should drive a flow

    of water through the Indonesian archipelago, which connects

    the two oceans.An estimate of the magnitude of this flow by

    Wyrtki gave a low value of only 1.5 Sv and was based on the

    assumption that the many narrow passages and channels

    through which the water has to pass would seriously estrict

    the flow. More recent estimates of the flow, which are summa-

    rized by Gordon [1986], give substantially higher values for

    this through flow. The neededdirect measurements f the flow

    are planned for the forthcoming ndonesian SeasThroughflow

    Experiment (INSTEP). These measurementsare designed o

    provide a quantitative determination of the flow and of its

    variation during 18 months and to relate the water transports

    to measured sea level differences. The sea level observations in

    turn will then allow us to monitor the flow in the future and

    to draw conclusionsbased on existing data about fluctuations

    of the through flow during the past 2 decades.

    This study is an attempt to shed some light on the annual

    and interannual variations of the through flow and on its

    vertical structure. Observations of sea level will be used to

    form and analyze time seriesof the pressuregradient between

    the Pacific Ocean and the Indian Ocean. Observations of dy-

    namic height will give the absolute value of the pressuregradi-

    ent and give insight into its vertical structure.

    SEA LEVEL OBSERVATIONS

    In the western Pacific Ocean, long time series of sea level

    exist at Davao and Jolo in the Philippines and at Guam and

    Truk. Records start in 1948. The record from Jolo is interrup-

    ted in 1959 and 1979 but otherwise resembles that of Davao

    very well. The records of all four stations are dominated by

    large drops of sea evel associatedwith E1 Nifio events.These

    Copyright 1987 by the American GeophysicalUnion.

    Paper number 7C0706.

    0148-0227/87/007C-0706505.00

    drops are slightly more pronounced at Guam and Truk than

    at Davao. The annual cycle is weak and is often over-

    shadowedby both the high- and the low-frequencyvariations.

    Its amplitude is less than 6 cm at all stations. Sea level at

    Davao risesslowly at a rate of 6.4 mm per year. This trend has

    been removed from the record shown in Figure 1. The other

    three stations do not show a trend significantlydifferent from

    zero. The detrended sea evel record at Davao is used o repre-

    sent the pressure head for the through flow in the western

    Pacific Ocean.

    Along the northwestern coast of Australia, sea evel stations

    exist at Dampier, Port Hedland, Broome, Wyndham, and

    Darwin. The annual cycle and the low-frequency variations at

    Port Hedland and Darwin agree very well. They also agree

    with shorter and interrupted records at Dampier and Wynd-

    ham but not with Broome, which probably has a record of

    low quality. Sea level along this coast is dominated by the

    annual cycle, which has an amplitude of about 10 cm. Super-

    imposed are low-frequency signalsof similar amplitude, which

    coincide with E1 Nifio events. No long-term trend is obvious

    in these short records. Because the record from Port Hedland

    has several short gaps and because it is further away from

    Indonesia, the time series rom Darwin is used to represent sea

    level along this coast, which is considered representative for

    the lower side of the pressure gradient between the two

    oceans. Unfortunately, no sea level records have been taken in

    Indonesia since 1940, but a 7-year-long record is available

    from Cilacap (previously Tjilatjap) at the south coast of Java

    for the years 1925 to 1931.

    The sea level record at Davao in the Philippines with the

    linear trend removed and the record at Darwin, Australia, are

    now used to determine the pressure difference between the

    Pacific Ocean and the Indian Ocean across the Indonesian

    waters relative to an unknown mean difference. The corre-

    sponding time seriesshown in Figure 1 exhibit a large annual

    signal and interannual fluctuations. The annual signal is very

    regular and has a mean amplitude of 15 cm. The interannual

    variations have an amplitude of about 5 cm, but they are no

    longer obviously related to El Nifio events as are the records

    of the two stations forming the difference. Maximum devi-

    ations of the sea level difference from its mean value are q-28

    cm.

    12,941

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    12,942 WYRTKI'NDONESIANHROUGHLOW NDPRESSURERADIENT

    -10

    -20

    66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 30

    i i i i i , i , , , i i i i , i ,

    DAVAO

    -2O

    -10

    -2O

    30

    20

    10

    o

    -10

    -20

    66 67 68 69 70 71 72 73 7• 75 76 77 78 79 80 81 82 83 8• 85 30

    i i • , , , , [ , , i , . , i , ,

    66 67 68 69 70 71 72 73 7't 75

    _ ....

    DAVA

    -30 66 ' 67 ' 68 ' 69 ' 70 ' 71 ' 72 ' 73 ' 7• ' 75

    -10

    -2O

    76 77 78 79 80 81 82 83 8• 85

    ......... 30

    20

    10

    -- -•- .-- •-- * ..... 0

    -10

    -20

    -30

    76 77 78 79 80 81 82 83 8• 85

    Fig.1. Seaevel tDavao,hilippines,ndDarwin,ustralia,ndhe eaevel ifferenceetweenavaondDarwin

    duringheperiod 966o 1985n centimeters.he hincurve iveshemonthly eans'heheavyurve iveshe

    12-month unningmean.A linear rendhasbeen emovedrom hedataat Davao.

    DYNAMIC HEIGHT DIFFERENCES

    A determination of the absolutevalue of the mean sea evel

    differences possibley theuseof dynamicopographies.he

    circulation n the westernPacific Ocean is dominated by the

    Mindanao Current in which large parts of the North Equa-

    torial Current are recirculated nto the North Equatorial

    Countercurrent.Whereas the Mindanao Current and the as-

    sociatedyclonic indanao ddyare permanenteatures f

    the circulation n this region,during he period rom May to

    October he SouthEquatorialCurrent lowsalong he coast

    of New Guinea and suppliessome water to the counter-

    current.The circulation n this region s such that high dy-

    namic opographys locatedbetweenMindanaoand New

    Guinea Wyrtki, 1974].Typicalvalues f dynamic eight ela-

    tive to 1000 dbar are 180 dyn cm, and they change ittle

    during the year.

    In the regionbetweenndonesia nd Australia, irculation

    is anticyclonicnd nvolveshe formation f the SouthEqua-

    torial Current in the Indian Ocean. A ridge of high dynamic

    topographytretchesrom hecenter f thesubtropicalyreof

    the Indian Ocean toward the Timor Sea, as is shown in the

    Indian Oceanatlas [Wyrtki, 1971]. Dynamic opographys

    low along the periphery f the anticycloniclow, namely,

    along he coasts f Australia nd Java.Lowest alues f dy-

    namic opographyelative o 1000dbar are near 150dyn cm

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    WYRTKI' INDONESIAN HROUGH FLOW AND PRESSURE RADIENT 12,943

    and occur from July to October, when the southeastmonsoon

    blows in full strength over this region. At this time the sea

    level difference between the two oceans has a maximum of

    about 30 cm.

    It is difficult to determine the mean value or the annual

    variation of dynamic height from the maps quoted above, and

    therefore hydrographic data have been used to compute dy-

    namic heights for two selectedareas thought to represent the

    head and the bottom of the pressure gradient governing the

    flow through the Indonesian waters. The data prepared by

    Levitus [1982] have been used to compute dynamic heights

    relative to 1000 dbar for 20 one-degreesquaresbetween Min-

    dano and New Guinea for each of the four seasons for which

    data are given. The results are shown in Figure 2 together

    with the mean annual variation of sea level at Davao. The sea

    level curve lies well within the scatter of dynamic height,

    which exhibits a similar annual cycle. The high values of dy-

    namic height near 190 dyn cm are all found north of New

    Guinea and east of Halmahera. We will use sea level at Davao

    relative to a mean dynamic height of 183 dyn cm as repre-

    sentative or the pressurehead in the area where the through

    flow originates.

    Corresponding omputationsof dynamic height have been

    made for the area south of Java, between 10øS and the coast

    of Java and between 104øE and 120øE. The data of Levitus

    [1982] give a mean dynamic height of 174 dyn cm and show

    no values below 167 dyn cm for any 1ø square or season.This

    is in stark contrast with the maps of dynamic height shown in

    the Indian Ocean atlas [Wyrtki, 1971], where several maps

    show values below 150 dyn cm. Consequently,we have used

    the data from the Indian Ocean atlas and have computed

    dynamic heights or all stations n the region south of Java.

    The results are shown in Figure 3 and indicate that dynamic

    height doesdrop below 150 dyn cm during the period July to

    October, n particular n the easternpart of the area. The data

    with low valuesof dynamic height come from Australian, Jap-

    anese,and Soviet researchvessels, nd we have no explanation

    why similar valuesdo not appear n the Levitusdata.

    SEA LEVEL DIFFERENCES

    The mean annual cyclesof sea evel at Cilacap and Darwin

    are shown n Figure 3 togetherwith the dynamicheights ela-

    190

    180-

    170

    .•. .... DAVAO

    /

    ß-• -\

    x•.,

    I 2 3 4 5 6 ? 8 9 I0 II 12

    TIME (months)

    +10

    -I0

    Fig. 2. Monthly mean sea evel at Davao, Philippines, uring the

    period 1966 to 1985 n centimeters right scale),and quarterly mean

    and extremedynamicheights n the area betweenMindanao and New

    Guinea in dynamic centimeters left scale).

    190

    180

    170

    160

    150

    140

    130

    1 2 3 4 5 6 7 8 9101112

    +1o

    o

    -10

    DARWIN

    +

    CILACAP +

    1 2 3 4 5 6 7 8 9101112

    Fig. 3. Monthly mean sea evel at Cilacap,Java, and at Darwin,

    Australia, in centimeters right scale),and dynamic height at individ-

    ual stations in the area south of Java in dynamic centimeters (left

    scale).Dynamic heights are shown by dots west of 110øE and by

    crosses east of 110øE.

    tive to 1000 dbar in the area south of Java. Sea level is plotted

    relative to a mean dynamic height of 168 dyn cm. It is appar-

    ent that the annual signals of dynamic height and sea level

    agreeand that the low valuesof dynamicheight n the second

    part of the year are real. It is at that time of the year that the

    sea level difference between the Pacific and Indian oceans has

    a maximum. The low values of sea evel and of dynamic height

    have two different causesof origin. During the southeastmon-

    soon between June and October, low sea level and dynamic

    height are located close o the coast of Java, where upwelling

    exists [Wyrtki, 1962]. During the period from December to

    April, low dynamicheight s found further offshoreand relates

    to the Java Coastal Current [Soeriaatmadja, 1957], but sea

    level along the coast is comparatively high. In view of the

    general agreementbetween the annual cyclesof sea level at

    Cilacap and Darwin and of dynamic height in the region

    south of Java, we consider sea evel at Darwin to represent the

    pressure t the bottom of the sea evel gradient rom the Pacif-

    ic to the Indian Ocean. It would, of course, be better to have

    data from a sea level station at the south coast of Java.

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    12,944 WYRTKI' NDONESIANHROUGHLOWANDPRESSURERADIENT

    The annual cyclesof sea evel at Davao and Darwin are out

    of phase,as can be seen rom Figures 2 and 3, and conse-

    quently he sea eveldifference etween he two locations x-

    hibits a very large amplitude. The annual cyclesat the two

    locations are also rather regular (Figure 1), and therefore he

    differenceof sea evel has a very regular annual cycle,which is

    due to the regularityof the monsoons. he existence f this

    strongand regularannual cycle n the pressure radientbe-

    tween the two oceans indicates that the Indonesian through

    flow will be governedby a large annual cyclehaving a maxi-

    mum during July and Augustand a minimum during January

    and February.

    The absolute value of the sea level difference between the

    western Pacific and the eastern Indian Ocean can be deter-

    mined from the differenceof dynamic height between the two

    areas Figure 4). This pressure ifference ecreasesrom the

    sea surface to about 500 m, where it reaches a minimum.

    Below the minimuma weak pressure ifferencerom the Pacif-

    ic to the Indian Ocean is again presentat the 1000-m level,

    indicating a deeper flow of water from the Pacific to the

    Indian Ocean.The mean pressure ifference t the sea surface

    relative to the minimum near 500 m is 16.3 dyn cm. Strong

    gradients re concentratedn a rather thin layer of only 250

    m. From February to April the pressure radienthas a mini-

    mum of about 9 dyn cm, whereasduring August o October t

    is as arge as 23 dyn cm. This annualvariation s concentrated

    in the uppermost 150 m.

    MEAN ANNUAL VARIATION

    The mean annual variation of the through flow can now be

    assessed y using he sea evel record from Davao to represent

    the pressurehead in the western Pacific and the sea level

    record from Darwin to represent he pressure n the eastern

    Indian Ocean and plotting them relative to a mean sea level

    difference of 16.3 cm (Figure 5). Accordingly, the sea level

    gradient governing he through low varies rom about zero

    during Januaryand February to a maximumof about 33 cm

    during July and August.

    Monthly meansof sea evel at Davao and Darwin do not

    correlate at all, despitean inversemean annual cycle,but the

    sea level difference between the two stations is correlated

    better with Darwin (--0.80) than with Davao (+ 0.60), indicat-

    ing that the sea evel differences governed hieflyby the sea

    level in the eastern Indian Ocean. In contrast, the 12-month

    24

    DYNAMIC HEIGHT DIFFERENCE

    20 16 12 8 4 0

    •• 200•

    '•400 Ld

    1-600

    -800 •

    I t I t ', ', I000

    MEAN

    FMA

    ASO

    Fig. 4. Difference f dynamicheightbetweenhe area southof

    Mindanao and the area south of Java from the sea surface to 1000 m

    in dynamic entimeters.he solidheavycurvegives he mean; he

    short-dashedine gives he averageduring February,March, and

    April; and the long-dashedine gives he averageduring August,

    September, nd October.

    +8

    +4

    -4

    -8

    1 2 3 4

    DAVAO

    DARWIN

    5 6 7 8 9 10 11 12

    ,,

    ,,

    i

    i

    ß

    ß

    ß

    s

    is

    /

    /

    s

    s

    s

    I I I I I I I I I I I

    1 2 3 4 5 6 7 8 9 10 11 12

    +8

    +4

    -4

    -8

    -12

    Fig. 5. Monthly mean sea evel at Davao and Darwin plotted

    relative o the mean pressure ifference f 16.3 dyn cm, representing

    the annual variation of the pressure radient rom the Pacific to the

    Indian Ocean.

    running means of sea level at the two stationscorrelate at

    +0.70, indicating that low-frequencysignals are coherent

    across he Indonesian waters, he importanceof which will be

    discussed later.

    THROUGH FLOW MECHANISM

    The mechanism for the transfer of water from the Pacific to

    the Indian Ocean has been outlined by Wyrtki [1961]. It is

    linked to the monsoonsand to the developmentof upwelling

    in the Banda Sea and along the south coast of Java. During

    the north monsoon from November to March, surface water

    flows both from the Java Sea and from the Pacific Ocean into

    the BandaSea,causing n accumulation f warm, ow-salinity

    water and a depression f the thermocline. he intertropical

    convergenceies southof Javaand stretchesoward northern

    Australia. Winds are not favorable for a removal of the water

    from the Banda Sea into the Indian Ocean, and consequently

    water accumulates in the Banda Sea and depresses he ther-

    mocline.The pressure radient rom the Pacific o the Indian

    Ocean s alsoweak (Figure4), and thus he through low from

    the Pacific to the Indian Ocean is rather weak during this

    season.

    During the southeastmonsoon rom May to September,

    strongsoutheastwindsblow over the entire region,and the

    South Equatorial Current of the Indian Ocean ormsbetween

    Java and Australia. Much of its water is apparently supplied

    from the Banda Sea, where strong upwelling occurs.Within

    the Indonesian waters, flow patterns seem to be more com-

    plex.There s a strongsouthwardlow n the MacassarStrait,

    as measured on an anchor station during the Snellius Ex-

    pedition [Lek, 1938]. The flow is concentratedn the upper

    200 m and reaches speedof 84 cm s-x at a depth of 50 m

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    WYRTKI' INDONESIAN HROUGH FLOW AND PRESSURE RADIENT 12,945

    I-Wyrtki, 1961]. Water is also flowing into the Banda Sea

    between Halmahera and New Guinea as an extension of the

    New Guinea Coastal Current, which flows stronglywestward

    during this season. Some of this water seems o return to the

    Pacific between Halmahera and Celebes. Some water leaves

    the Banda Sea to the west and enters the Java Sea, but it is

    most difficult to give a water balance of the area without the

    help of extensive urrentmeasurements.ea evel during the

    southeastmonsoon season s high on the Pacific side of the

    through flow and very low at Darwin and in the Indian Ocean

    south of Java. The sea level difference has a maximum of

    about 30 cm during this season, nd a very strong hrough

    flow can be expected.The lowering of sea level is directly

    related to the strong southeast winds and to the formation of

    upwellingand of the South Equatorial Current along the

    south coast of Java.

    INTERANNUAL VARIATIONS

    Interannual variations of the sea level difference across the

    Indonesian waters are apparent from Figure 1. The low-

    frequency variations of sea level at Davao and Darwin corre-

    late and show low sea level at both stations during E1 Nifio

    events. This is most pronounced in 1969, 1972-1973 and

    1982-1983 but also can be seen in 1976 and 1980. In contrast,

    the sea level difference does not show a pattern related to E1

    Nifio. This phenomenon can be explained by the behavior of

    the wind field over the Indonesian region. According to Bar-

    nett [1983] the convergenceof surface winds over Indonesia is

    subject to strong interannual variations in its intensity and

    location becauseof the coupling of the trade winds over the

    Pacific with the monsoons over the Indian Ocean. The prin-

    cipal time and space scalesof this coupling lead either to an

    intensification or to a weakening of the convergenceof winds.

    During strong convergence of the wind field, which is associ-

    ated with a high state of the Southern Oscillation, sea level is

    raised both in the western Pacific and in the eastern Indian

    Ocean nd s high n the •donesian aters. uringE1Nifo,

    winds are divergent over Indonesia, and sea evel drops within

    as well as on both sidesof the Indonesian archipelago.These

    characteristics f the wind field imply that the differenceof sea

    level between the western Pacific and the eastern Indian

    Ocean is only weakly affected by the principal wind patterns

    associated with E1 Nifo and the Southern Oscillation, and

    this is reflected in the sea level record.

    The slow interannual variations of the sea level difference

    between Davao and Darwin seen in Figure 1 are probably

    related to fluctuations of the wind field which are not associ-

    ated with the Southern Oscillation, or they may be due to

    uncertainties in the sea level records themselves.

    COMPARISON WITH MODEL RESULTS

    A global numerical model has recently been used by J. C.

    Kindle et al. (manuscript n preparation, 1987) to compute

    variations of the Indonesian through flow for the period 1977

    to 1984. The computations show the development of a very

    strong western boundary current which separates from the

    Mindanao Current, flows through the Celebes Sea and the

    Macassar Strait, continues through the Flores Sea and turns

    around Timor into the Indian Ocean. The model givesa mean

    annual cycle or the through flow with a maximum in August

    and a minimum in February in agreement with the sea level

    data. The interannual variations computed from this wind-

    driven model for the years 1977 to 1984 are shown n Figure

    6. They compare very well with the sea level difference Davao

    minus Darwin. The high maximum of through flow in July

    1979 and the low minima in January 1977 and January 1980

    are well represented, s is the small maximum of through flow

    in July 1981.Not properly represented re the high maxima of

    through flow in July 1977 and July 1982. The steady ncrease

    of the minimum of through low from 1980 to 1983 s appar-

    ent in both the model and the sea level differences. The dis-

    agreement between the low pass-filtered curves of the sea evel

    differenceand of the model shouldnot be surprising n view of

    the relative crudeness f the model, of the winds driving it,

    and of the possibilityof trends n the sea evel data.

    DISCUSSION AND CONCLUSIONS

    Dynamic height differencesbetween the areas south of Min-

    danao and south of Java show that a strong pressuregradient

    exists from the Pacific to the Indian Ocean. This pressure

    gradient is concentrated n the upper 200 m. The mean annual

    variations of the pressure gradient are reflected in the differ-

    ence of sea level between Davao in the Philippines and

    Darwin, Australia. The mean annual cycle and the interannual

    variations of the sea evel differenceagree well with the results

    of a wind-driven numerical model, which gives confidence n

    both the validity of the data and of the model. This agreement

    indicates hat the wind-driven changes n the structure of mass

    in the two adjoining oceans govern the variability of the

    through flow. The agreement also implies that the low-

    frequency ariability of the through low can be monitoredby

    means of sea level observations. Whereas sea level observa-

    tions can monitor the variability of the through flow, its mag-

    nitude will have to be measureddirectly by means of current

    30 77 78 79 80 81 82 83 84

    20

    _

    -I0

    -20

    cm

    14

    12

    I0

    .........

    Fig. 6. Variation of the sea level difference (in centimeters) be-

    tween Davao and Darwin from 1977 to 1984 and (bottom) transports

    (in sverdrups) hrough the Indonesian waters from a numerical model

    by Kindle et al. (manuscript n preparation, 1987).

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    12,946 WYRTKI: NDONESIANHROUGH LOWAND PRESSURERADIENT

    meter moorings, nd suchmeasurementsre planned n the

    forthcoming INSTEP project.

    The details of the sea evel gradient within the Indonesian

    waters will have to be determinedby a network of sea level

    gauges, hich s plannedor NSTEP. Data from hissea evel

    network will also contribute mportant information to the

    studyof the dynamics f the flow n this complex egionand

    in particular o thedynamics f cross-equatoriallow.

    Acknowledgments.upport or this researchwasprovidedby the

    National ScienceFoundationunder grant NSF OCE85-15404.This

    support s gratefully cknowledged.also ike to thank Gary Mit-

    chum and Roger Lukas or valuable omments. awaii Instituteof

    Geophysics ontribution 1917.

    REFERENCES

    Barnett,T. P., Interactionof the monsoon nd Pacific rade wind

    system t interannual ime scales,, The equatorial one, Mon.

    Weather Rev., 111,756-773, 1983.

    Gordon, A. L., Interocean xchange f thermoclinewater,J. Geophys.

    Res., 91, 5037-5046, 1986.

    Lek, L., Die Ergebnisse er Strom- und Serienmessungen,nellius

    Exped.East. Part Neth. East ndies1929-30,2, 169 pp., 1938.

    Levitus,S., Climatological tlasof the world ocean,NOAA Prof. Pap.,

    13, 173 pp., 1982.

    Soeriaatmadja,R. E., The coastalcurrent south of Java, Mar. Res.

    Indonesia, 3, 41-55, 1957.

    Wyrtki, K., Physical ceanographyf the southeast sianwaters, ol.

    2, NAGA report, 195 pp., Univ. of Calif., San Diego, 1961.

    Wyrtki, K., The upwellingn the regionbetween ava and Australia

    during the south-eastmonsoon,Aust.J. Mar. FreshwaterRes.,13,

    217-225, 1962.

    Wyrtki, K., Oceanographic tlas of the International ndian Ocean

    Expedition, 31 pp., National Science oundation,Washington,D.

    C., 1971.

    Wyrtki, K., The dynamic opographyof the Pacific Ocean and its

    fluctuations,Ref. HIG 74-5, 19 pp., Univ. of Hawaii, Honolulu,

    1974.

    K. Wyrtki, Departmentof Oceanography, ivision of Natural Sci-

    ences,University of Hawaii at Manoa, 1000 Pope Road, Honolulu,

    HI 96822.

    (ReceivedMay 11, 1987;

    acceptedAugust 6, 1987.)