Indian ocean circulation and heat budget in a numerical model

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Indian ocean circulation and heat budget in a numerical model

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Title:
Indian ocean circulation and heat budget in a numerical model
Creator:
Ji, Zaihua
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Tampa, Florida
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University of South Florida
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English
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ix, 142 leaves : ill. ; 29 cm.

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Ocean circulation -- Mathematical models -- Indian Ocean ( lcsh )
Heat budget (Geophysics) -- Mathematical models -- Indian Ocean ( lcsh )
Dissertations, Academic -- Marine Science -- Doctoral -- USF ( FTS )
Climate -- Mathematical models -- Indian Ocean ( lcsh )

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Includes vita. Thesis (Ph. D.)--University of South Florida, 1997. Includes bibliographical references (leaves 138-142).

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University of South Florida
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University of South Florida
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024648945 ( ALEPH )
39175575 ( OCLC )
F51-00204 ( USFLDC DOI )
f51.204 ( USFLDC Handle )

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Graduate School University of South Florida Tampa, Florida CERTIFICATE OF APPROVAL Ph.D. Dissertation This i s to certify that the Ph. D. Dissertation of ZAIHUA JI with a major in Marine Science has been approved by the Examining Committee on September 25, 1997 as satisfactor y for the dissertation requirement for the Doctor of Philosophy degree Examining Committee: Major Professor: Mark E. Luther, Ph.D. Member: Boris Galperin Ph.D. Member: Julian P. McCreary, Ph D Member: James J. O'Brien Ph.D. t-.' lemb er: Robert H. 'Weisberg, Ph.D.

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ACKNOWLEDGMENTS I am deeply gratef ul to my major professor Dr. Mark E. Luth e r for his valuable guidance, financial s upport precio u s fri e nd s hip in all yea r s o f my pursuing t h e re sea r ch for thi s t hesis. I a lso appreciat e hi s readin ess and patient for questions and suggestions. I can not ima g ine how I could have finished this thesis without his h e lp and e ncour age ment. T hank s Dr. O Bri e n Dr. McCreary Dr. Weisberg and Dr. Galperin to be kindly in m y defense co mmi ttee. I can not ignore my friends in the marin e scie n ce department. Without having all fun when playing soccer tennis and oth e r ente rtaining things with t hem many years o f my graduate life would have been much l ess interesting. The last but not t h e l east my family my par ents, gorgeous wife, Janyong, and lovely son, Hongzhao provides me the most precious support, and without their love and co mfort, it i s impossibl e for me to accomplish this thesis. It would be more wonderful if my parents cou ld be here to shar e my happin ess.

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LIST OF TABLES LIST OF FIGURES ABSTRACT TABLE OF CONTENTS CHAPTER 1 I NTRODUCTION 1.1 Indian Oc ea n Circul ation 1.2 Heat Budge t in Indian O cea n 1.3 Numerical Modeling 1.4 Summary ..... CHAPTER 2 DEVELOPMENT OF NUM ERICAL MODEL 2.1 Model G eo metrie s and Conditions ..... 2.2 Dynamic and The rmod y n a mi c Formulation. 2.3 Summary . . . . . . . . . CHAPTER 3 SEASO NA L VAR IABILITY 3.1 Annual Cycle in Mo d e l Fie ld s 3.1.1 D y n a mi c Fi e ld s . . 3 1.2 The rm o d y n a m ic Fi e lds 3.2 Heat Budget in the Indi a n Ocean 3.2.1 Annual Mean Heat Budget 3.2. 2 Annual Cycle in Heat Flux a nd Transport lll lV lX 1 1 3 4 6 7 8 12 20 22 22 23 33 40 42 45

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3.2.3 Heat Transpor t Ac r oss Equator 3.3 Summary . . . . . . . . CHAPTER 4 I NTERANNUAL VARIABILITY 4.1 The EOF ?vlethod ........... . 4.2 Mod e l Fie ld s with Inte r annua l Va riability 4.2.1 4.2.2 4.2.3 Inte rannual-Mean :\.nnu < l l Cycle .. Interannua l Variability i 1 Ylonthl y -:Vlean Fields EOF Analysis o f Inter a r nual Variabil ity Integ r a l Time Scal e o f tne : v lodel Fie ld s EOF Analysis o f the First-Layer \ 'e l oc ity EOF Analys i s of the First-Laye r Thick n ess EOF Analysis of the Ylixed-Layer Thickness ;Jl 51 56 60 60 66 73 74 76 8 7 95 EOF Analysis o f the .Ylixed-Layer Temperature 102 4.3 Inter annua l Variability in Heat Budget . . . . 109 4.3.1 .\!lean Annual cycle o f Heat Budget i n the Indian Ocean 111 4.3.2 Interannu a l Va ri ability in Heat Budget 114 4.3.3 Inter annua l Variability in t h e Running Mean Anomaly 116 4.4 Interannual Variability R e lated t o SOl 4.5 Summary . . . . . . . . CHAPTER.) SC'vl!\IARY AND CONCLlJSIO:\TS REFERENCE S VITA 11 125 129 132 138 End Page

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Table 2.1 Table 4.1 Table 4.2 Tab l e 4.3 Tabl e 4.4 LIST OF TABLES Ini t i a l mode l vertical structure compare d to Gent s [ 198 3 ] estimati o n 10 E i ge nvalues of t h e fir s t s i x EO F s of fir s t l ayer vel oc i ty E igenva lues of the first s ix EOFs o f first-l aye r thic kn ess E igen va lues of t h e firs t s i x EOFs o f mix ed -l ayer thic kn ess Eigen val u es o f t h e first s ix EOFs o f mix e d-l aye r temperature Ill 78 88 96 104

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LIST OF FIGURES Figure 2.1 Schematic d i agram of t h e mod e l l ayers . . . 9 F i g ure 2.2 The Indi a n Ocean area map cove r e d b y t h e m o d e l 10 Figure 2.3 The transport correction at the southern ope n boundary 11 Figure 3.1 Monthl y mean wind vel ocity (ms-1 ) field s in January a nd July 24 Figure 3.2a The fir s t l aye r vel ocities (ms-1 ) in January Figure 3.2b T h e first l aye r ve l ocities (ms-1 ) in Mar ch Figure 3 .2c The first l ayer velocities (ms -1 ) in May Figure 3.2d The first l ayer velocities (ms-1 ) in July Figure 3.2 e The fir s t l aye r velocities (ms-1 ) in September F i gure 3.2f The first layer veloc i t ies (ms -1 ) in Novembe r Figure 3.3 The secondlayer veloc i t i es (ms -1 ) in January and July Figure 3.4 The third-layer vel oc i ties (ms-1 ) in January a nd July Figure 3.5a T h e first-layer t hickn ess (m) in J a nu a r y and July Figure 3.5b The second-layer thickness (m) in January a nd July 25 25 26 27 28 28 3 0 31 32 34 Figure 3.5c T h e third -layer t hi c kn ess (m) in January a nd July 35 Figure 3.6 The net sea -surface heat fluxes (lVm-2)in January a nd July 36 Fig ure 3.7 The mix e d-layer t hi c kn esses (m) in J anuary a nd July 37 Figure 3.8 T h e t e m pe rature in January a nd July 38 F i gure 3.9 The obs e rved SST in January a nd July 39 F i gure 3.10a The correlati o n coefficient of the SST Figure 3.10b Diff e r e n ce o f the SST .. I V 40 4 0

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Figure 3.11 The second laye r temperature in January and July Figure 3.12a Heat budget of the whole Indian basin ...... Figure 3.12b Heat budget of the northwest Indian basin (Arabian Sea) Figure 3.13 Meridional heat transports across the whole basin .... 41 43 44 45 Figure 3.14 Ratio of eddy contribution to t h e total horiz ontal gyre e ffect 46 Figure 3.15a Sea-surface Heat flux es in the northern and so uthern basins 47 Figure 3.15b Heat exchange between the first and second laye rs 48 Figure 3.15c Ac ros s -equatorial heat transports . . . . 49 Figure 3.15d The long i tudinal heat transports across 80 E section 50 Figure 3.16 Heat transport through open boundaries . 52 Figure 3.17 Figure 4.1 Figure 4.2 Figure 4.3 F igure 4.4 Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8 Figure 4.9 Figure 4.10 Vertically integrated heat fluxes across equator Mean annual cycle of t he first-layer velocities Mean annual cycle of the first-layer thicknesses Mean annual cycle of the mixed-laye r depth . Mean annual cycle of the mixed-layer temperature Monthly-mean interannual velociti es in the first laye r The first-layer zonal velocity component on the equator Monthly-mean interannual layer thickness in the first l aye r Monthly-mean inte rannual mixedlayer thickness . . Monthly-mean interannual mixed-layer temperature fields Interannual correlation coefficient of t he SST . Figure 4.1la Integral time scal e o f t h e first-layer zonal Yelocity Figure 4.1lb Integral time scal e of the first-layer meridional velocity Figure 4.12 Integral time scale of the first-layer thickness Figure 4.13 Integral time scal e of the mixed-layer thick n ess v 53 62 64 65 66 68 69 70 71 72 73 75 75 76 77

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Figure 4.14 Integral time sca l e of the mixed-layer temperature . 77 Figure 4.15a Corre lati o n c oefficient o f the first-layer zo nal ve locit y 79 Figure 4. 1 5b Correlatio n coeffic i e n t of the first-layer meridional vel oc i ty 79 Figure 4.16 T he first temporal EOF of first-layer velocit y . . . . 81 Figure 4.17a A nomali es o f the first-laye r velocity centere d on April 1 966 82 Figure 4.17b Anomalies of the first-layer veloc i ty cente r ed o n July 1976 83 Figure 4.18 The seco nd temporal EOF of first-layer velocity . . . 84 Figure 4.19a Anomal i es of t he first-laye ; veloc i ty ce n te r ed o n October 1973 85 Figure 4.19b A n omalies o f the first-layec vel ocity cente r ed o n April 1 964 85 Figure 4.20 T h e t hird tempora l EOF of fir stl aye r vel oc i ty . . . 86 Figure 4.21a Anomalies of the first-layer ve l ocity cen tered o n October 1975 87 Figure 4.21b Anomalies of t h e first lay e r vel ocity centered o n July 1968 88 Figure 4.22 Cor r e l ation coefficient o f the first-layer t hi ckness 89 Figure 4.23 T h e first temporal EOF of first-layer thickness 90 Figure 4.24a Anoma li es o f the first-layer thickness cen te r ed o n January 1962 91 Figure 4.24b Ano m alies of t h e first-layer thi ckness centered on July 198 4 91 Figure 4.25 The second temporal EOF of fir stl aye r thickness . . . 92 Figure 4.26a A n omalies of the first-layer thickness cente r ed o n July 1 978 93 Fig ure 4.26b Anomalies of the first-layer thickness centered on Jul y 1971 93 Figure 4.27 T h e third temporal EOF of first-layer t hickn ess . . . 94 Figure 4.28a Anomalies of the first-layer thickness centered on January 1973 95 F igure 4.28b Anomalies o f t h e first-layer t hi ckness cen tered o n July 1974 96 Figure 4.29 Corre l ation coeffic i ent of the mixed-layer thickness 97 Figure 4.30 The first temporal EOF of mix edl aye r t hi ckness 98 Figure 4.31a Anomal i e s of the mixed-layer thickness cente red o n July 1961 99 Vl

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Figure 4.31b Anomalies o f the mixed-la yer t hickne ss cent e r e d on July 198 5 99 Figure 4.32 The second temporal EOF of mixed-layer thi ckness . . . 100 Figure 4 .33a A n o mali es of the mixed-layer thickness centered on Ap ril 1976 101 Figure 4.33b Anomalies o f t he mixed-la yer t hi c kn ess centered on July 1970 101 Figure 4.34 The third temporal EOF of mix ed -layer thickness . . . 102 Figure 4.35a A nomalies of the mixed-layer thick n ess centered on July 1968 103 Figure 4.35b Anomalies of t h e mix ed-layer thickness centered o n July 1969 103 Figure 4.36 Correlation coefficient of the mix e d-l aye r t e m peratu r e 104 Figure 4.37 The first temporal EOF o f mixed-layer temperature 10 5 Figure 4.38a a n omal i es of the mixed-layer temperature centered on A pril 197 8 106 Figure 4.3gb a nomali es o f the mixed-layer temperature ce n tered on July 1974 106 Figure 4.39 The second temporal EOF o f mixedl ayer temperature . . . 107 Figure 4.40a A nom al ies of the mixed-layer temperatur e c e n te r ed o n A pril 1979 10g Fig ur e 4.40b Anomalies of the mixed-layer temperatur e cente r ed o n July 1963 10 g Fig ur e 4 .41 The third temporal EOF of mi xe d l ay er temperature . . . 109 Figure 4.42a A nom alies of t h e mix e d-l aye r temperature centered on July 19g5 110 Figure 4.42 b Anomalies of t h e mixed-layer temperat ur e cen te r ed on July 19g4 110 Fig u re 4.43a Seasonal sea-s urfa ce heat fLu xes . . . . . . . . 111 Fig ur e 4.43b Sea s ona l h eat exc hang es between the first and seco nd laye rs 112 Figure 4.43c Seaso n a l cross-equator i a l heat fluxes . . 113 Figure 4.43d Seasonal heat transports across g o o E section 114 Figure 4.44a Inte rannual heat fluxes through the sea surface 115 Figure 4.44b Intera nnu a l h eat excha n ges between the first and seco nd layers 116 Figure 4.44c In te r a nnu al cross-equato ri a l heat fluxes . . 117 Figure 4.44d In te rannual heat transp orts ac r oss goo E sectio n 11g Vll

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F i gure 4.45 R unnin g-mea n sea surface heat fuxes 119 Fi g ur e 4.4 6 S p ectrum o f sea surface h eat fluxes 120 Fig ur e 4.47 Running-m ea n heat exc h a n ges betwee n the fist a nd seco nd l aye r s 1 2 1 Figure 4.4S Spectrum o f h ea t exc h a nge b e tween l aye r s .. 122 F i gure 4.4 9 Runnin g mea n cr o ss eq uatori a l heat t r a n sports 123 F i gu r e 4.50 S p ectrum o f c r oss eq uatori a l heat t r a n s p o rts 124 F i gure 4.5 1 Running-mea n heat tra n s ports ac r oss soc E sect i o n 12 5 F i gure 4.52 S pectrum of heat tran s po r ts a c r oss soc E 0 0 0 0 0 126 Fi g ur e 4.53a C r oss s p ect rum b e tween t h e firs t EOF o f H1 a nd t h e SO I 127 F i g ur e 4.53b C r oss spect rum b e tween t h e seco nd EO F of H1 a n d the SO I 12 S F i gure 4.53c C r oss spect rum b etwee n t h e t hird EO F of H1 a nd t h e SO I 12S Vlll

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INDIA N OCEAN CIRCULATIO AND HEAT BUDGET IN A NUMERICAL MODEL by ZAIHCA JI An Abstract Of a dissertation submitted in partial fulfillm e n t of the requirements for the degre e of Doctor of Philosophy Department of l\'larine Science University of South Florida D ecember 1997 Major Professor: :\tlark E. Luther, Ph.D. lX

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Several r esea r c h ers have show n a net annual h eat gain through sea s urfac e in the Indi a n Ocean north of 10 S. B ecause the northern boundary of the basin is closed by the Asian land mass a s ubstanti a l meridional so u t hward heat transport i s impli ed across the equator. In our thesis, a f ourl aye r t h e rmod y n a mi c numerical model is de sc r ibed to study t h e cir cu l atio n mixed-layer physics and meridional heat transport of the Indian Ocean. Two s imul ation experi m ents are designed and performed by usin g respectively the climatological and in te rannual forcing fields of solar radiation air temperature a ir specific humidity, < : nd surface wind stress The output model fields compa r e well agai nst ava ilabl e observatio ns In the climatological experiment with seasona l va ri ab ili ty the modeled heat budget is consistent with that derived from observations. Net a nnu a l heat gains and los ses occur in the northern a nd southern basins respectively, a nd southward and northw a rd net heat transports ex ist in the first and second l aye rs respectively. The heat budget of the northern basin i s closed by a shallow meridional overturning ce ll co nsisting of northward flow w i t hin o r just below t h e thermocline a nd southward flow in the s urfa ce layer. The heat t ran sport in eac h layer is further divided into contributions of overturning heat flux (93%), horizontal gy r e ( larg e scale, 2 5%) and eddy (small scale 4.5%) effects across t h e eq uatori a l sect ion The l engt h scale o f eddy decorrelation is 1200 km on the eq uator While there i s strong modulation of t h e cross-equatorial heat transport at seasona l and shorte r time s ca l es, the e dd y co ntribution to annual-mean heat transport is small. Littl e i s known about the interannu a l va ri ability of the c irculati on assoc iated wit h the a nnuall y-reversin g monsoon winds in the Indi a n Ocean. '0 /e per form a real-time exper im ent to i ntegrate the model under int eran nu a l monthly-mean f orc ing for a pe riod of t hir ty years ( 1960 19 89). The seaso n a l var iabili ty of the mean annual cycle of X

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the m o d e l fie l ds close l y match es that o f the ir cor r es pondin g climato l og ical integration. Hig h corre l atio n i s o btain e d betwee n the inte rannual var i abiliti es o f mix e d -layer t e rnp erature and t h e observed SST. An EOF method is appli e d to anal yze stati stic : all y the in terannual variabilit y o f running-m ea n a n oma li es of t h e m o d e l fie l ds. Abstract Approved: ------------------------------------------------Ylajor P ro f essor: Ylark E. Luth e r Ph.D. As soc iate Professor D epazment o f 'vlarin e S c i e nce Date Approved: I I 2 / 4 7 I X

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CHAPTER 1 INTRODUCTION In comparison with the Pacific and Atlantic Oceans the Indian Ocean is no t only smaller in dimen s i o n but also has received much less attention in theoretical and observational studies. The Indian Ocean i s unique in that it is land-locked in the northern low latitudes. It is important for global atmospheric processes because of the intense air-sea intera ct ion that occurs under the influence of the seasonally-reversing monsoons and the transient cyclonic storms over the northe rn and equatorial Indi a n Ocean [Find lat er, 1971; Diiing, 1979; Schott 1983] (see Knox [1987] for a review) Our main objectives in this study are to develop a num er i ca l model to investigat e the dynamics and thermodynamics of the upp e r ocean circulation and to quantify the heat budget in the Indian Ocean. W e begin b y presenting an overview of the Indian Ocean circulation in Section 1.1. A short discussion on the heat budget in the Indian Ocean is given in Section 1.2. A summary of prev ious model studies for the Indian Ocean and a short description of the model development f o r this thesis are given in Section 1.3. Finally we s ummarize this introdu ctio n and give an the sis outline in Section 1.4. 1.1 Indian Ocean Circulation During the bor ea l winter (th e winter or northeast monsoon, D ecembe r through March), a high pressure cente r i s form ed over :\.sia. It drives stro ng north east winds 1

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into a trough near the equator to meet the southeast trade winds in the southern hemisphere. Over the Arabian Sea these northeast monsoon winds blow southwest ward with a maximum strength of approximatel y 0.2Nm-2 During the summer (the southwest or summer monsoon, May through October), the high pressure center over Asia weakens; a high pressure center a round Madagascar intensifies the southeast trade winds and causes a strongly-sheared northeastward atmospheric jet, the Findlater Jet, over the Arabian Sea, with a maximum sustained magnitude of wind stress on the order of 0.6Nm-2 [Wylie and Hinton, 19 82]. The southwest monsoon represents one of the Earth' s most dynamic and thermodynamic interactions among atmosphere oceans and continents [Clemens et al. 1991 ] Associated with the atmospheric jet is a strong gradient in wind stress curl, which drives strong circulation ce ll s and open ocean upwelling. The circulation of the underlying ocean is unique and clearly monsoon-driven. South of 10 S, the westward flowing South Equatorial Current (SEC) is present throughout the year. During t h e northeast monsoon, the wind field most resembles the trade wind systems of the other two oceans, Pacific and Atlantic and so does the current system in the Indian Ocean. Especially, its equatorial current system is rather like the tropical Atlantic and Pacific with the exception that a countercurrent lie s in the South Hemisphere due to the strong northeast monsoon winds reaching across the equator at this season. The moderate equatorial eastward winds in the period of transition between mon soons, typicall y April and early May, or later October and November, creates a strong eastward jet, termed the Wyrtki [1973] Jet, within a few degrees of the equator and dominantly in the eastern portions of the basin. The onset of the southwest monsoon starts in 1 vlay. During the southwest mon-2

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s o o n typic ally from J ul y w S epte m be r t h e fully d e v e lop e d m o nSCJOn winds drive a gen e r ally eas tward flo w in the n o rth ern basin with a ppr opriate detours for land and island b arri e r s, the s o c alled S o uthw est .\lon s o o n C urr ent. Alon g t h e eas t A f ri can c o ast, a syste m of t w o antic yclo nic gyres, the S outhe rn G y r e clo s e t o the equator a nd t h e Great Whirl be twe e n 4 .V to 10 N, i s cr eate d in the e x t r e m e l y S\ vift n o rth e as t war d Somali Curre nt. \ Vind s al o n g t h e e qu a tor are lighte r t han in t he trans i t ion t ime. C urr ents t h e r e a r e l es s cohe r e nt t h a n the vVyrtki J e t and m a y eve n r e v ert to westwa rd ( Knox 1987]. B esides t he loca l act i o n s, t h e m onsoon w i nds a lso c an e x c i te p r o p agat in g signals in the f orm of e quator i a lly trappe d waYes. t ha t t rav e l l o n g d i s t a n ces t o aff ect t he ocean r e m o t e l y [ Lighthill 1969 ; Ande rson and R owlands, 1976 ; Luyte n and Roem m ich. 1982: T s a i et al., 1992 ; J ense n 1993 ] Further discussion o f the equato rial currents at t his season a r e give n in S ect i o n 3 .1. 1.2 Heat Budget in Indian Ocean The sun he ats t h e earth une, enly pre d o minantly in t he t ropic s, while the long wa\ e r adiation b ack int o s pa ce is distribut e d sm oothly. This giv es rise to a pol e war d heat transport in t he oc ean and causes the tro pi c al oc e ans t o play a key role in moduiari n g global atm osphe ri c p r ocesses. The o ceanic meridional e n e rgy transports hatoe lo n g bee n r ecogni z ed as a m a j o r f acto r in contro llin g climat e The land-locking in tthe nonhero low lat itudes. i nt e rrupts t h e n o rm a l c ir c ulati o n of heat rranspon in the I n d ian Ocean. It i s t h e interhemis ph e ri c h e atin g contras ts of land udl surlace that f orms the mechan i sm o f the mon soo n ph e n o m e non in Indi a n Ocearm [ Ha.
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annual heat gain through the surface of the Indian Ocean north of 10 S [Hastenrath and Lamb 1979b ] H yd rographic data analysis along 32 S also s hows a net gain of heat of Indian Ocean [Tool e and Rayme r 1985]. Because the basin is closed to t he north, this heat must be transported SOllthward, with a substantial heat transport across the equator. The c ritical questior. is which components of the Indian Ocean c irculation achieve the n et oceanic heat t ransport o n a seaso nal or an interannu a l basis 1.3 Numerical Modeling Both layer mod els [ Hurlburt and Thomson 1976 ; Lin and Hurlburt 1981; Luther and O 'Brien, 1985; McCreary and Kundu, 1988; Kindle and Thompson 1989 ; Wood bury et al., 1989 ; J ensen, 1990 ; Potemra et al., 1991] and level models [Cox 1970 1976 1979; Sch o tt 1986 ; Anderson e t al., 1991 ; Semtner and Chervin 1992] have b ee n applied to studies of the Indian Ocean circulation. McCreary and Kundu [1989 ] and McCreary et al. [1993] include mixed-lay e r physics in their layer model to simulate the seasonal thermod y namic process in the Indi a n Ocean. The y simulate successfully most of the observed features in the Indian O cea n circulation; howev e r some artificial heating and cooling terms are added in t he low e r layer temperature equation to keep the layer from being too cold or too warm. Consequently the heat input through the sea surface is removed primarily by these artificial terms, not b y so uthward advection of warm tropical waters eve n though a clos e d upp e r -ocea n overt urning circulation is simulated in t heir model. Wacongn e and Pa canowski [ 1996 ] use a general circulation model to study t h e seaso n a l heat transport of the t ropical Indian Ocean the same model as used by Ph ilander and Pa canows k i [1986] a nd Philander et al. [1987] in their studies for the annual cycles o f the tropical Atlantic and P ac ific Hig her vertical r es-4

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olution is achieved in their model with a major sacrifice of the horizontal resolution. (Refer to Godfrey et al. [ 1995 ] for a review of simulations of the Indian Ocean.) For the thermodynamic processes near the ocean surface. the mixed laye r is of great importance. Kraus and Turner [1967] developed a one dimensional mixed-lay e r model that takes into account the e ffects of the mechanical stirring due to wind heating and coo ling at the s urface and penetrative heating at depth. The model negl ects the dynamic response of the ocean to variable winds that is, horizontal ad vection and Ekman d y namics. The heat flux through the sea surface only contributes partially to the observed SST variance [Molinari et al., 1986]. In the real ocean, how ever cooling and heating and wind stirring interact with Ekman-driven upwelling and downwelling to cause water mass and heat e xchange between layers through entrainment (and detrainment), and to determine the mixed laye r ph ys ics. Absolute heat fluxes and transports may be calculated from model output [Raga and Ros s by, 1987 ; McBean 1991], as opposed to methods of relative heat flux calculations [ Diiing and Le e tmaa 1980 ] or indirect calculation using the air-sea flux method and heat storage evaluation [Hsiung et al. 1989 ; Schott et al., 1990]. The thermodynamic model used in this study is conceptually based on two ex isting models One is the 3.5-layer d y namic model described by Luth er and 0 'Brien [1985] and extended later by Jensen [ 1990] ; the other i s the 2.5-layer thermodynamic model developed by McCreary and Kundu [1989] and McCreary et al. [1993]. VVe choose a layer model to obtain high horizontal resolution that i s necessary for computation of the advection terms and filter higher vertical modes that may contribute to the solution in non-ph ys ical way Barnier et al. [ 1991]. The mod el e mployed in this research i s a 4-layer thermodynamic model with a surface mix edla ye r embedded in the upper lay e r and t h e lowest la yer kept at rest The mode l is for ce d by observed 5

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monthly-mean climatological atmospheric data, which include solar radiation longwave radiation from the sea surface, air temperature, air specific humidity and wind stress forcing from the Comprehensive Ocean-Atmo sphere Data Set (GOADS) as an alyzed by Rao et al. [1989] and b y Jones et al. [1995]. The model computes surface heat fluxes base d on these and on model SST as in McCreary et al. [ 1993]. From the horizontal heat transports in eac h layer and vertical heat exchange between the first and second layers we can determine if the meridional heat transport is mainly due to overturning in the meridional plan e, i e the southward movement of surface warm water compensated by the northward movement of colder deep water or due to horizontal gy re and eddy effects, where correlations bet,veen velocities and temperatures in the horizontal plane contribute to a meridional heat transport. 1.4 Summary The Indian Ocean is important for its contribution to global climate because of its land-locking in the northern low latitudes and representing an area of intense air-sea intera c tion under the influence o f the seasonally-reversing monsoons. The essential focuses in this thesis are to simulate the circulation and heat balance of the Indian Ocean especially the meridional heat transports that carry southward the net gain of heat in the northern Indian basin and to determine the dynamical, thermodynamical and mixed-layers proc esses that account for the prominent features of the solutions. In addition to this introduction we describe development of the numerical model in Chapter 2. Model r es ults with seasonal variability und e r climatological forcing is discussed in Chapter 3. The interannual variability of the general circulation and heat budget in the Indian Ocean is discussed in Chapter 4. Finally we provide a summary and list the co nclusions of this thesis in Chapter 5. 6

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CHAPTER 2 DEVELOPMENT OF NUMERICAL MODEL Multi-layer models are widely applied to the dynamic and thermodynamic studies in ocean circulation. The number of layers in a model is equa l to the number of the barolinic modes the model can simulate for the ocean circulation. Layered models focus only on the primary low-order vertica l modes in the ocean and therefore are able computationally to have the high horizontal resolution that is necessary for calculating horizontal advection. In addition thermodynamic processes in the oceans are primarily present in the upper layer; therefore, a reduced gravity assumption is usually used to eliminate the deeper ocean physics. A four-layer model is developed in this thesis to investigate the upper layer ocean circulation and heat budget in the Indian Ocean. The reduced gravity assumption leads to zero horizontal pressure gradient in the bottom layer, thereby removing the barotropic mode from the modeled ocean circu l ation. Although heat and momentum, as well as the water mass are allowed to exchange on l y between the first and second layers we add the third layer in the model to provide more baroclinic modes to give better simu lation of both the dynamic and thermodynamic processes in the Indian Ocean [Gent et al., 1983]. In this chapter we describe the development and parameterization of the numeric model. The initial and boundary conditions of the model as well as the model geometries, are discussed in Section 2.1. The modeled dynamic and thermodynamic processing is described in Section 2.2 A short summary of this chapter is given in Section 2.3. 7

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2.1 Model Geometries and Conditions The present version of the model has four layers with a surface mixed layer, of thickness hm and temperature Tm, embedded in the first layer and the horizontal pressure gradient assumed to vanish in tne lowest layer (the reduced gravity approx imation) as schematically illustrated in Figure 2.1. In addition, a fossil layer may exist within the first layer beneath t h e rnixed layer as described by McCreary et al. [1993]. The temperatures in the mixe c and fossil layers may be different but the velocities are identical. The second la : er spans the thermocline in which a linear chang e of temperatur e is assumed w ith temperature at the layer bottom equal to the temperature of the third layer. We use We and Wk to represent the entrainment vel ocities between the first and second layers and between the mixed and fossil l ay ers, respectively. When the fossil layer disappears, We includes Wk Since no mass exchange exists between the second and third l ayers, the temperature in the third layer is treated as a constant. The levels Zi represent the vertical coordinates of the interfaces between layers except that Z1 is the elevation of the sea surface. The model domain shown in Figure 2 .2, covers the Indian Ocean basin from 30 S to 26 Nand from 31 o E to 120 Eat a grid resolution of 1 /6 in latitude and longitude. The 200 meter isobath is used as the solid boundary lin e between ocean and land. Open boundary conditions are appli ed at the south and a lon g a portion of the east boundaries. The thickness and temperature of each layer are initially chosen to match observed density profiles [ Wyrtki 1971; Gent et al., 1983]. With three active layers the model resolves three baroclinic modes [Lighthill 1969]. The equ i valent depth and Kelvin wave speeds of the three modes are close to the estimated values from Gent et al. [1983], as li sted in Table 2.1. The thickness and temperature of the first layer are 8

PAGE 22

A1MOSPHERE MIXED LAYER U "> LAYER I -LAYER2 Z:3 --LAYER3 LAYER4 Figure 2.1. Schematic diagram of the model layers. Layer 1 includes mixed and fossil layers. Temperature in layer 2 is assumed linearly changing from T3 to Te. Zj are the vertical coordinates of the interfaces between layers except that Z1 is the elevation of the sea surface set at initial value of 80m and the observed sea surface temperature in December, respectively. The second layer has a thickness of 250m and contains the thermocline with a vertical average temperature T2 = l5C and Te (the entrainment temperature) at its top. A linear change of the temperature from Te to T3 (the third layer temperature) is defined in (8) for the second layer. A thick third layer is initially set at the thickness of 500m with a constant temperature of 9C A constant temperature of 6 C is chosen for the lowest layer. All the coasta l boundaries are treate d as vertical walls. Solid no-slip boundary conditions are chosen for all field variabl e s at the walls. The horizontal gradients of scalar variables normal to the wall and velocities normal and along the wall are all 9

PAGE 23

25N 20N 15N lON 5N EQ 5S lOS 155 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE Figure 2 .2. The Indian O cea n area map co vered b y the model. The 200 meter i sobat h i s used as the solid bounda r y line between ocean and l and. The shaded areas a r e counted as land in the model geomet ry. Table 2 .1. Initial model vert i ca l stru ctu r e compare d to Gent's [ 1983] est im ation Mode Equival e n t Depth (em) Kelvin vVave Speed (cms-1 ) Numbe r Model Gent Model Gent 1 96.9 79. 9 308 280 2 24.6 30.5 155 1 73 3 14.2 1 2.6 118 111 set to zero. For the open boundaries along the south ern and a portion of the eastern e dge of the model basin we appl y a zero-g radie n t condition for scalar Yariables and a r adiation condition f o r the ve lociti es, U and V. B eca u se of the fr ee passag e o f water mass through the eastern and southern open boundaries, t h e water volume in t h e model basin is not conserved In orde r to co nse r ve heat co ntent as well as mass in the basin we u se a r ela..'(ation correction sc h eme bas e d on volume transport thr ough t h e southern open boundary instead of a direct volume correction [McCreary et al., 1993], to fulfill the c onservati o n r equirement as illustrated in Figure 2.3 T h e m e ridion a l transports acr oss t h e southe rn boundary b efo r e and after the corre ction are d e noted as V o and V 1 = V 0 + 6 V respectiv e l y 10

PAGE 24

X Figure 2.3. The trans p ort cor r ec tion at the southern ope n bou ndary. Vo (sol id line) i s the transport before the correction sc h e m e, and V 1 (dashe d line) is t h e transport a ft e r t h e correct i o n sc h eme. The correct i o n va lu e of the current runnin g yea r 6 V is comp uted from t h e net, accu-mulate d transport of the prev i ous years through the open boundaries. The transport correction at each grid p o int i s lin e arl y proportiona l to its corresponding t ran spo r t befor e the correct i o n, V0 as s h o wn in the sc h ematic figur e of Figure 2 3 and t h e total correction at each time s tep i s con stant during eac h int egrating year. Water mass e n te ring t h e seco nd lay e r in t h e eastern porti o n of the southern ope n boundary is from a co l d southern source. Since t h e r e is a str ong exc hange o f heat and mass v i a detrainment betwee n t h e first a nd seco nd l ayer in the southe rn basin. the re s hould be a strong temperature gradient across t he boundary. U nder t hi s ci rcumstance the ze ro gradient o p e n boundary condi t i o n is no longer met. A fix ed tern -peratur e of T2 = l 5C i s c h ose n as the secon d layer temperature a l o n g t h e so uthern boundary acco rding to the obse r va tion [Wyrtki 1971]. 11

PAGE 25

2.2 Dynamic and Thermodynamic Formulation In the model formulati o n we apply nonlinear eq uations of motion and conservation of mass, heat and mom entum in sp her ical coordinates. In addition, conservation of turbulent kineti c e nergy is d esc ribe G by a modified Kraus-Turne r formulation. Momentum equatio n s in transport form are (la) and aVj 1 a (UjVJ) 1 a (UJtanB + ---+ --+ JU + ---"---"---at a cos(} a Hj a aB Hj 1 aHj +Wew(j) -We)+ i A(We)] = Hj aPj + ;:1 + r! pa aB J p (lb) where p-water density ; f Corio lis parameter (2S1 sin B); acoefficient of thermal expansion (0.00025C -1 ); g -acceleration of gravity (9.78ms -2); a -radius of the earth (6 3784 x 106m) ; r! are wind str ess components in east (), north (B) directions ; uj and Vj are vertica ll y integrated volume transports, defined as uj = fzi+1 Ujd z and Vj = J:j+1 Vjdz, where Uj and Vj are


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J:'' = A { 11. \J't ( v1 ) ) J 11. J 1 'Jf. [ v A 1 -2 + 2 5irJ o H1 :". (su1 )] } a r '(Jff 9 u.l/ J ( 2b ) w hnrc 11 (200()m,'t 111 ) i s iw 1:ddy ty ccHdfic.:ient; and for th e (mtrainment ( 3 ) w h ere t.hf: f o rwulations uf f:ntrainmtnt W11 and Wk used in this model are ()In those u s ed by McCreary ct al. [ 1993], a nd are discussed later in this section. The d cpthaveragcd h o rizontal pressure gradient in each layer i s where and the variables mth the subscription N are in the lowest layer. The vertically integrated form o f the cont i n uity eq uation is 8H1 fJt 1 8U1 tan 0 8\lj = A \72 H ..!.. H ,y, ( .) L} ::'} + ao h ) I e'j! J a cosu uo a a where .-\.h ( -t00m2s-l) is the diffusi,e coefficient for H i and ( 4 ) { 6 ) (ii] \Ve use thLs term ill the densit y equation to retain the integral propenies o n tr.hii:' density field by balancmng rbe d hergence o f a mean density fiu..x due to mesoscaire> 13

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eddies whi c h are removed by the coarse vertical layer average [Gent and Me Williams 1990]. Physically this diffusive term cau ses a net loss o f water mass. "vVe discuss the order o f mass r emovement in Section 3.2. Some special functions, which appear in the previous equations and will also be used late r are defined as and W(j) = { A(x) = { 1 j = 1 -1 j = 2 ) 0 j = 3 1 if X> 0 0 if X :S 0 ) = { 0 if X > 0 u X 1 if X= 0 (8a) (8b) (8c) Entrainment in the mixed layer i s determined by the interaction of cooling and solar heating through the sea surface and by the dynamical wind stirring. The temperature in the first layer is mainly controlled by sea surface heat flux and the entrainment between the first and second lay e rs. The temperature in the second layer decreases due to entrainment of its warmer upper water and increases due to detrainment of first-layer warmer water. Since no water and heat fluxes cross the interfaces between the second and third layers, the temperature in the third layer remains constant. So does the temperature in the fourth layer. The thickness and temperature of the mixed layer are oHm + 1 a ( U1 H ) V1Hm tan 0 + ( V1 H ) 8t a cos 0 a


PAGE 28

where Ar (2000m2s -1 ) is the temperature diffusive coefficient. When H m < H1 the fossil layer thickness and temperature are g iven by (5a) and 8TI + U1 8Tm = Ar\J2Tm + Qn 8t aH1 cos() 8 aH1 8() Hm -A(Ht-Hm)WkA (Wk) (Tm;;mTJ) (5b) \V'hen Hm = H1 the fossil layer does not exist and the thickness and temperature are defined as (6) The second layer temperature is given by (7) where the upper surface temperature of the second layer is ( 8 ) and its up-bound is T lvf We assume that the temperature in the second layer (spru:nning the thermocline) is changing linearly with depth. The temperature at t h e bottom is the same as the value in the third layer. The average temperature m l[be second layer is T2 whil e the temperature just beneath the first layer is Teas in (8). The temperature T e is used. instead of T2 when water mass entrains into l[]ne first layer from the second. Mixed-layer depth is determined through the interaction of upwellin g (or dol.'(1]]}welling) and entrninnwnt (or detrainment) [ P rice 1981 ; S chopf and Owe. 1983_. 15

PAGE 29

upw e llin g is primarily contro ll ed by a hydr ody nami c process while the entrainm ent i s determined by sea s urface wind stirrin g a nd cool in g as well as dir ec t h e a t input from so lar radiation. The modified formulations us e d in the model are bas e d o n tho se from K raus and Turn e r [1967] and M cCr e ary et al. [1993] The sum of w ind stir ring, solar radiation, sea s urf ace coo lin g, a nd ene r gy dissipa t i on g ives the net p r oducti o n o f turbulent kin etic e n ergy ( 9 ) where m (1.0) i s an adjustabl e paraml te r for deciding what portion of the wind e n e r gy contributes to mixin g turbulence; u. i s t h e friction v e locity at the sea surface; Variables Q R and Qn a r e the so lar radiation a nd net heat flux thro ugh the se a surface, respectively; A length scale /3 represents for the depth penetration o f s olar radiation QR. The heat p e n etrating into d epth needs l ess turbulent energy to carry it downw ard a nd effect iv e ly contributes positively to t h e t otal turbulence ener gy A heat dissipation param ete r c (1.0 x 10-10m2s -3 ) is us ed to account to the non linear energy dissipation in t h e vertical thermal e n e r gy convection [ G i ll and Turner 1976 ] Stronger dissipation occurs for deeper mixed layer. When P > 0, there i s mor e e n e r gy t h an n ee d ed to maintain t he current state of the mi.x.e d layer and then the mix ed -layer thickness is e x tende d a n d entrainmeDllt occurs at a speed o f p Wk =! H 2ag m ( lOa ) The temperature difference, i s assigne d as the difference benYeen t he temperature Tm and the temperature ( T1 o r T e ) dir ectly beneath it. we tak e t h e condit i o n D..T ;::: 4 C to a\oid unrealistically strong entrainment When P < there is not enoug h turbul ent energy to maintain the mixed l ay& at its c urrent depth The po t e ntial r educt i o n of the mix ed -l ayer depth is e \'alua ted from 1 6

PAGE 30

the Monin-Obukhov ene r gy balance by setting P = 0. The detrainment (sha llowing ) occ urs at a velocity of (lOb) where H; is the mixed-layer thickness at the previous time step. When strong solar radiation and weak wind stirring occur a minimum mixed layer Hmin =30m is set to avoid a mix e d lay e r that is too s hallow and may lead to w rong mixed-layer physics. When the mixed-layer depth is H m < Hmin: the water mass in the second layer i s forced into t he first layer by t he entrainment velocity W HminH; k 2.6.t ( 10c ) Whe n the subduction of the upper layer occ urs the decr ease of the mix e d layer is usually faster than that of the whole first layer. A fossil layer i s c r eated at this time. When the net heat input through the sea s urfac e is positi ve and the first l ayer depth (HI) is greater than its initial value (Hd = 80m) a slow detrainment of the first laye r is used to r e lax H1 back to Hd, as (11) where Q0 ( = 40W) is a sca le parameter of the mean heat flux into the ocean; td (180days) is an adjustable time sca l e to control the detrainment spee d The heat input from the sea surface is the sum of four parts, including incoming solar s hortwave radiation outgoing long wave radiation, latent heat flux and sensib le heat flux. The net heat ga in in t h e model can be calculated by (12) where Q R and Q B are the incomin g s hortwav e radiation from t h e sun and t h e outgoing lon gwave radiation from the ocean r espect iv e ly; and Qs and QL are sens ibl e heat flu.x 17

PAGE 31

(heat conduction) and latent heat flux (heat evaporation) respectively The sensible heat flux, caused by the difference between air temperature and SST (se a surface temperature), is given by (13) where Csdrag coefficient (0.001), Cpa specific heat capacity for air (1012Jkg_1oC_1 ), Vs -scale wind speed, Pair-air density (1.2kgm-3). The latent heat flux caused by sea surface evaporation with non-saturated air specific humidity is given by (14) where CLdrag coefficient [C L = 0.0015 + 0.00033(Tm Ta) and 0.001 < CL < 0.002], L -latent heat of evaporation of water (2.44 x 106Jkg-1), qa -air specific humidity, qm -saturated specific humidity at SST which is expressed as where and 17.3T e5 = 6.1078eT+235, 18 (15a) (15b)

PAGE 32

K,parameter (0.62197) P air pressure (1013 mbar) e5 saturated water-vapor pressure. The wind stresses mentioned in (la) and (lb) are expressed as (16) where Co (0.0014) is a wind stress coefficient and V 10 is wind velocity at 10m above the sea surface. Equations (13)-(16) are bulk aerodynamic equations (Bunker, 1976]. The mean meridional heat transport through any east-west section for each layer can be expressed as (17) If we define Ti = Ti + T/ and Vj = Vj + Vj', where Ti and Vj are temporal means of T and V ; T' and V' are their anomalies, the mean meridional heat transport can be separated into two parts as (18a) where Cpw is the specific heat capacity of sea water. The two terms in the parentheses represent the meridional heat advection by the temporal mean and the temporal effect of eddy components respectively. Comparing these two terms we can find out whether this temporal eddy effect which represents the integrated local eddy contribution is important for the meridional heat transport and its contribution to the heat budget in the Indian Ocean. Similarly, if we let Ti =< Ti > +Ti* and Ti =< Vj > +Vj*, where<> represents zonal average along a east-west section; < Ti > and < Vj > are spatial averages of 19

PAGE 33

T and V; T* and V* are their anomalies the average meridional heat transport can also be expressed as (18b) wh e re X is the width of the section (J:2 a cos (}d
PAGE 34

sensible heat flux The bulk aerodynamic e quations are employed to compute the wind stress, latent heat flux and sensible heat flux The model results under climatological and interannual forcing are discussed in the next two chapters, resp ect ively 21

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CHAPTER 3 SEASONAL VARIABILITY In this chapter we discuss the results of the model integration under the clima tologic a l forcing fields d e rived by Rao et al. [1989, 1991], the same forcing fields as used in McCreary et al. [1993] model. The model circulation fields begin to stabi lize after 10 years of integration forced b y a repeating annual cycle of climatological monthly-mean atmospheric and thermal fields. To collect long-term statistics on model stability, the integration is continued for a total of 50 years. Selected model results from the fiftieth year's output are discussed in this chapter. These include the solution's dynamic and thermodynamic fields, meridional heat transport, and heat transport through the open boundaries. The basin-wide fields are discussed with some comparison to the observations in Section 3.1. The heat budget of the Indian Ocean is described in Section 3.2. A summary of this chapter is given in Section 3.3. 3.1 Annual Cycle in Model Fields Monthly-mean climatological wind fields of the northeast and southwest monsoons are shown in Figure 3.1. In January, winds ex hibit the t y pical northeast (boreal winter) monsoon pat tern, with northeast winds across the Arabian Sea and the Bay of B e ngal, and southeast trade winds across the southern basin A band of less strong westerly (eastward) winds exists along latitud e 5S in the c onvergenc e between the 22

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monsoon winds and the trade winds. This wind pattern is comparable to the wind patterns of the Pacific and Atlantic. In July typical southwest (boreal summer) mon soo n, the southern Indian Ocean trade winds stre ngthen while the winds revers e direction in the Arabian Sea and the Bay of Bengal. The strongest winds occur over the Arabian Sea, reaching speeds of over 15 ms-1 in the monthly mean [ Hastenrath and Lamb, 1979a]. It is this southwest monsoon wind pattern that drives a unique Indian-Ocean circulation system. We focus on the annual cycle of model fields response to the driven forcing in this section. We organize this section into two subsections; the dynamic and thermod y namic fields are discussed in Section 3.1.1 and Section 3.1.2 respectively 3.1.1 Dynamic Fields The Figures 3.2a-3.2f show bimonthly the model velocity fields o f the first layer. They are qualitatively comparable to those in ship drift observations [Cutler and Swallow 1984 ; Rao et al., 1989 1991) and reproduce most of the known observed features of the upper Indian Ocean circulation. In January the South Equatorial Current (SEC) flows between latitude 10 S and 15 S, splitting at the Seychelles Mauritius Ridge, with the northward branch feeding the northward East African Coastal Current (EACC). The North Equatorial Current (NEC) flows along 2 N, feeding into the southward Somali Current The EACC and Somali Current meet at 23S and flow eastward into the South Equatorial Counter Current (SECC) This current pattern maintains until mid-March with only the NEC becoming weakened due to the weak winds over the northern basin at that time. The current pattern corresponding to the southwest monsoon begins to be established in April. The model reproduces the observed reversal in the Somali Current system with t he transition from the northeast to southwest monsoons. In May, the SEC and EACC 23

PAGE 37

25N 20N 15N ION 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 'OE BOE 90E lOOE llOE 0 .200+02 IUXIliUll VECTOR (a) January 25N 20N 15N ION 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE I!OE 0 .200+02 IUXIliUll VECTOR (b) July Figure 3.1. Monthly mean wind velocity (ms-1 ) fields in January and July from COADS data, repr ese nting the winter (Northeast) and summer (Southwest) mon soon wind fields, respectively. strengthen to feed a northward flowing Somali Current across the equator which reaches well into the northern h emis phere. An eastwa rd Wyrtki (1973] jet also exists along the equator in April and May driv en by the westerly winds during the monsoon 24

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transition. 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50 E 60E 70E BOE 90E lOOE llOE O .IOOE+ OI WAXIII11W VECroR Figure 3.2a. The first layer vel ocities (ms-1 ) in January. 25N 20N 15N lON 5N EQ 55 lOS 15S 20S 255 40E 50E SOE 70E BOE 90E lOOE llOE O .IOOE+ OI WAXIII11W VECTOR Figure 3 .2b. The first l ayer velocities (ms-1 ) in March. The upper-layer velocity field in July shows the classical southwest monsoon circu l ation pattern in the Indian Ocean [Knox, 1987 ; Ha stenrath and Greis char 1991]. A two-g y re system in the summer Somali Current exists as observed be twee n 2 3 S and 10 N. The southern gyre of the two-gyre system forms as a recirculation on the 25

PAGE 39

25N 20N 15N tON 5N EQ 5S lOS 15S 20S 25S 40E 50E 6 0E 70E 80E 90E lOOE llOE O .lOOE+Ol IWCIIIUII VECTOR Figure 3.2c. The first layer velocities (ms-1 ) in May. EACC originally south of the equato r while the great whirl forms to the north of 2 -3 N in response to the local along-shore winds. Flow from the .great whirl enters the Southwest Monsoon Current which crosses the Arabian Sea. By late July, the Socotra Eddy begins to form to the north and east of the great whirl but distinct from it [Swallow and Bruce, 1966; Bruce 1979 ; Luther et al., 1985]. Flow exits the. Arabian Sea between peninsular India and the Maldives feeding a strong eastward current south of Sri Lanka (across 80 E) into the Bay of Bengal. Southwestward flow exits the Bay of Bengal and crosses the equator to the east of 70 E and merges into the SECC which flows eastward along 5S and ultimately feeds into the westward SEC. At this time, the SECC only exists to the east of 70 E. A portion of the outflow from the Somali Current two-gyre system recirculates to the west of 70 E across the equator and to the east and south of the Seychelles, also merging into the westward SEC. The SEC in turn feeds the northward EACC along the western boundary which crosses the equator back into the Somali Current system. B y late August and into September, the southern gyre of the two-gyre system 26

PAGE 40

25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S ....... .... ....-.................... ..... "\'-\."--... .................. .... ....... ................ .. ''",."a ,. ... ,,. ...................... -----=---,.,., ...... ,,. ........................ :.:.:: ............... .6 ,. ,. ,. .. a.-..................... 40E 50E 60E 70E BOE 90E lOOE llOE O.IOOE+OI IUXDIUII VECTOR Figure 3.2d. The first layer velocities (ms-1 ) in July. moves northward to merge with the great whirl and their associated cold upwelled wedges merge too, as observed by Brown et al. [1980]. Cross equatoria l flow is strongly modulated by equatorial waves during August through October. The SECC begins to strengthen and extends across the entire basin by mid-September. During October, the great whirl decays via baroclinic instability [Jensen, 1991] and can no longer be seen in November, although remnants of the Socotra Eddy are still present. The win -ter Somali Current pattern appears in early December with southward flow extending from 7 N to just south of the equator by the en d of the month. The southward flow-ing Somali Current is fed from the interior by the westward NEC. To the north of 7 N and to the south of 2 3 S, the current still flows northward. At 2 3 S the southward Somali Current and northward EACC turn into the interior to feed the SECC Velocity fields of January and July in the second layer in Figure 3.3 shows typically undercurrent patterns in the thermocline for the northeast and southwest monsoons. In January, an eastward e quatorial undercurrent ex ists along the equator, 27

PAGE 41

25N 20N 15N l O N 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E lOOE llOE O .IOOE+Ol IWCilll1ll VECTilR Figure 3.2e. The first velocities (ms-1 ) in September. 25N 20 N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E lOOE llOE O.IOOE+Ol IWCilll1ll VECTilR Figure 3.2f. The first layer velocities (ms-1 ) in November. similar to the other two oceans This undercurrent is initiated by the end of Decem-ber to the east of the Maldives on the equator is fully developed to cover the whole equatorial Indian Ocean b y mid-February, and decays away beginning in April with the onset of the southwest monsoon A westward undercurrent along the equator is initiated from e astern boundary m late April and propagates westward reaching 28

PAGE 42

the western boundary in late June. In July however, eastward flow is seen from the Maldives to the Sumatra coast Beginning in late August until late October large amplitude antisymmetric oscillations are found in the western half of the basin with strong cross-equatorial velocities characteristic of mixed Rossby-gravity (Yanai ) waves These waves have westward phase propagation and eastward group propaga tion The deep signature of the Somali Current, the EACC, SECC and SEC are seen throughout the year, mimicking their upper layer counterparts. The two-gyre system of the southwest monsoon Somali Current is apparent as is the Socotra Eddy The great whirl disappears by December much later than in the upper layer, and the northeast monsoon Somali Current is southward all along the Somali c oast north of the equator in January and February in opposition to the upper layer flow. Large amplitude, westward-propagating oscillations are seen in the SEC-SECC system. The velocities in the third layer in Figure 3.4 show the deep-water current patterns beneath the thermocline Since there is no mass and momentum exchange across interface between the second and third layers the currents in the third layer are strongly controlled by geostrophy. Equatorial and extraequatorial planetary waves dominate the evolution of the velocity and interface depth fields The first layer thicknesses in January and July are shown in Figure 3.5a. Strong upwelling occurs in July, associated with strong coastal current near the Somali coast and along the western coast of peninsular Indian These unique upwelling features are distinctively related to the southwest monsoon. The ridge in the thermocline along 5S is much shallower east of the Seychelles in January than in July consistent with changes in the SECC. Layer thickness increases in the eastern tropical region due to downwelling Kelvin waves associated with the Wyrtki Jets during both monsoon 29

PAGE 43

25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E lOOE 110E 0.400+00 II.UDlUiol VECTOR (a) January 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E lOOE 110E 0 .400+00 II.UDlUiol VECTOR (b) July Figure 3.3. The second-layer vel ocities (ms-1 )in January and July, representing the current patterns in the northeast and southwest monsoons respectively in the thermocline. transitions. The reflection of these equatorial waves alters the distribution of layer thicknesses off the equator and away from the eastern boundary. In bot h January and July, the average first-la ye r t hickness is greater in the southern basin and shallower 30

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 5 0 E 60E 70E 80E 9 0 E lOO E llOE 0 .100+00 liAXIIIUll VECTOR (a) January 25N 2 0N 15N lON 5N E Q 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E lOOE HOE 0 .100+00 IWCIIlUII VECTOR (b) July Figure 3 4. The thirdl aye r ve l ocities (ms-1 ) in Janu ary and July, representing the current patterns in the northeast and southwest monsoons respective l y beneath the thermocline m the north basin, consistent with downwelling in the southern basin and upwelling in the northern basin The thickness distr i butions in the second layer, shown in Figure 3 .5a, are dynami-3 1

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E lOOE llOE (a) January 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E lOOE llOE (b) July Figure 3.5a. The first-layer thickness (m) in January and July, representing the layer thicknesses in the northeast and southwest monsoons respectively. cally related to the upper layer thickness, while their differences between January and July are not as significant as compared to the differences in the first layer thicknesses. In both January and July the thinnest areas occur along 10 S and in the Bay of Bengal while the thickest area is in the western basin near the southern boundary Although a thicker second layer corresponds locally to the strong upwelling areas of 32

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the first layer the average second-layer thickness is also greater in the southern basin and less in the northern basin similar to the distribution of the first layer thicknesses. This thickness distribution implies that the downwelling in the southern basin and upwelling in the northern basin extend through the second layer and deeper into the third layer, which is against the initial assumption that exc hange of water mass is not allowed between the second and third layers. The third layer shown in Figur e 3.5c, is a compensating layer for the upper layers typically decreasing in thickness when layers 1 and 2 are increasing and vice versa Since there is no mass exchange between the second and third layers in this model, this indicates a predominance of the secon d baroclinic mode as indicated by Gent et al. [1983]; Jensen [1993]. 3.1.2 Thermodynamic Fields Cooling (and heating) through the sea surface is one of the dominant factors that determine the mixed-layer thickness Figure 3.6 shows the net heat fluxes through the sea surface for the northeast and southwest monsoons, respectively. During boreal winter, cooling occurs in most areas of the northern basin due to both less direct solar radiation and the strong winds of the northeast monsoon. However more heat from direct solar radiation enters the southern basin during the this period. During the southwest monsoon cooling occurs in the southern basin due to less direct solar radiation. The different net heat inputs through the sea surface between the northern and southern basins will be discussed later in this section. Figure 3. 7 shows the mixed-layer thickness typically for the northeast and south west monsoons respectively. In spite of higher solar radiation input, the strong wind of the southwest monsoon still causes a net heat loss in the northern basin. The strong cooling leads to a deep mixed layer in the southern basin and the strong upwelling 33

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25N 20N 15N 1 0N 5N E Q 58 lOS 1 58 2 0 S 2 5 S 40 E 50E 60E 70E BOE 9 0 E 100 E 110E (a) January 25N 20N 15N lON 5N EQ 58 l O S 1 5 8 2 0 S 2 5 S 40E 50 E 60E 70 E BOE 9 0 E lOO E llOE ( b ) Jul y Figu r e 3.5 b The seco n dl ayer thickness {m) in January and July, rep r esenting the layer thicknesses in the no r t h east and southwest monsoons, respective ly. ca u ses a shallow mixed l ayer along the Somal i coast and a l ong 5 S in the western par t of the basin. The distr i bution of mixed -l aye r thickness i n Januar y shows deeper va l ues in the north and shall ower va lues i n the south associated wit h the n et heat input through the sea su r face. Fig u res 3 8 AND 3.8 shows the d i stributions of the mixed -l ayer and sea surface 34

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE (a) January 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE 110E (b) July Figure 3.5c. The third-layer thick n ess (m) in January and July, representing the l ayer thicknesses in the n ortheast and southwest monsoons r es pectively. temperatures respectively. We still plot the data fields in January and J ul y to represent their distributions in the northeast and southwest monsoons The highest temperature area moves southward in the boreal northeast and northward in t he summer, following the mov e ment of the peak solar radiation input. The distribution of the mixed-layer temperature matches the field of observed SST although cold 35

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25N 20N 15N lON 5N EQ 55 lOS 155 205 255 40E 50E 60E 70E 80E 90E lOOE 110E (a) January 25N 20N 15N lON 5N EQ 55 lOS 155 20S 255 40E 50E 60E 70E BOE 90E lODE llOE (b) July Figure 3.6. The net heat input fluxes (wm-2)through the sea surface in January and July representing net heat flux pattern in winder and southwest monsoons respectively. wedges associated with the two gyre system i n the Somali Current merge only in the model 's mixe d-lay er temperature field Figure 3.10a shows the spatial distribution of the temporal correlation coefficient, r2 between mode led mixed-layer temperature and observed climatological SST. The model output and observation are highly corre lated over most of the basin except near 36

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE (a) January 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE (b) July Figure 3. 7 The mixed-layer thicknesses (m) in January and July, the typical mixed-layers in northeast and southwest monsoons respective ly. the Somali coastal zone where strong upwelling causes low temperatures with sharp spatial g r adients and large temporal variability during the southwest monsoon in the model. These sharp gradients are observed in SST fields for individua l years [Evans and Brown 1981; Brown et al., 1980) but are not captured in the climatological monthly mean fields. Figure 3.10b shows the root mean square of the difference 37

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E lOOE llOE (a) Januar y 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E lOOE llOE (b) Jul y F igure 3 .8. The Mixed-layer temperature (C) in January and July, for repre sent ing the northeast and southwest monsoons respectively betw ee n mixed-layer temperature and the observed SST. Despite the fact that the mixed-layer temperature has a strong annual cycle, the distribution of temperature in the second layer is comparati vely steady. Comparing the temperature distributions of the second layer between January and July, as illus-trated in Figure 3.11, we can see that the in c rease of the mixed layer thickness in the 38

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lODE llOE (a) January 25N 20N 15N lON 5N EQ 5S lOS l5S 20S 25S 40E 50E 60E 70E BOE 90E lODE llOE (b) July Figure 3.9. The observed SST (C) in January and July, representing the SST fields in northeast and southwest monsoons, respectively. southern basin causes entrainment of warmer water of the upper second layer into the first layer and s li ghtly reduces the vertical average temperature of the second layer along 10 S during the southwest monsoon. The detrainment occurring during t he northeast monsoon in the southern basin causes the dumping of warm water from the first layer into the second layer which increases the temperature of the second layer. 39

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25N 20N 15N lON 5N EQ 5 S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE Figure 3.10a. The correlation coeffic : ent of the SST. The spatial distribution of the temporal correlation are calculatec : between the mixed-layer temperature and the observed SST 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE Figure 3 .10b. Difference of the SST. The the r oot mean square of difference is calculated between mixed-layer temperature and the observed SST 3.2 Heat Budget in the Indian Ocean In this section, we focus on the annua l cycle and annual mean of the Indian Ocean heat budget. To do this, we first analyze the annua l-m ean heat budget in Section 3.2.1 and then discuss the annual cycle of heat fluxes and transports through differ-ent interfaces and sections including heat flux through sea surface, meridional heat transport across equator zona l heat transport across 80 E section between the equa40

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E lOOE llOE (a) January 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE 110E (b) July Figure 3.11. The second layer temperature (C) in January and July, the typical distributions in northeast and southwest monsoons, respectively. tor and the north boundary, the heat exchange between the first and second layers and the heat transports through both the eastern and southern open boundaries in Section 3.2.2. Both temporal and spatial variations of the meridional heat transport across equator are discussed in Section 3.2.3. 41

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3.2.1 Annual Mean Heat Budget Shown in Figure 3.12a is a schematic diagram of the annual mean heat budget for the northern and southern basins. Oceanic heat transport is accomplished by a vertically-overturning circulation, with a net upward heat transport via entrainment in the northern basin driven by the southwest monsoon and a net downward heat transport in the southern basin via detrainment. Warmer water is carried southward in the first layer while colder water is carried northward in the second layer resulting in southward and northward heat transport in the first and second layer respectively. Heat gained through the sea surface and through entrainment in the northern basin is carried southward into the southern basin, where additional heat is gained through the open boundaries. A portion of this heat is lost to surface cooling, while the remainder enters the second layer via detrainment. In the second layer, most of the heat detrained from the first layer in the southern basin is carried into the northern basin while the remainder is carried out of the Indian basin across the southern open boundary. In the second layer of the northern basin heat from the south is transported upward via entrainment, to close the meridional overturning circulation. The net heat gain in the first layer through the open boundaries may not precisely represent the heat transport process of through flow in th Indian ocean The the layer thickness diffusion effect, as we described for (6), removes the water mass at an average rate of O.lM/Year in the first layer throughout the modeled basin. This net loss in the water mass reduces the southward mass transport across the southern op e n boundary. In addition the removal of water mass may be non-negligible to the heat budge in the Indian ocean Further study is necessary to decrease the diffusion coefficient of the layer thicknesses and hence to reduce the rate of removal of the water mass. 42

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Unit: 1 O"W NET HEAT OUT 1.1 NET HEAT IN 1.4 t EQ Net -in through LAYER 1 East Boundary 1.0 j_ ...,.---2.9 DETRAINMENT 2.8 1 t 1 LAYER 2 Net -out throug h I South Boundary 1.3 1 ENTRAINMENT 1.5 I --------------i---------------z L:UTH BASIN q (North) 1 I I I NORTH BASIN Figure 3.12a. Heat budget of the who le Indian basin. The heat budget for the northwest Indian Ocean (the Arabian Sea) is illustrated in Figure 3.12b Comparing to the values in Figure 3.12a, we not e that the net heat input through the sea surface and the heat exchange between the first and second lay ers in the Arabian Sea dominate the heat budget of the enti re northern Indian Ocean In the first layer only a small portion of the heat transport across the equator occurs between the western boundary and goo E while most of the heat is transported eastward across goo E between the equator and Sri Lanka, and then across the equator to the southern basin between goo E and the eastern boundary In the second layer however, the net northward heat transport mainly crosses the equator between the western boundary and goo E, and then moves upward through entrainment with only a small portion of it moving eastward. The distribution of meridional heat transport are plotted against latitude in Figure 3.13. The zonally-integrated meridional heat transport can be calculated at differ-ent latitudes by tempo ral averaging of (17). The total heat transport can be divided 43

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Uni t : lO ,. W SOMAU A KENYA EQ J' 2.1 .. \( .03 .. ., INDIA Figure 3.12b. Heat budget of the northwest Indian basin (Arabian Sea). into advection either by temporal mean and temporal effect of eddy components as in (18a) or by overturning and horizontal gyre components as in (18b). The temporal mean heat transport is obtained via temporally averaging on temperature and merid ional volume transport separately and then spatially integrating their product, while the overturning heat transport is obtained via spatially averaging on the temperature and the meridional volume transport separately and then temporally averaging their product. The temporal mean component is closer to the total heat transport and the difference between them, the tempora l eddy effect is extremely small. The horizontal gyre effect to the meridional heat transport is the difference between the total and the overturning t ransports which is stronger than the temporal e ddy effect through most sections. The largest difference occurs south of 20 S due to the Indonesian throughflow 44

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5 ,---... :! 0 0 .......... X -5 ::> _j Total LL. 1--10 ........ Overturning <( w ___ Advection I -30 -20 -10 0 10 20 30 LATI TUDE () Figure 3 13. Meridional heat transports across the whole basin. The yearly averaged total flux and its components of overturning and advection are plotted against the latitude. Strong eddy patterns associated with equatorial waves are found along the equator. The temporal eddy effect is less than 1% of the total heat transport implying that the local eddy effect. However the horizontal gyre effect, including the spatial contribution of small-scale eddies and large-scale gyres, is much stronger, contributing 7.2% and 6.0% to the total meridional heat transports across the equator in the first and second layer s, respectively. The ratio of heat transport by small-scale eddies to the total horizontal gyre effect is shown in Figure 3.14. The accumulated eddy contribution increases with the eddy's maximum spatial scale until reaching the size of 12 (1200km). The spatial distance of the 1200km is the same as the ed dy decorrelation distance we obtain from the correlation coefficient analysis. The eddy contributions to the total heat transports are 4.9% and 3.0% for the first and second layers, respectively 3.2.2 Annual Cycle in Heat Flux and Transport Net heat flux through the sea s urface is spatially integrated over the northern (north of the eq uator) and southern basins sepa rately, with the total heat input as 45

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100 80 "" .., 60 u cu .... .... tol >. 'tl 'tl tol 40 2 0 0 0 5 ...... ----__ .............................. --------F irst Layer -Second Layer ----1 0 15 2 0 25 30 3 5 Spacial Eddy S c ale (Degree) 40 F i g ure 3.14. Ratio of eddy contribution to the total horizontal gyre effect. The increase of eddy contribution is dramatically reduced at the scale of 12 l ongitude. a function of time shown in Figure 3 15a. From the time series of the heat input to the northern basin we see that the net heat input is strongly affected by the monsoons. From mid-November through the end of January, net heat output and strong cooling of the sea surface occur. Reduced solar radiation decreases the direct heat input over this period and the increase in wind strength of the northeast monsoon enhances evaporative cooling and provides more turbu l ent energy During the southwest monsoon although the wind strength reaches its maximum the net heat output is not as strong due to the simultaneous increase of solar radiation. In spring and fall monsoon transitions, net heat input occurs from February through May and from August through October due to decreased evaporative heat l oss resu lting from the weaker winds. Since the strengths as well as the directions of the winds are comparatively steady in the southern basin direct solar radiation becomes the dominant factor in the heating or cooling process. From the time s eri e s of heat input for the southern basin in Figure 3.1 5a, we see that the maximum net heat input and output occur in the boreal winter and summ e r, respectiv e ly, while the transition from net input 46

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,....... J!:-0 .-'---" X :::J ..... 0 Q) I 30 2 0 1 0 0 -10 I I / / I / --7 ------/ ' \ __ Nort h Bas i n ___ S o u t h Basi n \ \ Jan Feb Mar Apr May Jun J u l Aug Sep Oct No v Dec Jan Month Figure 3 1 5 a Sea-surface Heat fluxes in the northern and southern basins. The heat fluxes (1014W) are integrated over northern and southern basins separately. Positive values indicate outward heat fluxes from the sea water into the air. (output) to output (input) occurs in the spring (fall) months. Net heat flux through the sea surface is totall y d i fferent between the northern and southern basins. In contrast to the net heat flux through the sea surface, the integrated net heat exchange between the first and second layers has similar seasonal variations for the northern and southern basin as illustrated in Figure 3.15b The heat exchange is associated with entrainment and detrainment across the interface between the first and second l ayers. From mixed-layer physics, we know that mixedl ayer depth is strongly affected by wind and net heat flux at the sea surface. Strong southwest monsoon winds in the northern basin cause strong entrainment due in part to direct wind stirring and to sea surface cooling which causes convective overturn ing and increased mixed-layer depth, and in part due to the curl of the monsoon wind stress which creates strong upwelling or downwelling through Ekman pumping. Downward heat transport associated with detrainment dominates only during spring in the northern basin, while detrainment dominates most of the time in the southern basin, except during the summer and early fall when strong southwest monsoon winds 47

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......... t:-0 ..__, v cr> C 0 ..c u X w ....-0 v I 40 20 I 0 / / / -20 / / -40 I I I I '. __ North Bas i n ', _ Sou t h Bas in \ \ \ ----""-,-----=-=-= \ \ / Jan Feb Mar Apr May J : Jn Ju l Aug Sep Oct Nov Dec Jan Mon t h Figure 3.15b. Heat exchange betwe e n the first and second layers The heat exchanges (1014W) are calculated over northern and southern basins, separately Positive values indicate upward heat transports from the second layer into the first layer. and decreased solar radiation l ead to deep mixed-layer and allow entrainment to dominate. Yearly-averaged heat transports are upward and downward in the northern and southern basins, respectively. Integrated heat transport across the equator over the annual cycle in the first and second layers is shown in Figure 3.15c. Heat transport is strongly driven by the reversing monsoons. Northward heat transport during the northeast monsoon and southward heat transport during the southwest monsoon occur across the equator in the first layer In the second layer the heat transport is in the opposite direction to that in the first layer. Southward heat transport dominates in the first layer while heat transport is predominantly northward in the second layer. The cross-equatorial seasonally-averaged heat transport during the southwest monsoon is comparable to the corresponding result of Hastenrath and Greischar (1993] from July to October while the heat transport in May and June is much weaker in the mod el. In addition the northward cross-equatorial h eat transport is stronger in the model during the northeast monsoon ; therefore we obtain a smaller annual mean cross-equatorial heat 48

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.,...._ ;:. 0 '--' ....-'-0 0... (/) c 0 '-1-....-0 Q) I 20 1 0 0 -10 -20 Jan __ Layer1 -Layer2 \ .\ \.-..I / . _J '/ .\' '.'\'''/ --:.. .. -..:. .:.:-:....-.. Feb Mar Apr May J un Ju l Aug Sep Oct Nov Dec Jan Month Figure 3.15c. Across-equatorial heat transports. The meridional heat transports (1014W) across equator sections are integrated in the first and second layers sep arately. Positive values indicate northward cross-eq uatorial heat t ransports from the southern basin into the northern basin transport in the model. The calculations of Hastenrath and Greischar [1993] were based on the surface ship observation and surface temperature casts to 400 m, while the mod e l calculations are from the mixed layer and thermocline layer which typically span the upper 250 m of the water column at the eq uator. The int egrate d heat transport across a section at 80 E between the equator and the northern boundary is shown in Figure 3.15d. Heat transport is mostly eastward in the first lay er, except for a short period during the northeast monsoon. The north equatorial current contributes to westward heat transport from the beginning of December to the end of March. The strongest heat transport occurs when the weakest north eq uatorial current (NEC) occurs during May. During most of the southwest monsoon the integrated eastward heat transport is not as stro ng as in May due to the ex istence of the NEC, eve n though the flow is very strong b etwee n India and the Maldives. In the seco nd layer the heat transport across this section is in the opposite direction to that in the first layer during most of the yea r but its low amplitude contributes little to t he heat budget of the Arabian basin. 49

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0 ......_ 0 0... (J) c 0 .._ f-20 10 0 __ Layer1 -Layer2 ...--10 0 v I Jan Feb Mar Apr May Jun Jul Aug Sep Oct No v Dec Jan Month Figure 3.15d. The longitudinal heat transports across sao E section. The heat transports (la14W) across se c tion at sao E are integrated in the first and second layers separately. Positive values indicate eastward heat transports across the sao E section from the Arabian Sea into the Bay of BengaL There is significant large amplitude time variability in heat transport across the equator and across sao E. Heat transport across the equator in the first layer shows a strong annual cycle and is northward from November to April and southward from May through October, with heat transport in the opposite direction in the second layer. Higher frequency oscillations with periods of 20 to 30 days are seen from mid July through October. These oscillations in meridional heat transport are driven by equatorial mixed Rossby-gravity waves as seen by Tsai et al. [1992]. Similar variability is seen in heat transport across sao E, with annual, semiannual, and higher frequency signals present. The semiannual signal is the result of equatorial Rossby and Kelvin waves which are nearly resonant in the Indian Ocean as shown by Jensen [1993]. Advection through the open boundaries carries a great amount of heat Heat transport spatially integrated along the open boundaries is illustrated in Figure 3.16 for the first and second layers. Net heat transport is always inward (westward) through the eastern boundary and outward (southward) through the southern boundary. Through the eastern boundary, strong heat transport in both layers occurs during 50

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the southwest monsoon and comparatively smaller peak va lues occur for the north east monsoon The relation betw e en variations of heat transport through the eastern open boundary and the monsoon reversals is through the equatorial wave guide and the Indonesian coastal wave guide, leading to a delay of one to two months between the peak of the southwest monsoon and heat gain through the boundary Comparing the heat transport through the southern and eastern boundaries for the first layer we see a six month delay between their peak values 3.2.3 Heat Transport Across Equator Interesting wave patterns along the equator are seen in Figure Figure 3.17. In the first layer, strong mixed Rossby-Gravity (Yanai) waves are initiated in May with the onset of the southwest monsoon and continue through the southwest and north east monsoons unti l February of the following year, with the dominant wave pattern beginning at the end of the southwest monsoon. These waves have eastward group velocity of 0.66ms-1 and westward phase speed around 0 .12ms-1 between October and January. These waves are exited by the strong eddying motions in the Somali Current during the late phase of the southwest monsoon as in Kindle and Thompson (1989). The wave pattern in the second layer is similar to that in the first layer though with much lower amplitude. The westward propagating phase speed is larger (0.56ms-1 ) and the group speed is slower (0.41ms-1 ) than the values in the first layer. The role of these waves in cross-equatorial heat transport needs further study. 3.3 Summary The model faithfully reproduces obser v ed variability in SST and conserves heat over a long-t e rm integration; therefore, we may conclude that the model circulation balances heat in some reasonable way consistent with the model physics In the 51

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0 ..... 1... 0 0... (/) c 0 1... f--0 -2 -4 -6 ..,. _ .,., __ Layer1 ____ Layer2 / .. # ................ ___ / .. _ ........ 0 -8
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40E 50E 60E 70E 80E 90E lOOE llOE (a) The first layer 40E 50E 60E 70E 80E 90E lOOE llOE (b) The second layer Figure 3.17. Schematic diagram of the vertically integrated heat fluxes (108wm-1 ) of the two layers across the equator versus time are shown in (a) the first layer and (b) the second layer. the first layer and northward in the second layer. The heat transported southward has two fates in the southern basin with a portion being pumped into the second layer by 53

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detrainment process and a portion being lost to the atmosphere through latent heat flux Part of the heat detrained from the first layer into the second is transported northward in the western half of the basin and then is entrained upward into the first layer, primarily in the Arabian Sea, while the remainder is carried out through the southern open boundary in the second layer. Overturning in the meridional plane is the primary mode of the heat transport, with only about 7 % c ontribution from t h e horizontal gyre effect. Significant large amplitude time variability in heat transport is seen across the equator and across 80 E. This variability is modulated by e quatorially-trapped waves at annual semiannual and 20 to 30 days periods. The higher frequency oscillations in meridional heat transport are driven by equatorial mixed Rossb y -gravity waves as seen by Tsai et al. (1992]. The semiannual signal is the result of equatorial Rossby and Kelvin waves, which are nearly resonant in the Indian Ocean as shown by J e nsen [1993]. This time variability has implications for constructing a heat budget for the basin from hydrographic sections that are occupied only once or that take longer than 20 days to complete as in the WOCE Hydrographic Program. The model in its present form gives reasonable results to explain the seasonal heat budget of the upper Indian Ocean As Knox [1987] pointed out in his concluding remarks, it is the interannual changes in the typical monsoon cycle that disturb the lives of people in this region. Based on an understanding of the c limatological seasonal variability, we c an further investigate and understand the interannual variability in Indian Ocean circulation and heat budget. In addition the simplified formulations for the complicated mixed-layer physics needs further impro v ement. Work is in progre s s to addre ss both these issues 54

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CHAPTER4 INTERANNUAL VARIABILITY In the previous chapter, we described the model integration responding to clima tological monthly-mean forcing, termed climatological integration for short. In the annual cycles of the mod e l fields, we simulated most of the major observed features in Indian Ocean circulation. However as Knox (1987] pointed out in his concluding remarks it is the interannual changes in the typical monsoon cycle that disturb the lives of people in this region Based on the understanding of the climatological an nual cycle, we further try to investigate and understand the interannual variability in Indian Ocean circulation and heat budget in this chapter. We concentrate on a real-time experiment by integrating the model under an interannual monthly-mean forcing for a period of thirty years (1960-1989) We refer to this as to interannual integration to differentiate it from the climatological integration David Legler et al. of the Florida State University provide the forcing data which are originally from the GOADS data set [Slutz et al., 1985; Legler et al., 1989; Jones et al., 1995] In order to simulate higher eddy resolution we reduce the coefficient of eddy viscosity to 1000m2s-1 (instead of 2000m2s-1); effectively, this change reduces th momentum removal in the equation. Correspondingly, we choose a smaller wind friction coefficient (0.001 instead of 0.0014) to reduce the momentum input of the winds and to maintain the steadiness of the model integration. Except for these changes, the parameterization and the initial and boundary condit i ons us ed for the 55

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interannual integration are id e ntical to those used for the climatological integration The mod e l i s initially integrated by using th e forcing fields of 1960 for ten years before we start the thirty-y ear integration An EOF method is used to analyze the t e mporal and spatial variations of the model r e sults. We start this chapter by introducing the EOF technique in Section 4 .1. The analysis and discussion of the modd results are divided into two sections the temporal and spatial variability of basin-wide fields in Section 4.2 and the integrated c ross-s e ction heat fluxes and transports in Section 4.3 In each of these two sections, we first look at the monthly-mean climatology for the thirty-year integration, termed interannual mean annual cycle or simply mean annual cycle, compared to the results of climatological annual cycle discussed in the previous chapter. We then focus on the interannual variability about the mean annual cycle. The interannual variabilities of the EOF anomalies of the first-layer thickness are analyzed against the Southern Oscillation Indices (SOl) in Section 4.4. Cross spectrum technique is used to evaluate th correlation between them. Finally a short summary is given in Section 4.5. 4.1 The EOF Method EOFs, the empirical orthogonal function analysis which is more generally referred to as principal component analysis(PCA), is a powerful mathematical tool to analyze the spatial and temporal variability of physical fields in meteorology and oceanogra phy [Preisendorfer 1988]. Similar to the Fourier transformation used for spectrum analysis of time-series of singular signals, the EOF method is used for analysis of time series of spatial fields to obtain principal patterns in spatial distribution of the fields and their corresponding temporal variabilit y The EOF method has frequently been employed to analyze spatial patterns and 56

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temporal variations of both the scalar and vector data fields. Lorenz [1956] success fully made prediction studies of the 500mb height anomaly field for January ( 19471952) over a grid of 64 points covering the mainland United States Southern Canada, and parts of the surrounding oceans. Kutzbach [1967] provided a clear description of scalar EOFs in his study of monthly-mean sea level pressure, surface temperature, and precipitation over 23-point grids of North American. Later, EOFs were modified to analyze winds and currents as vector fields by Hardy and Walton [ 1978], Legler [1983], and Breidenbach [1990]. In our study, a scalar EOF method is used to analyze each individual scalar field, consisting of running-mean anomalies of the first-layer thickness mixed-layer depth and mixed-layer temperature while a vector EOF method is applied to the running mean anomaly of the first-layer velocity field. The EOF analysis procedures in these two methods are basically identical, except that a complex representation is applied to the two dimensional vector field rather than a single real variable field in the scalar EOF analysis. Let F be a two dimensional M x N matrix that represents a physical field f(x, y, t) with M rows and N columns; each column records the variation of a spatial data field with M grid points at an instant time and each row represents the temporal variation of the data at each spatial grid point. Hence, a matrix element fmn represents a specific value of the data field at grid point m and time step n. Therefore, both the spatial and temporal variations of a scalar (vector) data field f ( x y t ) are contained in this real (complex) matrix F. For an EOF method based on the temporal domain, M time series can be rep resented in an N-dimensionallinear vector s pace spanned by a arbitrary unit basis, En, a N dimensional unit vector To obtain the principal distribution patterns, we 57

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maximize the sum of squares of the projections of all the M time series on the unit basis En. In mathematical terms, the sum of squares of the projections is expressed as where P a Hermitian matrix, is equal to 1/MFtF, where is a transpose of the real, or a conjugate transpose of the complex En. The maximizing of En constitutes a variational problem leading to a characteristic problem of computing eigenvalues and eigenvectors. Thus we obtain an equation of the form or (P->.I)En = 0, where the vector En is the characteristic vector associated with each characteristic value An, 1 :::; n :::; N, and I is a unit matrix of order N. The N unit vectors, E = {E1 E2 ... ,EN}, are called the Empirical Orthogonal Functions (EOFs). Since P is symmetric its trace, the sum of the diagonal elements of the matrix, is invariant under a basis transformation and thus is equal to the sum of the eigenvalues Since the trace of P is equal to the total variance, each eigenvalue An denotes the portion of the total variance explained by each EOF mode and the fraction of the total variance explained is An/ Z:f:,1 Ai E is expressed in temporal space in our analysis and is thereby called temporal EOFs. The associated spatial EOFs are the coefficients of projecting F on E as C=FE. Each column of C, i.e. Cn, represents a spatial pattern associated with the eigenvalue An, 1 :::; n :::; N, which has the same units as the original data fields. Each corre-58

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sponding eigenvector En constitutes a time series that modulates the contribution of the spatial EOF, Cn, to the total variance. An error estimation method described by North et al. [1982] is used to check the independence of each EOF mode under consideration. For a particular eigenvalue ,\ associated to an EOF mode its estimated e rror is where N1 is the average number of degrees of freedom for the temporal variation of the data field at the spatial grid points where high correlation occurs between the EOF field and the original field. The number of degrees of freedom for a time series of N records at each grid point is expressed by Davis [1976] as where t:::..t is the resolution of the time step (three months in our analysis) and Tis the integral time scale. T is a rough measure of time interval over which the time series is correlated with itself [Tennekes and Lumley, 1972]. With R(t) as the autocorrelation function, the integral scale can be obtained through an integration that is, T = R(t)Ot. For a limited number of data records, a finite upper-bound time tu is chosen to calculate the integration Conservatively, we choose the upper-bound time as the first zero amplitude of the autocorrelation function that is R(tu) = 0. The longer the integral time scale is, the slower the temporal variability of the signals would be and vice versa. The spatial distribution of the integral time scale for each model field is illustrated and discussed in Section 4.2.3 to show the interannual variability. 59

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4.2 Model Fields with Interannual Variability In this section we discuss the interannual variability of the model fields to investi gate and understand the interannual, monsoon-cycle related variability in the Indian Ocean circulation. An EOF technique is employed to identify the dominant modes of interannual variability in the model. We concentrate on the upper-layer dynam ics and thermodynamics focusing on the model fields of the first-layer velocity, the first-layer thickness, the mixed-layer dep t h, and the mixed-layer temperature. We first compute a monthly-mean cEmatology from the interannual integration, which we will denote as the mean annual cycle. We then compare these mean an nual cycles with that from the climatological integration discussed in Section 4.2.1. The individual monthly-mean results from the interannual integration are discussed in Section 4.2.2. Interannual variability is isolated by removing the mean annual cy cle, computing a 12-month running-mean of the resulting anomaly fields, and then performing an EOF analysis in Section 4.2.3. 4.2.1 Interannual-Mean Annual Cycle An mean annual cycle is computed by temporally averaging each month over the thirty-year integration. We present model fields in January and July to represent the northeast and southwest monsoons. First, let us look at the mean annual cycle of upper-layer velocity fields in January and July, as shown in Figure 4.1. In January, the velocity field shows a similar current pattern north of 5S to that of the climatological annual cycle shown in Figure 3.2a on page 25, though with subtle differences. The SEC (South Equatorial Current) between 10 s and 15 s is much weaker due to reversed (eastward) flow through the eastern open boundary at this time. The SECC (South Equatorial Counter Current) 60

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is stronger and closer to the equator near the western boundary, shifting southward toward s o S at Seychelles similar to the climatological model SECC. Affected by the SECC the NEC (North Equatorial Current) is located farther to the north, feeding the southward winter Somali Current, which meets the EACC (East Africa Coastal Current) to feed the SECC. Strong westward flow associated with the NEC extends farther east of Maldives. The SEC is stronger in July than in January, although it is weaker than that in the corres ponding climatological annual cycle shown in Figure 3.2d on page 27. The sout hern gyre of the two-gy re system is much stronger, with more recirculation across the eq uator than that in the corresponding climatological integration. The most notable difference occurs along the equator between 60 E to 78 E where the cross-equatorial current (outflow from the two-gyre system of the Somali Current) has an eastward-dominated component. This ECC (Equatorial Counter Current) meets the southwestward cross-equatorial outflow from the Bay of Bengal (originally from the two-gyre system) and turns south at 78 E to feed the SECC along so S in the eastern Indian ocean. One notable mismatch in the annual cycles of velocity fields between the inter annual and climatological integrations is the Indonesian throughflow across the east ern open boundary. In the climatologi ca l annual cycle, we obtain the direction and strength of the throughflow close to the observed values, but the interannual integra tion results in a different direction and amplitude of the velocity through the eastern open boundary. It is the interannual wind field that cause this different result. Since the model utilizes a radiation condition at the open boundary, the throughflow is totally controlled by physics insid e the model basin. This is one of the drawbacks for regional models. We plan to improve our simulation model in its future version by 61

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25N ZON 15N lON 5N EQ 5S lOS l5S zos 25S 40E 50E 60E 70E BOE 90E lOOE llOE 0 100&+01 ILUDIUII VECTOR (a) January 25N ZON l5N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE 0 100& + 01 ILUDIUII VECTOR (b) July Figure 4.1. The upper-layer velocity (ms-1 ) fields in January and July, represent ing the current patterns in the northeast and southwest monsoons respectively. controlling the throughflow with the observed data at the eastern open boundary. The mean annual cycle of first -layer thickness distributions in January and July are shown in Figure 4.2 The dominant variabi l ity of the thickness patterns closely 62

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match es t he annual cycle of their corresponding climatological integration in Fig ure 3.5a on Page 32. However it is apparent that the first layer in the northern and equatorial Indian Ocean is thinner for the mean annual cycle than for the climato logical annual cycle, due to the fact that the interannual monthly-mean forcing fields for individual years may be stronger than the averaged climatological monthly-mean forcing, especially for vector fields of the winds. Therefore stronger upwelling occurs to cause thinner upper-layer in the northern basin and the equatorial area. Figure 4.2 shows the mean annual cycle of mixed-layer thic kn ess fields of the northeast and southwest monsoons The variability of the mean annual cycle of mixed-layer thicknesses match their corresponding climatological annual cycle shown in Figure 3.7 on Page 37, though with less detail due to the thirty year average. The stronger upwelling caused by the interannual monthly-mean forcing leads also to thinner mixed-layer in the northern and equatorial Indian Ocean during the southwest monsoon. Anoth e r notable difference is that a shallower mixed-layer in the southern basin occurs during t he late period of the southwest monsoon. This result is associated with the weaker Indonesian throughflow discussed previously. In addition, the smaller drag coefficient used for the interannual integration reduces the production of turbulent kinetic energy in (9) that determines the mixed-layer depth. Associated with less fluctuation of mixed layer thicknesses, less water mass is entrained into, and detrained out of, the mixed-layer. The effect of the reduced entrainment on the heat budget will be discussed in Section 4 3 1. The mean annual cycle of mixed-lay e r temperature fields are shown in Figure 4.3 of the north east and southwest monsoons The mixed-layer temperature in January matches that in its corresponding climatological integration in Figure 3.8 on Page 38 63

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE (a) January 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE (b) July Figure 4.2. The first-layer thickness (m) fields in January and July representing the first-layer thicknesses in the northeast and southwest monsoons, respectively. with less than lC difference throughout the basin. In July, shown in Figure 4.3(b), we see l ower mixed-layer temperature than the climatological annual cycle in most area, but it matches closer to the observed SST illustrated in Figure 3.9(b) on Page 39. The mean annual cycle from the interannual integration matches well with the annual cycle from the climatological integration. The differences between the mean 64

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25N 20N 15N lON 5N EQ 58 lOS 158 208 258 40E 50E 60E 70E BOE 90E lOOE 110E (a) January 25N 20N 15N lON 5N EQ 58 lOS 158 208 258 40E 50E 60E 70E BOE 90E lOOE 110E (b) July Figure 4.3. The mixed-layer thickness (m) fields in January and July repre senting the mixed-layer distributions in the northeast and southwest monsoons, respectively. annual cycles of interannual integration and the annually seasonal integration are mainly due to the changes of the parameterization adjustment. Based on this match we are encouraged to further analyze the int e rannual variability of the model fields in the following two sections 65

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25N 20N 15N l O N 5 N E Q 55 lOS 155 205 255 40E 50E 60E 70E 80E 90E lOOE llOE (a) Janu ary 25N 2 0N 15N lON 5N E Q 55 l O S 1 5 5 205 255 4 0 E 50 E 60E 70 E 8 0 E 90E lOOE llOE ( b ) July F i g ure 4 .4. The mixed-layer temperature ( oC) fiel ds in January and July, representing t h e temperature distributions in t h e northeast and so u thwest monsoons, respective ly. 4.2.2 Interannual Variab ility i n Monthly -Mean Field s To inv e stigate the interannual variabilit y of the model fiel ds we first look at the interannual month l y-mean fields in 1960, 1975 and 1989 which represent t h e model result at the beginning midd l e, and end of the thirty year integration respectively. We a l so choose January and Jul y to represent the northeast and sout h west monsoons. 66

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The interannual monthly-mean first-layer velocities of the northeast and southwest monsoons in 1960, 1975, and 1989 are shown in Figure 4.5 Although similar current patterns exist in January and July, respectively, interannual variability is apparent in the velocity fields In January, a stronger SECC occurs in 1960, while a stronger NEC exists in 1989 In July, more obvious differences can be seen for the two-gyre system of the Somali Current The southern gyre of the two-gyre system is stronger in 1989 while it is weaker in 1960. The SEC is stronger in July 1960 and weaker in July 1975. Interesting variability of the eastward Wyrtki [1973) jet can be seen during the thirty years. The Wyrtki jet is driven directly by the monsoon transition winds on the equator; however it is heavily modulated by equatorial waves initiated by the monsoons. The Wyrtki jet is seen consistently along the equator in the eastern Indian Ocean during the monsoon transition, but it is less as persistent in October and November as in April and May; for example, the fall Wyrtki jet occur strongly in 1981 and weakly in 1982 and 1984, as shown in Figure 4 .6. The interannual monthly-mean of the first-layer thicknesses for the northeast and southwest monsoons in 1960, 1975, and 1989 are shown in Figure 4.7 Associated with the interannual variation in equatorial waves and forcing fields the first-layer thickness shows also interannual variability in January and July, respectively In January, the thermocline ridge along 5S to 10 S is much shallower in 1960 than in 1989. Differences in phase of the incoming and reflected equatorial waves at the eastern boundary in both January and July leads to a thicker layer in 1989 and a thinner layer in 1960 in the eastern equatorial Indian Ocean. The downwelling associated with the southern gyre does not appear in July 1989 while it is fully developed at the same time in 1960 a nd 1975. 67

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25N 25N 20N 20N 15N 15N IO N ION 5N 5N EQ EQ 5S 5S lOS lOS ISS ............................ ISS .. .. .. .. .. .. .. .. . .. .. .. . .. .. . ... 20S :::: : :: :::: .... ::::::: :: ... u 44 .... : ::::::::::::::::::::-:..::: :::::: 205 25S .... . ...................................... ::::::::::::::::::::::::::::::::::: .... 255 4 0E 50E 60E 70E BOE &OE lODE 110 40E 50E 60 70E BOE ;oe 100 110 0.1-.01 0.1...01 --.....,._ ,.._...,... (a) J an uary, 1960 (b) July, 1960 25N 25N 20N 20N 15N 16N ION ION 5N 5N EQ E Q 5S 55 lOS IDS 15S ISS 20S 20S 25S 25S 40E 50E 60E 70E 60 go lODE 110 401 50E 60E 7 0 80 go IOOE 110E G.l -.01 0.1-+01 --,.._..,. ....... .,.,.. (c) Janu ary, 1975 {d) July, 1975 25N 25N 20N 20N 15N 15N ION ION 5N 5 N EQ EQ 5S 5S lOS !OS .................................. ISS ............................. ........ ISS ........... ...... ... ..... .... .... ................................... 20S ................................... 20S .................................... . .... ................ ................. 253 ... ............ .... ............... ... ....................................... ....................................... 6 25S 40E 50 60E 70E BOE ;as IOOE 110E 40E 50E 60E 701'! BOE go IOOE 110 0.10:.:+01 0.10:.:+ -...._...,....,.. ....... ...,... (e) January, 1989 (f) July, 1989 Figure 4 .5. Month l y-mea n interannual first-layer velocities (ms-1 ) in January and July of 1960 1975 and 1989 68

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40E 50E 60E 70E BOE 90E lOOE llOE Figure 4 6 The first-layer zonal velocity component on the equator. Temporal variation of the velocity component on the equator is plotted from January 1981 to December 1984. A strong spring Wyrtki jet occurs every year, while the fall jet is strong in 1981 and weak in 1982 and 1984. The interannual monthly-mean mixed-layer thickness for the northeast and southwest monsoons of 1960 1975, and 1989 are shown in Figure 4.8 The complex mixedlayer physics leads to complex temporal fluctuation of the spatial mixed-layer distribution. In January, similar mixed-layer thickness exists in the Arabian Sea, while notable interannual variation occurs in the eastern Indian Ocean. The interannual variability of mixed-layer thickness associated with the two-gyre system can be seen also in July. The interannual monthly-mean mixed-layer temperature for the northeast and southwest monsoons in 1960, 1975 and 1989 are shown in Figure 4 9 One cold wedge exists to the north of the great whirl in July 1960 ; however a second cold wedge develops to the south of the great whirl later in August. The southern cold 69

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20N I !IN ION !IN EQ lOS IllS 209 2119 21111 2011 1511 I O N 511 EQ 59 lOS !59 20S 25S 21111 2011 IIIII lOll !Ill EQ !IS lOS IllS 20S 25S 40E .or; 40 50 60 70E 80 90 (a) January, 1960 50 60E 70 80 90 (c) January, 1975 50E 60 70 BOE 90 (e) January, 1989 25N 20N 15N ION 5N EQ !OS 15S 20S 25S !00 110 40 50 60 70 80 90 100 IIOE (b) July, 1960 25N 20N 15N ION 5N EQ 5S !OS 15S 20S 25S IOOE 110 .WE 50E 60 70E 80 90 I OOE 11 OE ( d) July, 1975 2511 20N 1511 lOll !IN EQ 5S lOS 15S 20S 25S IOOE 110 4011: 50E 60E 70 80 90E 1001! 11011: (f) July 1989 Figure 4 7. Monthly-mean interannual first-layer thicknesses (m) in January and July of 1960, 1975 and 1989 wedge is stronger in July 1989 with a weaker northern cold wedge, indicating a stronger southern gyre and weaker great whirl as seen in the first-layer velocities in 70

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25N 20 N 15N ION 5N EQ 5S lOS HIS 20S 25S 25N 20N 15N ION 5 N EQ 5S !OS ISS 20S 255 25N 20N I liN ION SN EQ ss lOS 155 20S 25S 40E 40 40 50E 60E 70E 60E 90E 100 110 (a) January, 1960 SOE 60E 70 60 90E IOOE 110 (c) January, 1975 SOE 60 E 70E 60 90 IOOE 110 (e) January, 1989 25N 20N ISN ION 5N EQ 55 lOS ISS 205 255 40E SOE 60E 70E 60E 90E 100 110 { b ) July, 1960 25N 20N 15N ION 5N EQ 55 !OS !55 205 255 40E SOE 60 70E 60E 90E 100 110 { d ) July, 1975 25N 20N 15N ION 6N EQ 5S !OS 155 20S 255 40E SOE 60E 70E 60E 90E IOOE IIOE {f) July, 1989 Figure 4 .8. Monthly-mean interannual mixed-layer thickness (m) in January and July of 1960 1975 and 1989. Figure 4.5. The co l d wedges in July 1975 are similar to the "cl assic two-gyre system described by Brown et al. (1980). 71

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25N 25N 20N 20N 15N !liN ION ION 5N 6N EQ EQ 6S 55 !OS lOS !55 !55 205 205 265 255 40 50E 60 70 80E 90 !OOE llOE 40 50 60 70 60 90E IOOE llOE (a) January, 1960 (b) July, 1960 25N 25N 20N 20N 15N 15N ION ION 5N 5N EQ EQ 5S 5S !OS !OS 165 165 205 205 25S 25S 40 501: 60 70E 80E 90E IOOE llOE 40 50E 60E 70 60E 90E IOOE llOE (c) January, 1975 {d) July, 1975 25N 25N 20N 20N 16N 15N ION ION 5N 5N EQ EQ liS 55 lOS lOS 165 165 205 205 25S 25S 40 50 80E 70E BOE 90E IOOE 110& 40E 50 80E 70E 80 90E !OOE liOE (e) January 1989 {f) July, 1989 Figure 4.9. Monthly-mean interannual mixed-layer temperature (C) fields m January and July of 1960, 1975 and 1989. Figure 4.10 shows a spatial distribution of temporal correlation between the mixedlayer temperature and the observed SST during the 30 integration years This distri-72

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE Figure 4.10. Interannual correlation of the SST. The spatial distribu tion o f the temporal correlation coefficient are calc ulated between the mixed-layer temperature and the observed SST from 1960 to 1989 bution indicates that the modeled mixed-layer temperature is highly correlated with the observed SST throughout the Indian Basin though slightly less values exist along the equator due to possibly the phase differences of the propagating eq uatorial waves between th model result and the observation. Lower correlation coefficient also exists along the western coastal area in Arabian Sea because of the same reason as we described for the same correlation coefficient of the seasonal variability in the previous chapter From the discussion of the four model fields at the beginning, middle, and end of the model integration we see that the interannual variability exists more or less in different fields. Further statistical analysis of the interannual variability will be discussed in the next section via EOF analysis. 4.2. 3 EOF Analysis of Interannual Variability In this section, we analyze statistically the interannual variability of the model fields. To do this, we first compute the interannual monthly-mean anomalies for each field by subtracting the mean annual cycle discussed in Section 4.2.1. Then we 73

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calculate a twelve-month running mean on these monthly-mean anomalies, retaining every other spatial grid point and every third month temporally The running-mean computation essentially filters away variability at periods of less than twelve months. The integral time scale for the running-mean anomalies are calculated for each grid point to show the spatial distribution of the time scale of the interannual variation in the model fields Furthermore, EOFs are computed and analyzed on the running mean anomalies of each model field, which will be termed simply EOF of a field. Integral Time Scale of the Model Fields Spatial distribution of the integral time scale of each model field is computed on the running-mean anomalies of the model fields and is analyzed in this section. The integral time scale represents the length of time over which a model field is correlated significantly with itself at each grid point, and thus is a measure of the memory" of the model ocean. At time scales longer than the integral time scale, realizations from the model integration can be considered statistically independent. This time scale is related to the time scales of interannual variability in that it will be greater where the time scales of variability are longer The distributions of the integral time scale are shown in Figure 4 .1la and Fig ure 4.1lb for the zonal and meridional velocity fields respectively. Both the zonal and meridional components of the equatorial flows have a time scale less than a year. However, the time scale of the zonal component at higher southern latitude is on the order of 30 to 40 months. The short integral time scale for the flows associated with the equatorial wave guide indicates a frequent variation driv e n by e quatorial wave activity Distribution of the integral time scale of the first-layer thickness is shown in Fig ure 4.12. Long integral time scale of 40 to 50 months in the eastern and central 74

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25N 20N 15N lON 5N EQ 58 lOS 158 208 258 40E 50E 60E 70E 80E 90E lOOE llOE Figure 4 .11a. Integral time scale of the first-layer zonal velocity. The integral time scale (in months) is calculated for the running-mean anomalies of the first layer zonal velocity. The time scale in the equatorial area is less than one year while multiple year time scales dominate the southern basin. 25N 20N 15N lON 5N EQ 58 lOS 158 208 258 40E 50E 60E 70E 80E 90E lOOE llOE Figure 4 .11b. Integral time scale of the first-layer meridional velocity. The in tegral time scale (in months) is calculated for the running-mean anomalies of the first-layer meridional velocity. Time scales of less than 10 months cover much of the Indian basin. equatorial Indian Ocean indicates a slow interannual variability of the upper-layer thickness contrasting to the fast variation of the velocity driven by equatorial waves. This difference in time scales implies that there is a net redistribution of mass in the upper layer at longer time scales as a result of rapid velocity field fluctuations 75

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25N ZON 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E lOOE 110E Figure 4.12. Integral time scale of the first-layer thickness. The integral time scale (in months) is calculated for the running-mean anomalies of the first-layer meridional velocity. This time scale is much longer in the eastern equatorial area than that of the velocity field. associated with equatorial dynamics and thermodynamics. Distribution of the integral time scale of the mixed-layer thickness is shown in Figure 4.13. The dominant time scale is from ten to fifteen months. The memory associated with mixed-layer physics is notably shorter than that for first-layer thickness, which indicates a faster interannual variability of the mixed-layer thickness, i.e., the memory of the upper ocean is contained in the equatorial dynamics and not the thermodynamics. Distribution of the integral time scale of the mixed-layer temperature is shown in Figure 4.14. A ten-month time sca l e covers the who l e Indian Ocean except for limited coastal regions. This time scale matches well with that of mixed-layer thickness. This time scale matches well with that of mixed-layer thickness. EOF Analysis of the First-Layer Velocity In Table 4.1 we list the eigenvalues of the first six EOF modes for the runningmean first-layer velocity anomalies. Estimated errors for the eigenvalues show obvious 76

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Z5N 20N 15N 10N 5N EQ 5S lOS 15S zos 25S 40E 50E 60E ?OE BOE 90E lOOE llOE Figure 4.13. In tegral time scale of tl:e mixed-layer thickness. Integral time scale (in months) is calculated for the runni.lg-mean anomalies of the mixed-layer thick ness. The integral time sca l e (in month3) is calcu la ted for the running-mean anoma lies of the mixed-layer thickness. The time scale for these anomalies is much shorter in the eastern equatorial area than that of the first-layer thickness Z5N ZON 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E ?OE BOE 90E 100E llOE Figure 4.14. Integral time scale of the mixed-layer temperature. Integral time scale (in months) is calcu l ated for the running-mean anomalies of the mixed-layer temperature overlap between the consecutive eigenvalues after the fourth. A slight overlap also exists between the eigenvalues of t h e first two EOF modes. It is possible that the first two vector EOF mode s are not totally independent, or simpl y that our error estimates are very conservative as described in Section 4.1. However, the cumulative 77

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Table 4.1. Eigenvalues of the first six EOFs of first-layer velocity EOF Eigenvalue Error Individual Percentage Cumulative Percentage 1 0.017 4 0.0029 16.23% 16.23 % 2 0.0146 0.0025 13.65% 29.88 % 3 0.0101 0.0017 9.44 % 39.32% 4 0.0071 0.0012 6.65% 45.97% 5 0 0065 0 0011 6 .07% 52.04% 6 0.0054 0.0009 5.08% 57.12% contribution of the first three EOFs are ind ependent to the higher EOF modes The first three EOFs collectively account for 39.32% of the total variance of the velocity anomalies. While this is not a particularly high percentage of the total variance it is still a significant fraction, given the complicated nature of variability in the velocity field on many time and space scales. The first three EOFs collect variation of the velocity fields dominantly in their zonal components. The reconstructed fields from the first three velocity EOFs and the running-mean anomalies of the first-layer velocity are highly correlated for their zonal components and comparatively l ess correlated for their meridional components, as shown in Figure 4.15a and Figure 4.15b, respectively The larg est corre lations for zonal velocity extend in a band from the throughflow region to the equatorial wave guide and in the region of the EACC and Somali Current. This suggests that the dominant mode of interannual variability is in zonal velocity, or upper ocean transport, and primarily occurs in these r egio ns Furthermore this suggests a conne c tion between the Indon esian throughflow the western boundary c urrents and the eq u atoria l wave guide. The first EOF of first-layer veloc ity is shown in Figure 4.16. This EOF con t ributes 16.23% to the total variance of the velocity anomalies. The amplitude of the temporal EOF modulates the contribution of its associated spatial EOF over time. The phase 78

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E lOOE llOE Figure 4.15a. Correlation coefficient of the first layer zonal velocity. Spatial distribution of correlation coefficient is evaluated between the reconstructed anomaly fields from the first three velocity EOFs and the running-mean anomalies of the first-layer velocity for their zonal component. The high correlation shows that the first three velocity EOFs retain most of the strong interannual variations of the zonal velocities in limited regions of the Indonesian throughflow the equatorial wave guide, and the western boundary near the equator. 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE Figure 4 .15b. Correlation coefficient of the first-layer meridional velocity Dis tribution of correlation coefficient is evaluated between the reconstructed anomaly field from the first three velocity EOFs and the running-mean anomalies of the first-layer velocity for their meridional component. The correlation is generally low and indicates that there is not large-scale interannual variability in the meridional velocities in the first layer associated with these modes. corresponding to the amplitude of the temporal EOF is either zero or 180 when the amplitude is significant, which implies that the EOFs are dominated by their primary 79

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components [Legler, 1983]. A zero phase indicates that the associated spatial EOF contributes positively to the amplitude of the velocity anomalies, while a 180 phase indicates negative contribution. The spatial EOF shows dominant interannual va riability in the western equator i a l Indian basin. Variability can be seen in the two gyre system along the Somali coast Strong eastward velocity anomalies dominate between Seychelles and Maldives near equator In the annual cycle of currents in this area, there are eastward and westward currents during the northeast and southwest monsoons respectively. The positive anomalies therefore, indicate the enhancement of the eastward Equatoria l Counter Current (ECC) during southwest monsoons. Strong westward vel ocity anomalies between 5 S and 10S can be also seen in this spatia l EOF. When the tempora l EOF has l arge amplitude and zero (180) phase the recirculation among the EACC, SEC, and SECC is stronge r (weaker) than in their mean annual cycles. Concurrent l y with this strengthening (weakening) of the recirculation is a strengthening (weakening) of the Indonesian throughflow and the SEC a l ong 10 S. Running-mean anomaly field of the first-layer velo city centered on April 1966 is shown in Figure 4.17a. During this period the first EOF has large amplitude and zero phase, while the other modes contribute relatively little. The positive (i.e. zero phase) contribution of this EOF shows an e nhan ced recirculation in the western equatorial Indian Ocean From analyzing directly the anoma l y field we can see that more of the flow from the southern gyre of the two-gyre system is recirculated to the east and south with less flow to the northeast in the Somali Current during the southwest monsoon of 1966. The anomalies in this season dominate the 12-month running-mean anomalies. Concurrently, there is also stronger incoming flow through the eastern open boundary 80

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S .... "' ... ... .. .. .. ...... ... J: ..... r ............ ......... """"' J ...... --.,. c 't c I ......-: '-.........: -, ....... .,. ..... 'f ............. .,. ., .... .. .. ___ .. .......... ......... .,. ..... .. j,:: :::: . .:::::::::::::::: ::: a.f ........... ........................... .. .. .. ............. -c., ... :#> .................................... .. .. .... "' .............. ,. .,. ............................... .. ., .. .. .. ............... ,. ................................ .. .. ., ., ............. .............................. ., .......... ... 40E 50E 60E 70E BOE 90E lOOE llOE 1965 (a) Spatial EOF 1970 1975 Year 1980 (b) Amplitude of Temporal EOF 0.800+00 IIAXDliJll VECTOR 1985 1990 -nL_ __ __ 1960 1965 1970 1975 Year 1980 (c) Phase of Temporal EOF 1985 1990 Figure 4.16. Spatial pattern (a) is modulated by the temporal amplitude (b) and the temporal phase (c) of the first vector EOF of the first layer velocity Running-mean a nomaly field of the first-layer velocity center ed on July 1976 is shown in Figure 4.17b to illustrate a period when the first EOF has large amplitude 81

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25N 20N 15N lON 5N EQ 58 lOS 158 208 258 40E 50E 60E 70E 80E 90E lOOE llOE 0 .200+00 IIAXJilUW VI!!CTOR Figure 4.17a. Anomalies o f the first-layer velocity centered on April 1966 The velocity pattern during this period is dominated by the first EOF mode while the contribution from other EOF modes is relatively sma ll. and 180 phase. The negative (180 phase) contribution of the first EOF indicates a weaker recirculation in the western equatorial Indian Ocean. A closer look at the the velocity anoma lies reveals that there is less recirculation to the east and south of the southern gyre of the two-gyre system and more flow into the northeastward Somali Current and the great whirl during the southwest monsoon of 1976. A reduction in the throughflow is se e n a l so during this time. The second EOF is shown in Figure 4.18. This EOF contrib u tes 13 .65% to the total interannual variability of the first-layer velocity anomalies. The spatial pattern of this EOF shows a band of eastward zonal velo city anomalies a c ross the basin, which starts from the western boundary along the equator, shifts south between 60 E to goo E, and remains along 10 S afterward. Notab l e westward veloc i ty anomalies a lso exist a l ong 5S, between 46 E and 62 E with eastward anomalies south of peninsular India. The positive contribution of this EOF implies a intensified SECC, while its negative contribution indicates a weaker SECC 82

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Z5N ZON 15N lON 5N EQ 5S lOS 15S zos 25S ., ........ ., .. .. "" ........ ............. r. ..... .. ..... ............ .... ........... .. l.L//, rl .............. ,. ...... .. ....... __ .. ., "" ........ ..... ..... _,. __ ,," .... I' '' ......... ............. lit .... -.,.. .. .. .. .. .. "" ................. .. .. .. ... .. .. .. ... 1,. ............ "9"" ... ........................ .. ........................ ..... .................... ".,. ..... '" ............................................ ... / .. ................................................. .. : ............................................ ... .... ........ .,"' ...................................... ... ..... .. ........ 4 ................................. .. ................. ..... .. .. .. .. . .. .. .. .. .. .. ... 40E 50E 60E 70E 80E 90E lOOE llOE 0 .200+00 WAXIIIIIll VECroR Figure 4.17b. Anomalies of the first-layer velocity centered on July 1976. This pattern is negatively dominated by the spatial pattern of the first EOF mode Running-mean anomaly fields of the first-layer vel ocity are shown in Figure 4.19a and Figure 4.19b to illustrate periods when the seco nd EOF has large amplitude, with zero and 180 phases, r e spectively. The velocity pattern associated with the positiv e contribution of this EOF can be seen during the period centered on October 1973 a period including the so uthwest monsoon of 1973 and the northeast monsoon of 1974 and shows an intensified SECC system. The negative contribution of the second EOF centered on April 1964 indicates a weaker SECC during both the northeast and southwest monsoons of 1964. The throughflow shows eastward anomalies around October 1973 and westward anomalies around April1964. The third EOF of the first-layer velocity is shown in Figure 4.20, which contributes 9.44% to the total interannual variability of the vel ocity anomalies. This EOF retains notab l e interannual variability for the NEC and SECC NEC is a northeast-monsoon r elated phenomenon, while the SECC is persist ent in all seasons The positive contribution of this EOF indicates a stronger westwar d NEC close to the equato r across the whole equator ial Indian Ocean with more enhancement in the western eq uatorial 83

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S u 0.25 ] 0.20 0 .15 < 0 .10 u.. @ 1960 PI u Pl/2 ..c Q.. 0.0 u.. 0 -PI/2 Ul -PI 1960 .. .. ....... .. ., .. .. .. .. "' --.... __ ______....._- "' ............ ., .. 4 ...... 4 .. ,. .. "' ... t ........ ............................................... 4 .., ..... ................. .. ""' ............................................... .. ..... : "' .. .., t "' .,,.,..,..c4<14Ccccccc"ccccc ................................................. .................. ., .,.,.,., ............. ......... ...... .. 4 0E 5 0E 60E 70E 80E 90E lOOE llOE 1965 (a) Spatial EOF 1970 1975 Year 1980 (b) Am plitude of T em poral EOF 1965 1970 1975 Year 1980 (c) Phase of Temporal EOF 0 .800+00 IWalll1ll VECTOR 1985 1985 1990 1990 Figure 4.18. Spatial pattern (a) is modulated by the temporal a mpli t ude (b) and temp o r a l phase (c) o f the second v ecto r EOF o f the first -layer velocity. area. This stron g NEC drives the SECC farther south. Po r tion o f t h e NEC turns south a nd f eeds directly the SECC east of the Seychelles. 84

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25N 20N 15N lON 5N EQ 58 lOS 158 208 258 40E 50E 60E 70E BOE 90E lOOE 110E 0.200+00 --'J> IWmll1ll VECI'OR Figure 4 .19a. Anomalies o f the first-l aye r vel ocity centered o n October 1973 This pattern i s po s itivel y dominated b y the spatial pattern o f the second EOF mode. 25N 20N 15N lON 5N EQ 58 lOS 158 2 0 S 25S ......... ,. "' ., ... "' ... -, ... .................... .. ............. ........... r ... ....... .. ...... -__.,.r;-...... . -. ... ... '._._ ........... c p ...... .. .... ---,. ,, ...... ..... .. ..... 1' "' .. "' .. t' ....... ... ........... ..._ ______ -..... ;; IWmll1ll VECI'OR Figure 4.19b. Anomalies o f the fir st-layer velocity centered on April 1964. This pattern i s negatively dominated b y the spatial pattern of the second EOF m ode Two running-mean anoma l y fields of the first-layer velocit y centere d on October 1975 a nd July 1968 are s hown in Figure 4.21a a nd Figure 4.21b to illustrate the periods w h e n t h e third EOF mode has l arge amplitude, wit h zero and 180 phases r espective ly. The positive contribution o f t hi s EOF i ndicates an en h a n ced NEC sys -85

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S G) 0.25 "0 0.20 ]' 0.15 < 0.10 u.. 0.05 ............... ., .. ................. .. .. .. .. ... ... ... .. .. .. .. ........ .. .... -........ .. L "'--........ ... ,/.,......._......___ .... ... .,. ..... .. ..,. ..... r 4. \ ........ ----.. \ ........ .. ........... ..
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25N 20N 15N lON 5N EQ 58 lOS 158 208 258 ............ ,. .... ........................................ .. ,.. ,. ........................... " .. ,. " .............. ,. .......... I .......................................... .. .. ,. ..... ,. .................................................. ,. ..... :"'""'".,.. ......................... ....... .. ...... ....................... ,. .............. ........ .. .. .. .. .. ............................. ,. ...... ,. .......... .. ....................................... ".&.""""""" .. .. 40E 50E 60E 70E BOE 90E lODE llOE 0.200+00 lllXIlrull VECTOR Figure 4.2la. Anomalies of the first-layer velocity centered on October 1975. This period exhibits a dominant positive contribution from the spatial pattern of the third vector EOF. lies in Figure 4.19a match only partially with the pattern of the third EOF, because of the smaller contrition of this EOF. The negative contribution of the third vector EOF indicates a weakened NEC in the northeast monsoon of 1968 and a reduced SECC during both the northeast and southwest monsoons of 1968. EOF Analysis of the First-Layer Thickness A scalar EOF technique is applied to the running-m ean anomalies of first-layer thickness. In Table 4.2 we list the eigenvalues of the first six EOF modes. The first two EOFs are dominant modes, while the third and fourth EOF modes contribute much less and are not independent due to overlap of their estimated eigenvalue errors. As we did for the velocity EOFs we concentrate on the first three EOF modes in our analysis of the interannual variability of the first-layer thickness. The first three EOFs collectively account for 67.38% of the total variance of the running-mean anomalies during the thirty years. The reconstructed thickness anomaly field from the first three EOFs and the running-mean anomalies of the first-layer thickness are highly 87

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25N 20N 15N lON 5N EQ 55 lOS 155 205 255 \ ;_ 7.--;:[ _:..,;.: ::..:. : : \ \ ----..... "' (C I /. '\ \ "'_..___. _.._. "llll\ \ ----. ......... ..... ..... .................. ... ... .............. ............................................ ................................................................ ,: : : : ; : : : : : : : : : : ; : : : : : : : : : : : : : : Jf" ..... ........................ .,. ............................. ., .... ........ .,. .................. .. ... .. ., .......................... ., .... ., .. ., ....... ., ...... .. .. .. ............................................. ., .... .. ....... .,. ........................... ., ........ ., .............. .. 40E 50E 60E 70E 80E 90E lOOE llOE O .ZOOE+OO IIAXIIIUW VECTOR Figure 4.21b. Anomalies of the first-layer velocity centered on July 1968. This period exhibits a dominant negative contribution from the spatial pattern of the third vector EOF. Table 4.2. Eigenvalues of the first six EOFs of first-layer thickness EOF Eigenvalue Error Individual Percentage Cumulative Percentage 1 711.05 159.00 40.40% 40.40% 2 355.12 79.41 20.18 % 60.58% 3 120.66 26.98 6.86 % 67.43% 4 106.02 23.71 6 .02% 73.46% 5 73.20 16.37 4.16% 77.61% 6 41.44 9.26 2 .35% 79.97% correlated in the eastern equatorial area and along the 10 S, as shown in Figure 4. 22, indicating that the first three EOFs contribute dominantly the interannual variation of the first-layer thickness in these areas. The first EOF of the first-layer thickness i s illustrated in Figure 4 23, which contributes 40.40% to the total interannual variability of the first-lay er thickness anomalies. A long-t e rm trend in the time series of this EOF indic ates that this modulation is varying from positive to negative contribution during the thirty yea rs of the integration. The spat ial distribution of thi s EOF s hows dominant int e rannual variability 88

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25N 20N 15N lON 5N EQ 55 lOS 15S 20S 25S 40E 50E SOE 70E 80E 90E lOOE llOE Figure 4.22. Corre l ation coefficient of the first-layer thickness. Spatial distribution of the temporal correlation coeffic ent are evaluated between the reconstructed thickness anomaly field from the first three EOFs and the running mean anomalies of the first-layer thickness. The strong correlation in the eastern equatorial area and along the 10 S shows that the first three EOFs contribute to the interannual variations of the first-layer thickness primarily in these areas. in layer thickness both in a region along the eastern boundary and extending into the equatorial wave guide, possible indicating reflection of equatorial waves at the eastern boundary, and in a region to the north of the thermocline ridge in the central Indian Ocean along 10 S. It is the eastward Wyrtki jet during the monsoon transition that initiates the piling-up of water mass in the equatorial area near the eastern boundary and leads to the thicker upper layer correspondingly. The westward NEC reflected from the eastern boundary leads to shallower layer thicknesses in the eastern equatorial area. However, the thin layer above the thermocline ridge is in geostrophic balance with the SECC and SEC. Intensified upwelling in this area is associated with a stronger eastward Wyrtki jet. The negative (positive) anomalies of layer thickness of the eastern equatorial area is correlated with positive (negative) anomalies of the thickness above the thermocline ridge. This is the major component of the interannual variability contained in the first spatial EOF. 89

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S u.. 0.2 0 Ul 0.1 8.. 0.0 -0.1 E-< 1960 40E 5 0E 60E 70E 80E 90E lOOE llOE 1965 (a) Spatial EOF 1970 1975 Year (b) Temporal EOF 1980 1985 1990 Figure 4 .23. Spatial pattern (a) is modulated by the time series (b) of the first EOF of the first-layer thickness. Two running-mean anomaly fields of the first-layer thickness are plotted in Figure 4.24a and Figure 4.24b to show the periods when the first EOF of the thickness anomalies has predominantly positive and negative contribution, respectively. The positive contribution of the first EOF mode to t he running-mean first-layer thickness anomalies centere d on January 1962 shows less piling-up of water mass in the eastern equatorial area due to the weaker Wyrtki jet during both fall of 1961 and spring of 1962. The negative contribution of this pattern is seen in 1984. A strong s pring Wyrtki jet in 1984 leads to larger thickness anomalies along the eastern boundary a nd the eastern equatorial region. This negative contribution also indic ates stronger 90

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE Figure 4.24a. Anomalies of the first-layer thickness centered on January 1962. This pattern is positively dominated by the spatia l pattern of the first EOF. 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE 110E Figure 4.24b. Anomalies of the first-layer thickness centered on July 1984. This pattern is negatively dominated by the spatial pattern of the first EOF. upwelling a lon g the thermocline ridge about 10 S in the central Indian Ocean. The second EOF is illustrated in Figure 4 .25, which contributes 20 18% to the total interannual variability of the first-layer thickness. A opposite trend in the time series of this temporal EOF indicates that the modulation is varying from negative to positive amplitude throughout the thirty years of the model integration. The spatial EOF shows also dominant interannual variability in the depth of the thermocline ridge in the central Indian Ocean along 10 S Different from the first EOF mode, 91

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25N 20N 15N 10N 5N EQ 58 lOS 158 208 258 40E 50E 60E 70E 80E 90E 100E 110 E (a) Spatial EOF ""' 0.2 0 Ul 0.1 .... 0 0.. 0.0 E -0.1 cu E-< -0.2 1960 1965 1970 1975 1980 1985 1990 Year (b) Temporal EOF Figure 4.25. Spatial pattern (a) is modulated by the time series (b) of the second EOF of the first-layer thickness. however this anomaly pattern is independent of the eastern equatorial layer thickness anomalies Two running-mean anomaly fields of the first-layer thickness are plotted in Figure 4.26a and Figure 4.26b to show the predominantly positive and negative contribution of the second EOF of the thickness anomalies, respectively. Thicker upper layer above the thermocline ridge is seen in 1978 while the annual oscillation of the layer thickness in the eastern equatorial region is close to its mean annual variation. Analyzing directly the interannual monthly-mean first-layer thickness and velocity fields we see that a weaker SECC with strong southward component occurs through-92

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25N 20N 15N lON 5N EQ 58 lOS 158 208 258 40E 50E 60E 70E BOE 90E lOOE llOE Figure 4.26a. Anomalies of the first-layer thickness centered on July 1978 This pattern is positively dominated by the spatial pattern of the second EOF. 25N 20N 15N lON 5N EQ 58 lOS 158 208 258 40E 50E 60E 70E BOE 90E lOOE llOE Figure 4 .26b. Anomalies of the first-layer thickness centered on July 1971. This pattern is negatively dominated by the spatial pattern of the second EOF. out this year This component flows southward over the thermocline ridge and feeds SEC directly. The n egative contribution of the second spatial EOF to the running-mean firstlayer thickness anomalies centered on July 1971 indicates that a shallower thermocline ridge occurs during 1971. A stronger SECC with major eastward components turns southward and feeds the SEC in the very eastern portion of the southern basin The third spatial EOF is illustrated in Figure 4 .27, which contributes only 6.86 % 93

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S u.. 0.2 @ 0.1 '(; 0.0 ... 8. -0.1 E -0.2 40E 50E 60E 70E 80E 90E lOOE 110E (a) Spatial EOF 1960 1965 1970 1975 Year (b) Temporal EOF 1980 1985 1990 Figure 4.27. Spatial pattern (a) is modulated by t he time series (b) of the third EOF of the first-layer thickness. to the total interannual variability much less than the first and second EOF modes. The spatial anoma l y distribution in the third EOF shows interannual variability of the upper-layer thicknesses both temporally and spatially along 10 S. Positive anomalies in the western basin corresponds to negative anomalies in the eastern basin. The anomaly distribut i on in this EOF mode indicates that the thicker layer occurs in the eastern basin corresponding to the shallowest depth of the thermocline ridge in the western basin at the latitude of 10 S and vice versa Two running-mean anomaly fields of the first-layer thickness are plotted in Figure 4.28a and Figure 4.28b to show t h e dominantly positive and negatiYe contribution 94

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 60E 90E lOOE llOE Figure 4.28a. Anomalies of the first-layer thickness centered on January 1973. This pattern is positively dominated by the spatial pattern of the third EOF. of the third EOF of the thickness anomalies respectively. The running-mean firstlayer thickness anomalies centered on January 1973 show a spatial pattern resembling the third spatial EOF. This mode shows that a shallow thermocline ridge is limited to the western basin during the period including the southwest monsoon in 1972 and the northeast monsoon in 1973 Correspondingly flows of the SECC turn to the south at the Chagos Archipelago to feed the SEC The running-mean first layer thickness anomaly pattern in July 1974 is negatively dominated by the third spatial EOF, which shows a shallow thermocline ridge is limited to the eastern basin during 1974 The associated SECC extends farther east before turning south to feed the SEC during this time. EOF Analysis of the Mixed-Layer Thickness Scalar EOF analysis is also applied to the running-mean anomalies of the mixedlayer thickness In Table 4 3 we list the eigenvalues of the first six EOF modes for the running-mean mixed-layer thic kness anomalies. The first three EOFs collectively account for 50.51% of the total variance of the running-mean anomalies of the mixed-95

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE Figure 4 28b. Anomalies of the first-layer thickness centered on July 1974. This patt e rn is negativel y dominat ed by the spatial pattern of the t hird EOF. Table 4 3. Eigenvalues of the first six E OFs of mixed-lay er t hickness EOF Eigenvalue Error Individual Percentage Cumulative Percentage 1 286.14 52.24 30.54% 30 54% 2 100 27 18.31 10.70 % 41.24% 3 86.82 15.8 5 g .27% 5 0.51 % 4 5 1.80 g.46 5.53% 56.04% 5 46.77 8.54 4.gg% 61.03 % 6 36 .0 7 6.5g 3.85 % 64 .8 8% layer thickness. The r eco n structed mixed-layer thickness a nomal y fie ld from the first three EOFs and t h e running-m ean anomalies of the mix e d -layer thic kness are highly correlated, especially in the eas tern Indian basin, as shown in Figure 4 2g, indicating that the first three EOFs capture the dominant interannual variability of mixed-layer thic kn ess in t h ese areas. The first EOF o f the mixed-layer thickness i s illus trated in Figure 4.3 0 which contributes 30 54% to t h e total int e rannu a l variability of mix edl ayer t hi ckness. The spatial anomaly distribu tio n in t his EOF s hows dominant interannual variability in two areas: t h e so u t h ern part of the Bay of Bengal centered at 5 and goo E and the southeast Indian basin ce nter ed at 17 N and goo E. g6

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E lOOE llOE Figure 4 .29. Correlation coefficient cf the mixed-layer thickness. Spatial distribu tion of the temporal correlation coeffi is evaluated between the reconstructed mixed-layer thickness anomaly field from the first three EOFs and the running mean anomalies of the mixed-layer thickness The strong correlation in south of the Bay of Bengal and southeast Indian basin shows strong contribution of the first three EOFs to the interannual variations of the mixed-layer thicknesses in these areas. During the southwest monsoons, a deep mixed-layer develops in the southern basin primarily in response to both strong monsoon winds and colder southern-winter air temperature. The strong interannual variability of the mixed-layer thickness in the southeast Indian Ocean indicates a long-term variation of the thermodynamic forcing. However, the strong southwest monsoon winds and the reflection of the equatorial waves at the eastern boundary lead to a deep mixed-layer in the south of the Bay of Bengal during the southwest monsoon. Two running-mean anomaly fields of mixed-layer thickness are plotted in Figure 4 .3la and Figure 4.3lb to show periods when the first EOF mode contributes positively and negatively to the mixed-layer anomalies respectively. The positive contribution of the first EOF mode to the running-mean mixed-layer thickness anomalies centered on July 1961 shows shallower mixed-layers in both the southern part of the Bay of Bengal and the southeast Indian basin in the summer of 1961. The opposite 97

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S u.. 0.2 0 Ul 0.1 -;;; 8. 0 0 5 -O.l E-< 40E 50E 60E 70E 80E 90E lOOE llOE 1965 (a) Spatial EOF 1970 1975 Year (b) Temporal EOF 1980 1985 1990 Figure 4.30. Spatial pattern (a) is modulated by the time series (b) of the first EOF of mixed-layer thickness. situation occurs during the period centered on July 1985. This negative contribution of the first mode indicates deeper mixed-layers occur in both the southeast basin and the south of the Bay of Bengal in the summer of 1985. The second spatial EOF is illustrated in Figure 4.32, which contributes 10.70% to the total interannual variability of the mixed-layer thicknesses. This spatial EOF shows dominant interannual variability in mixed-layer thickness in the southern basin; deeper mixed-layer in the southeast basin is associated with shallower mixed-layer in the southwest basin, and vice versa. Two running-mean anomaly fields of mixed-layer thickness are plotted in Fig-98

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E ?OE BOE 90E lOOE llOE Figure 4.31a. Anomalies of the mixed-layer thickness centered on July 1961. This pattern is positively dominated by the spatial pattern of the first EOF. 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E ?OE BOE 90E lOOE llOE Figure 4.31b. Anomalies of the mixed-layer thickness centered on July 1985. This pattern is negatively dominated by the spatial pattern of the first EOF. ure 4.33a and Figure 4.33b to show periods of positive and negative contribution of the second EOF of mixed-layer anomalies, respectively. Thicker and thinner mixed layers compared to their corresponding mean annual values, are found in the southeast and southwest Indian Ocean, respectively, about Apri l 1976. The negative contribution of the second EOF mode to the running-mean mixed-layer thickness anomalies centered on July 1970 indicates that shallower and deeper mixed-layers occur in the western and eastern regions respectively of the southern basin during this period. 99

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S u.. 0.3 @ 0.2 0.1 ;;; 40E 50E 60E 70E BOE 90E lOOE llOE (a) Spatial EOF 8. 0.0 E -0.1 -0.2 -0.3 1960 1965 1970 1975 1980 1985 1990 Year (b) Temporal EOF Figure 4.32. Spatial pattern (a) is modulated by the time series (b) of the second EOF of mixed-layer thickness. The third EOF of the mixed-layer thickness is illustrated in Figure 4.34. This EOF contributes 9.27% to the total interannual variability of the mixed-layer thickness. The spatial anomaly distribution in the third EOF shows interannual variability of the mixed-layer thickness in the two areas similar to the variability in the second EOF mode, that is, the south of the Bay of Bengal and the southeast Indian basin i however, the variations in these two areas are negatively correlated in this spatial EOF. This mode captures the out-of-phase variability in these two regions while the second mode captures the in-phase variability. Two running-mean anomaly fields of mixed-layer thickness are plotted in Fig100

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E lOOE llOE Figure 4.33a. Anomalies of the mixed-layer thickness centered on April 1976. This pattern is positively dominated by the spatial pattern of the second EOF. 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E 80E 90E 100E 110E Figure 4.33b. Anomalies of the mixed-layer thickness centered on July 1970. This pattern is negatively dominat ed by the spatial pattern of the second EOF. ure 4.35a and Figure 4.35b to s how the predominantly positive and negative con-tribution of the third EOF of the mixed-la ye r anomalies, respectively. The positive contribution of the third EOF mode to the running-mean mix edl ayer thickness anomalies shows that the mixedl ayers are deeper and shallower than their co rrespending inte rannual-mean depth s in the southeast Indian Ocean and the southern part of the Bay of Bengal respectively in 1968. The ne gative contribution of this EOF indicates the opposite s ituation durin g a period centered on July 1969. 101

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S ""' 0 2 0 0 1 Ul -a 0 0 8. -0. 1 E -0. 2 40E 50E 60E 70E 80E 90E 100E llOE (a) Spatial EOF 1960 1965 1970 1975 1980 1985 1990 Year (b) Temporal EOF Figure 4.34. Spatial pattern (a) is modulated by the time series (b) of the t hird EOF of mixed-layer thickness EOF Analysis of the Mixed-Layer Temperature The mixed-layer temperature h&S less interannual variability than its corres pond ing mixed-layer thickness, in comparison with the amplitude of the annual cycl e In Table 4.4 we list the eigenvalues of the first six EOF modes for t h e running-mean:n mixed-layer temperature anomalies The first three EOF modes are inde pen dent and collectiv e ly account for 67.38 % of the total variance of the running mean anomalies of the mix e d-l a y e r t e mperature The reconstructed anomaly fiel d from the fiTh-t EOFs a nd the runnin g-me an anomalies of the mi.xed-layer t empe rnturt" are hlgWy ootr-102

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25N 20N 15N I ON _...,...,.....,. EQ --iiii 5S lOS 155 205 255 40E 50E 60E 70E 60E 90E lOOE llOE Figure 4.35a. Anomalies of the mix ed -lay e r thickness centered on July 1968. This p attern is positively dominate d by th! s patial patt e rn of the third EOF. 25N 20N 15N lON 5N EQ 55 lOS 155 205 255 40E 50E 60E 70E 80E 90E lOOE llOE Figure 4 .35b. Anomalies of the mixed-layer thickness cen te red on Jul y 1969. This pattern is negativel y domin ate d by the spatial pattern of the third EOF related over most of the basin except for a low c orrelation along the western coastal zone es p ec i a ll y in t h e Arabian Sea, as shown in Figure 4.36, indicating that the first three EOFs ca p ture t h e dominant interannual variability o f mixed layer temperature exce p t in t h ese strong upwelling regions. T h e first EOF of mix e d-la yer temperature is shown in Figure 4.37. This EOF m o d r n c e c mnt s lor 36 .:. 1 % o f the total va rian ce in t he temperature a nomali es. T he in this EOF s hows int e rannual variability over most of the b asin. 103

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Table 4 .4. Eigenvalues of the first six EOFs of mixed-lay e r temperature EOF 1 2 3 4 5 6 E igenvalu e Error 2.0861 0.4665 1.1135 0.2490 0.6756 0.1511 0.3897 0.081 4 0.2774 0.0620 0.1747 0.0391 25N -B&:::::;:; 20N 15N ION 5N EQ Individual Percentage 36.27 % 19.36 % 11.75 % 6.78 % 4.82% 3 04 % 55 \'="-"""Ia. lOS ISS 20S 25S Cumulative Percentage 36.72 % 55.64 % 67 .38% 74 16 % 78.98 % 82.02% 40E 50E SOE 70E 80E 90E IOOE llOE Figure 4.36. Correlation coefficient of the mixed-layer tem perature. Spatial dis tribution of the temporal correlation coefficient is calculated between the recon structed mixed-layer temperature anomal y field from the first three EOFs and the running-mean a nomalies of the mix e d-layer temperature Strong correlation is over most of the Indian basin with relatively l ess correlation along t he western coastal zone, especially in the Arabian Sea. Two running-mean anomaly fields of the mixed-la ye r temperature are plotted in Figure 4.38a and Figure 4.38b to show periods when the first EOF mode contributes positivel y and negativel y to the mLxed-layer temperature anomalies respectively. A notable positive match can be seen between the running-m ean mixed -l ayer temper-ature a nomali es and the first spati a l EOF during t he period cente r e d on July 1974 The mix edlayer temperature is high er t h a n its interannual-mean value in most of the mode l ed Indian Ocean except the southeast basin from October 1977 to September 104

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u.. 0 .... 0 0. E 25N 20N 15 N lON 5N EQ 5S lOS 15S 20S 25S 0.2 0.1 1960 40E 50E 60E 70E 80E 90E lOOE llOE 1965 (a) Spatial EOF 1970 1975 Year (b) Temporal EOF 1980 1985 1990 Figure 4.37. Spatial pattern (a) is modulated by the time series (b) of the first EOF of mixed-layer temperature 1978 As noted pre vio usly, the amplitude of the anomalies in mixed-la yer temperature is small compared to that of the annual cycle as indicated by this pattern. The negative contribution of the first EOF mode can be noted during the period centered on July 1985. The mixed-layer temperature is lower than its mean annual cycle value in most of the Indian Ocean in 1974. The maximum anomalies are in the central southern basin. The secon d EOF is illustrat ed in Figure 4.39, acco unting for 19.36% of the total variance of the mixed-layer te mpera t ure anomalies. This EOF shows interannual variability in mixed-layer temperature in the coasta l zone a l ong the nor theast boundary 105

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE Figure 4.38a. anomalies of the mixed-layer temperature centered on Aprill978. This pattern is positively dominated by the spatia l pattern of the first EOF. 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE Figure 4.38b. anomalies of the mixed-layer temperature centered on July 1974. This pattern is negatively dominated by the spatia l pattern of the first EOF. the northern part of the Bay of Bengal, and around Madagascar. We see also a notable variability in the southeast Indian Ocean ; however, this var iabili ty i s negatively correlated to that in the coastal zone. Two running-mean anomal y fie ld s of the mixed-layer temperature are plotted in Figure 4.40a and Figure 4.40b to show the predominantly positive and negative con -tribution of the second EOF to the mixed-layer temperature anomalies respectively. Higher temperature, compared to its corresponding mean annu a l cycle va lu e is along 106

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25N 20N 15N ION 5N EQ 58 lOS 158 208 258 IJ. 0 20 0 0.10 Ul 0.00 ] -0.10 e -o.zo 40E 50E 60E 70E 80E 90E IOOE IIOE (a) S J a tial EOF -0 .30 -0.40 1960 1965 1970 1975 1980 1985 1990 Year (b) Temporal EOF Figure 4.39. Spatial pattern (a) is modulated by the time series (b) of the second EOF of mixed-layer temperature. the northeast boundary and around Madagascar and lo wer mixed-layer temperature in the southeast Indian Ocean during the period centered on April 1979. The negative contribution of this EOF during the period centered on July 1963 shows the opposite s i tuation. The third EOF is illustrated in Figure 4.4 1 which accounts for 11.75 % to the total variance of the temperature anomalies. The spatia l anomal y distribution of this EOF mode retains the interannual variability of the mixed-layer temperature in the southern Indian basin. Out-of-phase variabilities are captured in this EOF mode for the southeast and southwest basins. 107

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25N 20N 15N lON 5N EQ 5S lOS 155 205 25S 40E 50E 60E ?OE BOE 90E lOOE llOE Figure 4.40a. Anomalies of the mixed-layer temperature centered on April1979. This pattern is positively dominated by the spatial pattern of the second EOF. 25N 20N 15N lON 5N EQ 55 lOS 15S 20S 25S 40E 50E 60E ?OE BOE 90E lOOE llOE Figure 4.40b. Anomalies o f the mixed-layer temperature centered on July 1963. This pattern is negatively dominated by the spatial pattern of the second EOF. Two runnmg-mean anoma l y fields of the mixed-layer t e mperature are plotted in Figure 4.42a and Figure 4.42b to show the periods when the third EOF mode makes its maximum positive and negative contribution resp ec tively. Evidence of this mode's pattern can be seen during the period centered on July 1986. Mixed-layer temperature is lower than its corresponding mean annual cycle va lu e in the sout h east Indian Ocean whi l e the temperature in the southwest basin has mix e d positive and negativ e anomalies. The dominantly n egativ e co ntribution of the this EOF mode ca n 108

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S u. 0.20 0 0 .10 [.lJ 000 -;; 40E 50E 60E 70E BOE 90E lOOE llOE (a) Spatial EOF 8. -0.10 E -0.20 -0.30 -0.40 1960 1965 1970 1975 1980 1985 1990 Year (b) Temporal EOF Figure 4.41. Spatial pattern (a) is modulated by the time series (b) of the third EOF of mixed-layer temperature. be seen in the temperature anomaly field during the period centered on July 1969 which shows a lower (higher) temperature in the southwest (southeast) basin 4.3 Interannual Variability in Heat Budget In this section we discuss the interannual variability of heat fluxes and transports across the four interfaces and sections as we have discussed for the climatological integration including the heat fluxes through sea surface the meridional heat transport across equator, the zonal heat transport across 80 E section between the equator 109

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25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE Figure 4.42a. --\.nomalies of the mixed-layer temperature centered on July 1986. This pattern is positively dominated by the spatial pattern of the third EOF. 25N 20N 15N lON 5N EQ 5S lOS 15S 20S 25S 40E 50E 60E 70E BOE 90E lOOE llOE Figure 4.42b. Anomalies of the mixed-layer temperature centered on July 1984. This pattern is negatively dominated by the spatial pattern of the third EOF. and Sri Lanka, and the heat exchange between the first and second layers. Through investigating these heat fluxes and transports, we try to understand the interannual monsoon-cycle related variability in the Indian Ocean heat budget. vVe begin by discussing the mean annual cycle of heat fi lLxes and t ransp o rts and comparing them with their corresponding climatological integration results in Section4.3.1. The interannual monthly-mean results are discussed in Sect i on4.3 2 Inte rannual variability of the running-mean anomalies of the model fields are ana110

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.......... 0 '---"' X ::J c;:: .....-0 Q) I 30 20 / / I 10 I I 0 ..... --10 ' __ North Basi n ____ South Basin \ Jon Feb Mar Apr May JJn Jul Aug Sep Oct Nov Dec Jon Month Figure 4.43a. Seasonal sea-surface h eat fluxes. The mean annual cycle of heat fluxes (1014W) are calculated through ;.he sea surface of the northern and southern basins. Positive values indicate outward h eat fluxes from the sea water into the air. lyzed in Section4.3.3 by filt e ring out oscillations with periods shorter than twehe months. 4.3.1 Mean Annual cycle of Heat Budget in the Indian Ocean The mean annual cycle of heat fluxes and transports are computed by temporally averaging for each month these heat fluxes and transports through different interfaces and sections over the thirty years of model integration. These heat fluxes and transports are discussed and compared with their corresponding climatological integration results in the following The mean annual cycle of heat fluxes through the sea surface are shown in Figure 4.43a for the northern and southern Indian basins. These heat fluxes are quite similar to their corresponding climatological results in Figure 3.15a on Page 47 except that the peak values of the heat loss are weak e r for the mean annual cycle for both the north e rn and southern basins during the southwest monsoon. This reduction of the heat loss leads t o a little stronger total heat input (1.5P\iV P\\ = 101 4lV) in the northern basin and a weaker total heat loss ( .3PW) in the southern basin. 111

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.....--.. 0 '--" Q) 0' c 0 ..c u X w --0 Q) I 40 20/ 0 -20 / __ North Basin _. South Basin \ -"' _-,,__,_ __ =-= \ \ Jon Feb Mar Apr May Jun Jul A u g Sep Oct Nov Dec Jan Month Figure 4.43b. Seasonal heat exchanges between the first and second lay e rs. The mean annual cycle of heat exchanges (101 4 W) are calculated between the first and second lay e rs of northern and southern basins. Positive values indicate upward heat transports from the second layer into the first layer. The mean annual cycle of heat exchange through the interface between the first two layers are shown in Figure 4.43b for the northern and southern Indian basins Comparing these heat exchanges to their corresponding climatological integration results in Figure 3.15b on Page 48, we see similar variability in both the northern and southern basins but a large difference in the amplitudes in the southern basin. As we mentioned early in Section 4.2.1 shallower mixed laye r occurs during the late phase of the southwest monsoons. Correspondingly less entrainment and detrainment across layer interface leads to l ower fluctuation in heat exchange between the first and second layers in the interannual integration. The mean annual cycle of cross-equatorial heat transports are shown in Figure 4.43c for t he first and second l ayers, respectiv ely. These heat transports are quite similar to their corresponding clima t ological integ ration results shown in Fig-ure 3.15c on Page 49, though without the short period oscillation. This nearly perfect match indicates a consistent heat overturning in a vertical c irculation throughout t he thirty years of the model integ ration. 112

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20 0 1 0 __ Loyer1 ____ Loyer2 -+-' '-0 0.. (f) c 0 '-1-0 ----. :::.::: ------+-' -10 0 Q) I Jon Feb Mar Apr May Jun J ul Aug Sep Oct Nov Dec Jon Month Figure 4.43c. Seasonal cross-equatorial heat fluxes. The mean annual cycle of heat fluxes (1014W) i s evaluated across equator in the first and second layers. Pos itive values indi cate northward cross-equatorial heat transports from the southern basin into the northern basin The mean annual cycle of heat transport across a meridional section at sao E from the equator to the northe rn boundary are shown in Figure 4.43d for the first and second layers. These heat transports also match well their corresponding climatological integration r es ults shown in Figure 3.15d on Page 50. The dominant eastward heat transport in the first layer indicates a similar pathway of heat transport in the model results of the interannua l and climatologica l integrations ; most of the heat input through both the surface and the layer interface is transported eastward across 80 E between the equator and Sri Lanka and then across the e quator to the southern basin between sao E and the eastern boundary. The mean annual cycle of heat budget in the Indian Ocean matches their correspending results of the climatological model integration, except for diff ere nces caused by the Indon es ian throughflow which is lowe r in the interannual integration. In addition we further a nalyze and discuss the interannual variabilit y of t h ese a nnual cycles in the heat fluxes and transports in the following sections. 113

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....--... 0 ...._..... ...... .._ 0 0... (/) c 0 .._ f-...... 0
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Figure 10 5 'i 0 0 ;;: 0 :X: 'i 0 M :> ;;: 5 I -10 1960 10i -10l -2J 1 960 4.44a. North Ba s i n llill r 1 965 1970 1975 1 980 198 5 1990 Year 3outh Bas in 'I v v 1 965 1970 1975 1 980 1 985 1990 Year Int erannual heat fluxes through the sea surface Int erannual monthly-mean heat fluxes (1014W) are eva luated through the sea surface of the northern and southern basins Positive values indicate outward heat fluxes from the sea water into the air. retreating respectively during and after the southwest monsoons. The cross-equatoria l heat transports are shown in Figure 4.44c for the first and second layers. Steady annual oscillation is seen for the cross-equatorial heat transport in the first layer, whi l e the corresponding interannual va ri ability of the heat transport in the second layer is more obvious The heat transport across a meridional sect ion at 80 E from the equator to the northern boundary are shown in Figure 4.44d for the first and second layers. A slow interannual var i ation in the amplitude of the annual oscillation can be seen in the t i me series o f both t h e first a nd second layer. Positive values indicate eastward heat transports across t h e 80 E sect ion from the Arabian Sea into t h e Bay of Bengal. 115

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North Basin 1960 1 965 1970 1975 Year 1980 1 985 1990 South B a s in 20 0 .. "' c 0 .c UJ g -20 :r 19 6 0 1965 1970 1975 Year 1980 1985 1990 Figure 4.44b. Interannual heat exchanges between the first and second lay e rs Interannual monthly mean heat exchanges (1014W) are calculated between the first and sec ond la yers for northern and southern basins. Positiv e values indicate upward heat transports from the second layer into the first layer. The interannual monthl y -mean heat fluxes and transports show both annual and interannual variability, implying a strong interaction with the mon soons. The interan-nual variability of these heat flux e s and transports is further studied in the following section via analysis o f their corresponding running-mean anomalies. 4.3.3 Interannual Variability in the Running Mean Anomaly In t his section, we in vest igat e the inter a nnual variabi li ty of the Indian Ocean heat budget by focusin g on t he running-me a n anomalies of heat flux es and transports through the sam e four interfa ces and sections as we dis c u sse d in the prev ious sections. We cal culate the inte rannual running-mean heat flux or transport a nomali es in the following pro ced ure As b e for e, we first compute t h e anomalies for each in-116

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20 "i 1 0 0 1 0 I :-20 1960 A I 1965 1970 Loyer 1 1 9 75 Y eo r ( I 1 1980 1985 3 .)" I v 1 1990 L o yer 2 0 2 g. c 0 I 1 960 1965 1 97 0 1975 Year 1980 1 9 85 1 99 0 Figure 4.44c. Interannual cross-equatorial heat fluxes. Interannual monthly mean heat transports (1014W) are evaluated across equator in the first and second layers. Positive values indicate northward cross-equatorial heat transports from the southern basin into the northern basin. terannual monthly-mean heat flux or transport by subtracting its mean annual cycle discussed in Section 4.3.1. Then, for the heat flux or transport across each interface or section, we average their interannual monthly mean anomalies for a twelve-month period sub-sampled at three month intervals. The median time of each twelve-month period represents the time of the running-mean value calculated over that period. The running-mean computation filters away oscillations with periods less than twelve months in the monthly-mean anomalies. FFT technique is appli e d to the runningmean anomalies to analyze the spectrum and further diagnose the dominant periods of the interannual variability in these heat fluxes and transports. The interannual running-m e an heat flux anomalies through the sea s urface are s hown in Figure 4.45 for the northern and southern Indian basin s Comparing the 117

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0 Q. .. c 2 -10 .... 0 -20 t# =--30 1 960 1 \ J IV i t (\ 1965 1970 rn 1 r 1975 Year I i/ p 1980 3 3 = j :1i :l = 1985 1990 Loyer 2 0 z 1960 1965 1970 1975 Year 1980 1985 1990 Figure 4.44d. Interannual heat transports across 80 E section Interannual monthly-mean heat transports (1014W ) are calculated ac r oss section at 80 E in the first and second layers two t ime series, we see that most of their peak values are in phase. Their interannual oscillations are simi l ar, with p e riod varying from two to five years, t hroughout the the thirty yea rs. The maximum negative anomaly occurs in 1976 f or the heat flux in the northern basin. T hi s indi cates more heat input throug h the nor thern basin surface in 1976. A positive peak va lu e in earl y 1974 indicates a reduction of heat input during a yea r period covering the southwest monsoon of 1973 and the northeast monsoon of 1 974. For the heat fluxes through the so uth ern basin sur f ace, positive peak values in 1968, 1974 and 1978 imply a intensified heat l oss in these yea r s, and t he negative peak va lues in 1969 1973, a nd 1987 impl y a r educed heat loss at these time. The s pectrum of int e rannual va ri ability of the heat fluxes through t he sea surface 118

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North Basin '1 1.0 0 >. 0 E 0 0.0 c < X :l -0.5 G: 0 "' -1.0 I 1960 196 5 1970 1975 1980 1985 199 0 Year Basin 'i 1.5 0 1.0 >. 0 .5 0 E 0 0 0 c < X :l G: 0 "' -1. 5 I i960 196 5 1970 197 5 1980 19 8 5 1990 Year Figure 4.45. Running-mean sea-surface heat fluxes. Running-mean heat flux anomalies arc calculated through the sea surface of the northern and southern basins. Positive heat flux anomalies indicate that the outward heat fluxes are intensified or the inward heat fluxes are reduced. of the northern and southern Indian Ocean is shown in Figure 4.46. The amplitude of the heat flux is plotted against the frequ e nc y Since the model integration is done over thirty years and the running mean is performed over twelve months, amplitude with frequency lower than tenth year-1 and higher than one year-1 is removed from the plots. Dominant periods are at 2.8 3.8 and 6 years for the heat flux through the northern basin surface, and dominant periods are at 2 7 and 3 7 years for the heat flux through the southern basin surface. Running-mean anomalies of the heat exc hange between the first and second lay ers are s hown in Figur e 4.47 for the northern and southern basins. The running-mean anomalies of the heat exchange between the first and second laye rs in the northern basin are not closely correlated either to their corresponding heat exchange anomalies 119

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Figure 4.46. Spectrum of sea-surface heat fluxes. Spectrum of the running mean heat flux anomalies is evaluated through the sea surface of the northern and southern basins. in the southern basin or to the heat flux anomalies through the northern basin surface. The uniqueness of this time series implies that the interannual variability of the heat exchange across the layer interface in the northern basin is controlled by more complicated physical processes the combination of the thermodynamics and dynamics driven by the reversing monsoons. Running-mean anomalies of the heat exchange between the first and second layers in the southern basin however are positively correlated to the heat flux anomalies through the southern basin surface. The close correlation of these two time series indicates that the heat exchange between the first and second lay ers is more thermo-dynamically controlled ; strong heat loss through sea surface is accompanied by less heat detrainment simultaneously and vice versa 120

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'i North Basin 0 1.0 >. 0.5 0 E 0 c <{ 0.0 ., "' c 0 .<: u )( w 0 -1. 0 ., I 1960 1965 1970 1975 1980 1985 1990 Year 'i South Basin 0 4 >. 2 0 E 0 c <{ ., "' c 0 .<: u )( w 0 -4 ., I 1960 1965 1970 1975 1980 1985 1990 Year Figure 4 47. Running-mean heat exchanges between the fist and second layers. Running-mean heat exchange anomalies between the first and second layers are calculated for the northern and southern basins. Positive anomalies indicate a intensified heat entrainment from the second layer in to the first la yer or a reduced heat detrainment. As we concluded from the analysis of the climatological model integration, the c ross-equatorial heat transported southward in the first layer has two fates in the southern basin with a portion being pumped into the second lay e r by detrainment and a portion being lost to the atmosphere through latent heat flux. If the heat loss is intensified through the southern basin surface, the mix ed-layer temperature should be reduced and the heat detrainment through the lay e r interfac e may be also reduced correspon dingly. The most notable l arge anomalies in 1973 and 1977 show resp ect iv ely a significant r ed uction and increase of the h eat ent rainm ent through t he northern basin layer int e rf ace. The negative peak va lues in 1969 and 1987 indicat e the intensified heat 121

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North Basi n 0 1 0 0 0 8 0 .:.:. 0.06 GJ 0.04 a. 0.02 0.10 0.20 0.30 0.40 0.50 0.60 0. 70 0.80 0.90 1.00 F requency (YEAR"' ) South Basin 0.25 ,-----.------..---.----r---r-----,---,.-----.------, 0 .20 0 .:.:. 0 15 0.00-0.1 0 0.20 0.30 0.4 0 0.50 0.60 0. 70 0.80 0.90 1.00 F req uency (YEAR"') Figure 4 .48. Spectrum of heat exchange between layers. Spectrum of the running mean heat exchange anomalies is evaluated through the layer interface of the north ern and southern basins. detrainmen t in the southern basin, and the posit ive peak values in 1971 and 1982 show the opposite result Spectrum of interannual variability of the heat exchanges between the first and second layers in northern and southern Indian Ocean is shown in Figure 4.48. The heat exchanges through the l ayer interface are domi nantly at per iods of 2 5, 3.3 and 5 years in the northern basin and at periods of 2 and 3.8 years in the southern basin. Running-mean anomalies of the c ross-equatoria l heat transport are shown in Figure -Ll9 for the first and seco nd layers. As it is the cross equatorial flow that carries h ea t across the equator. and the c ross-equatoria l flow is strongly modulated by equatoria.l waws as discussed abO\e. the cross-equatoria l heat transport is also dynamically ('Ont rolled by these eq uatorial waves. 122

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F Loyer 1 2 0 c ]:-. 0 E 0 c < '-0 a. (/) -t \ ; c: ,_ -2 0
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Loyerl 0.15 "f 11> "0 :> 0.05 E 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.8 0 0.90 1.00 Fr equenc y (YEAW ) Loyer2 0.20 0 "' 0.10 "0 :> E a. E 0.05[-0.00 0.10 0.20 0.30 0.40 0.50 0 .60 0.70 0.8 0 0.90 1.00 Fr equency (YEAR ) Figure 4.50. Spectrum of cross-equatorial heat transports. Spectrum of the running-mean heat transport anomalies across the equator in the first and second layers. we concluded from the climatological model integration, heat gained in the Arabian Sea in the first-layer from both surface heat input and entrainment from the thermocline layer is transported primarily eastward across the sao E section into the Bay of Beng a l and then across the equator into the southern basin The heat transported across sao E however, has strong interannual variability during t he thirty yea rs. This eastward heat transport is also modulated by equatorial d y namics. The positive peak values in 1979 19S5, and 19SS indicate that stronger eastwa rd heat transport occurs in the firs t layer in these years, and imply that more heat is transported southward across the e quator east of sao E. From Figure 4.43d, we see a weak interannual-mean heat transport ac ross the sao E section in the seco nd l ayer and, comparativ ely, the interannual Yariability of this heat transport is strong. Heat is transported eastward 124

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'i Layer 0 2 >1 0 E 0 0 c <( '1 0 0.. "' c 2 >-0 -3 \1) I 1960 1965 1970 1975 1980 1985 1990 Year Layer 2 0 1 0 >-0 E 0 c <( 0 0.. "' c >-0 -1.0 \1) I 1960 1965 1970 1975 1980 1985 1990 Year Figure 4.51. Running-mean h eat transports across 80 E sect i on. Running-mean heat transport anomalies across sect i on at 80E are calcu l ated between eq u ator and Sri Lanka in the first and second layers. Positiv e anomalies indic ate a stronger eastward, or a weaker westward heat transport across the section. in the second l ayer between the equator a nd Sri Lanka in 1961 1973 1977 and 1 982, and westward in 1962 1970, 1981 and 1983. Spectrum of interannual va riability is shown in Figure 4 .52 for heat transports across an 80 E sectio n between equator and Sri Lanka in the first and second layers Dominant perio ds a re at 2, 3, 3 8, and 5 years in the first l ayer, and at 2 and 5 years in t h e second l aye r 4.4 Interannual Variability Related to SOl In t h is sect ion we a nal yze t h e cor r elatio n between the inte rannual va riabilit y of the mod e l result s and the Southern Oscillation Indic es (SO l ) ass o ciate d to El N ino in the Pacific Ocean from 1960 to 1989. To simplify our evaluat ion we focus on 125

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Loy erl 0.25 'i 0.2 0 0 .:::. 0.15 QJ "U 0.1 0 a. E < 0.00 0.10 0.20 0.30 0. 4 0 0.50 0.60 0.7 0 0.8 0 0.90 1.00 Frequ e ncy (YEAR"') Loyer2 0.15 'i 0 0.10 QJ "U :;:J %. 0.05 E < 0.00 0.10 0 .20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Fr eq uency (YEAR"') Figure 4.52. Spectrum of heat transports across 80 E. Spectrum of the running mean heat transport anomali es across the 80 E in t h e first and second layers. corre l ation between the SOl and t h e interannual variabilities of the temporal EOFs of the running-mean anomaly the firstl ayer thickness HL Cross spectra are eva lu ated between the first three primary temporal EOFs of H1 and the SOL The time se ri es of SOl and the EOFs are normalized by first r e moving the t h eir mean va lues and then taking ratio of their va lu es to their standard deviations, respective l y The first EOF accounts for 40.40 % of interannual va ri abi lit y of tempo r a l EOFs of HL Figure 4 53a illu strates t h e amp l itudes and t im e dela ys o f c ro ss spectrum b e twe e n the first EOF of H1 and SOL It s hows a dominant peak amplitude value at a p e riods o f 5 years and its corresponding time d elay is abou t zero. Hi gh corre lati on at a p e riod of 5 yea r s ca n a l so been seen in Fi gure 4.53b of the c ro ss spectr um between SOl the seco nd temporal EOF of H1 that con t ribut e 20.18 % 126

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E 2 0.050 3 u 3 1J 0.020 "' N 0.01 0 0.10 0.20 0.30 0.4 0 0.50 0.60 0.70 0.8 0 0.90 1.00 Fr., q ue ncy (YEAW') 1 0 0 "' c ,.., 0.5 0 o; 0 "' E >= 0 10 0.20 0.30 0.40 0.50 0.60 0. 70 0.8 0 0.90 1 .00 F req u e n c y (YEAW') Figure 4.53a. Cross spectrum between the first EOF of Hl and the SOL to total variability of Hl. This peak value corresponds to a 3-month delay for the second EOF of Hl. Negative value of time delay indicates that the EOF variability is after SOL The third EOF of Hl accounts only about 7 % of the total variance of Hl, and its correlation with SOl is much less important than the first EOFs mentioned above. However, a peak v alue at 5-year period shows a consistent correlation between Hl and SOl at this period. The time delay shows that the the variability of this EOF is one year ahead of SOL All three temporal EOFs of the first-la yer thickness show a correlation to the SOl at a variability with period of five years A s e condary correlation at a period of 2.5 years can also been seen throughout these three cross spectra. 127

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1 0 ., 0.8 "0 .2 0 6 :g w 0.2 a:: 0.2 0 4 0 6 0.8 1.0 Frequency ( YEAW') 1.0 '-0.5 0 ., 0.0 G. >-0 -0. 5 w a ., 1.0 E ;;: 1.5 0.2 0.4 0.6 0.8 1.0 Fr equency (YEAW ) Figure 4 .53b. C r oss s p e c trum betwee n the sec ond EO F of Hl and the SOL E 2 0.10 u ., t5r 0.08 (I) 0.06 u "0 0.04 ., E o.o2 0 z 0.1 0 0.20 0.30 0 .40 0.50 0.60 0 70 0 .80 0.90 1.00 F r equency (YEAW') 0.10 0 .20 0.30 0.40 0.50 0 .60 0.70 0.80 0.90 1.00 Frequency (YEAR' ) Figure 4 .53c. C r oss s p ectrum b e tw ee n the t hird EOF o f Hl a n d t h e SOL 128

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4.5 Summary I n this chap ter we desc rib e a hindcast expe rimen t in wh i ch we int eg rate t h e model und er interannual mo n t hl y -m ea n f o r c in g f o r a p e riod of thirty years ( 1960-1989 ). The mode l i s integrate d under the f o r c in g data from 1960 for ten yea r s to p rovid e t he initial cond iti o n for the thir ty-year integration. The anal ys is of the interannual variability o f the model result a r e performed for the basin wide fields and t h e integrated c r oss sect i on heat fluxe s and tran s ports sepa r ate ly. Four mode l field s fr o m the interannua l in teg ration a r e discussed in this chapter; t h ey are the velocity a nd t hi c kn ess fields f o r the first layer a nd the t hickn ess and temperature o f the mix e d l ayer. The mean annual cycle of these fields matc h es both spati a ll y and tempo r a ll y closely to those from the climatolo gica l integrati o n discussed in t h e previous chapter, with on l y a few exceptions. The most notable diff erence in t h e first l ayer velocity fie ld s is the Ind o n es i an thro u g hflow: w hi ch is wea k ened, and at times reversed in t he inter ann ual m ode l integ rati o n An othe r diffe r ence i s the reduced mixed-layer depth in the sout h east Indian Ocean during the late so u t h west m o n soo n Interannua l variabi li ty in all of the four fie lds i s o b v i o us in the interannu al monthly m ea n fie ld s. An EOF a n a l ys i s is applied to the r unnin g-mean a nomali es o f t hes e fie l ds To co n centrate on int e r a nnu a l variabi li ty, we anal yze and discuss o nl y the three p rimar y EOFs o f eac h fie ld. The firs t three vecto r EOFs of t h e fir st-laye r ve l ocities capture interannua l var i abil i ty in t h e equato ri a l currents (the NEC, SECC, and SEC), t h e two gy r e system in the So m a li Current, and the EACC. The EOFs o f the first-layer thickness s how t h e major inte r a nnu a l va r iabi l ity assoc iated with the r eflect i o n of eq u a t o ri a l waves at t h e eastern boundary and the depth and locat i on o f t h e t h ermocli n e ridge in the cent r a l Indi an Ocean. Cross-sp ectrum analys i s indi cates 129

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that a variability with five-year period in the temporal EOFs of the first-layer thick ness are highly correlated with the SOL In the primar y mixed-layer EOFs, strong interannual variability can be seen in the southern portion of the Bay of Bengal due to the reflection of equatorial waves. In addition large scale interannual variability in mixed-layer thickness is seen in the southeast basin. The mixed-layer temperature field has the least interannual variability among these four fields as compared with its large annual cycle. The interannual variability shown in the first three mixed-layer temperature EOFs is in areas associated with the strong upwelling, dominantly lo cated over the thermocline ridge along 10 S and in the the coastal upwelling areas in the Arabian Sea and Bay of Bengal. Interannual variability in the Indian Ocean heat budget is analyzed by focusing on the heat fluxes and transports through four interfaces and sections: the heat flux through sea surface, the meridional heat transport across the equator, the zonal heat transport across 80 E section between the equator and Sri Lanka, and the heat ex change between the first and second layers. The mean annual cycle of these heat fluxes and transports match very well to that resulting from the climatological in tegration except for the weakened heat entrainment and detrainment due to less seasonal fluctuation of the mixed-layer thickness in the southern Indian Ocean in the interannual model integration. Interannual variability is apparent in the the time series of the running-meaning anomalies of these heat fluxes and transports. Oscillations with periods of multi ple years are seen in all these anomalies and are quantified in the spectra of these anomalies. The interannual variability in heat flux through the sea surface in the northern and southern basins is in phase at most of the peak values. This indicates that the intensified surface heat gain in the northern basin occurs simultaneously 130

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with a reduced surface heat loss in the southern basin. The interannual variability of the heat exchange betw ee n the first and second layers in the northern basin is con trolled by a combination of the thermodynamic and dynamical processes driven by the reversing monsoons (wind stirring, smface heat flux Ekman pumping, planetary wave propagation, etc.) while the corresponding heat exchange in the southern basin is more thermodynamically controlled and is dominated by surface heat loss. The heat transport across the equator and across goo E is modulated by equatorial waves and strong interannual va riability in heat transport exists across these sections dur ing the thirty year integration. However, there i s not an obvious correlation between the heat transports across the equator and the goo E section. Positive anomalies for the cross-goo E heat transport indicates that more heat gain in the Arabian Seas is carried eastward into the Bay of Bengal and then transported southward back the the southern basin across the east portion of the equator. 131

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CHAPTER 5 SUMMARY AND CONCLUSIONS The essential focuses in this thesis are to simulate the dynamics and thermo dynamics of the Indian Ocean circulation, driv e n by observed atmospheric forcing functions, so as to investigat e the heat budget of the basin and its va riability. A four layer thermod y namic model is described to simulate the Indian Ocean cir culation and heat budget. The layered model has t he advantage that it retains a higher horizontal resolution necessary for computation of the advective terms while filtering higher vertical mod e s that may contribute to the solu t ion in non-physical ways [Barnier e t al. 1991]. The thermodynamic model used in this study is concep tually based on two existing models. One is the 3.5-layer dynamic model described by Luther and 0 'Brie n (1985] and extended later b y Jensen (1990]; the other is the 2.5-layer thermodynamic model developed by McCreary and Kundu (1989]; M c Cre ary et al. (1993]. In the present version of our num e rical model a KrausTurner mixed-layer is embedded in the upper l aye r of a four-layer reduced gravity model i.e., the depth-integrated transport vanishes in the lowes t layer. The r e duc e d gra,ity approximation has the effect of filtering the barotropic mode leaving in effect, t hree baroclinic mod es. The modified formulations used in the mod e l are based on those from Kraus and Turner (1967] and M cCre ary et al. (1993]. The s um of wind stirring. solar radiation sea surface cooling, and e nergy dissipation gi,es the net pr oducti on of t urbul ent kin et i c energy as s hown in (9). vVe retain the p e n et r a t in g term cont ribu ted 132

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from the solar radiation originally suggested by Krau s and Turner [1967] and adjust the heat dissipation changing quadratically in thickness of the mixed layer [ G i ll and Turner, 1976]. We derive a gen e ral formulation to comput e the depth-averaged horizontal pre s sure gradient in each layer through the layer thicknes s and temperature as given in ( 4). To realisticall y simulate the temperature in the thermocline we assume that the temperature in the second la y er is changing linearl y with depth ; the temperature at the bottom of the layer is the same as the value in the third layer and the temper ature at the top i s exp ressed in (8). Volume transport through the southe rn open boundary i s a dju s ted at every time step according to a frac t ion of the net gain of the water mass accumulated in the modeled basin from all of the previous yea rs. The four components of heat flux through the sea surface considered as thermal forcing in the model are incoming solar shortwave radiation, outgoing longwave radiation latent heat flux, and sensible heat flux. Precipitation and salinity are neglected in the current version of our mode l and may be includ e d in the future versions. The high horizontal resolution of our model explicitly captures the details of eddy interactions that are importan t in the annual cy cle of the Indian Ocean circulation faithfully reproducing the major c urrent patterns as observed. This is not accom plish ed by other, coarser resolution models such as the 1/2 degree 2.5 layer model of McCreary et al. [1993] or the 1.5 degree, 24 l eve l GCM model of Lee and Marot zke [1997]. The model also r e produ ces the observed annual cycle in SST and conserves heat over a long-t erm int eg ration under climatological for c ing. We may co nclud e that the model c ir culat ion balances h eat in some reasonabl e way co nsisten t with the model physics. In the annual mean t h ere is a n et heat input through the sea surface in the northern basin as observed. Nearly all of the heat gain occurs in the Arabian Sea a nd 133

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is first tran sported eastwa rd across goo E between Sr i Lanka and t h e equato r int o the Bay of Bengal, t hen across the equato r into t h e sout h e rn basin. Heat transport ac r oss t h e eq uator is accomp l ished primarily through a meridi ona l overt urnin g ci r c ul ation so u t hward in the firs t l aye r a nd nor thwa rd in the seco nd layer. The heat transported so uthw a rd has two fa tes in t he so uthern b as in with a portion b e in g pumped int o t h e seco nd layer by detrainment process a nd a portion be in g lost to t h e atmosphe r e through l atent heat flux Part of the heat detrained from the first layer into the sec o nd is tran spo r ted n o rthw a rd in the western half of t h e bas in and then i s e n trained up wa rd in to the first l aye r pri maril y i n t h e Arab i a n Sea, w h i l e the remai nd er i s car ri e d out through t h e sout h ern ope n boundary in t h e seco nd layer. Overt urning in the mer i dional pl a n e i s the prim a r y m ode of the heat transport, with only about 7% co ntribution from the hori zo ntal gy r e effect. Significant a mplitud e,s h o r t-per i od var iabili ty in heat t r a n sport i s see n across the eq uator a nd across goo E. T hi s va ri ab ili ty is modulated by eq u atoria ll y-t r apped waves at a nnu a l se mi a nnu a l a nd 2 0 to 30-day periods. The sho r t period oscillations in meridional heat transpor t a r e driven by eq uat or i a l mixed Rossby gravity waves as seen by T sai et al. [1992]. The sem i a nnu a l s i g n a l i s the r esult of equatoria l Rossby a nd Kelvin waves, w hi c h are nearl y resonant in t h e Indian Ocea n as show n by J ensen [1993]. This time va riabilit y has implication s f or co nstructin g a heat bud get f o r t h e basin fr o m h y drograp hi c sectio n s that a r e occ upi e d only o n ce or t hat take l o nger t h an 20 days to co m plete as in the \ VOCE H ydrog r ap hi c Program. The strong ann u al cycle in the ocean circu lati o n a nd heat budget see n i n the model r esults suggests that observat i ons made in one season can n ot r epresent the annual mean in the Indian Ocean. As Knox [19g7] pointed out in his concludin g remarks, i t is the in terannual changes 134

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in the typical monsoon cycle that disturb the lives of people in this region Very few studies have considered the interannual variability of the annual cycle in ocean circu lation and heat budget driven by the reversing monsoons [Luther and O'Brien, 1989 ; Luther, 1997; Valenti et al., 1997]. on an understanding of the climatologi cal annual cycle we further investigate t he interannual variability in Indian Ocean circulation and heat budget by perforrr.ing a model integration under interannual monthly-mean forcing for a period of thirty years (1960-1989). The model is integrated under the forcing data of 1960 for ten years as a spin-up for the thirty-year integration. The analysis of interannual variability in the model results is performed on the basin-wide fields and on cross-sections of heat fluxes and transports separately. Selected model fields from the interannual integration are discussed in this the sis The mean annual cycles of these fields match their corresponding climatological integration results with only a few exceptions. The most notable difference in the first-layer velocity fields is the Indonesian throughflow which is weakened, and even eastward dominated, in the mean annual cycle. Another difference is the reduced mixed-layer depth in the mean annual cycle in the southeast Indian Ocean during the late summer monsoon Interannual variability in these model fields is studied through an EOF analysis. The reconstructed velocity field from the first three primary EOFs of the first-layer velocity capture the interannual variability in the equatorial currents (the NEC, SECC, and SEC), two-gyre system in the Somali Current, and the EACC. The primary EOFs of the first-layer thickness shows the major interannual variability associated with the reflection of the equatorial waves at the eastern boundary and the depth and location of the thermocline ridge in the central Indian Ocean. Cross-spectrum analysis indicates that a variability with five-year period in the temporal EOFs of 135

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the first-layer thickness are highly correlated with the SOL In the first three mixed layer EOFs, strong interannual variability can be seen in the southern portion of the Bay of Bengal due to the reflection of equatorial waves. In addition the inter annual variability of mixed-layer thickness exists also in the southeast basin. The mixed-layer temperature field has the least interannual variability among the model fields relative to amplitude of its annual cycle. The interannual variability shown in the first three mixed-layer temperature EOFs are in areas associated with the strong upwelling, dominantly located along the thermocline ridge at 10 S and in the the coastal upwelling areas in the Arabian Sea and Bay of Bengal. Mean annual cycles of heat fluxes and transports of the interannual integration match well their corresponding results of the climatological integration except for the weakened heat entrainment and detrainment due to the reduced seasonal fluctuation of the mixed-layer thickness in the southern Indian Ocean for the interannual inte gration Spectral analysis on the running-mean anomalies of these heat fluxes and transports show do11.1inant periods between two and six years. The interannual vari abilities of the heat fluxes through the sea surface in the northern and southern basins, respectively, are in phase in most of their peak values. These matches indicate that the intensified heat gain through the northern basin surface happens simultaneously with the reduced heat loss through the southern basin surface The heat exchange between the first and second layers in the northern basin is controlled by a compli cated physical process the combination of the thermodynamics and dynamics of the reversing monsoons while the corresponding heat exchange in the southern basin is more thermodynamically controlled and strongly related to the heat loss through the sea surface above. Both the cross-equatorial and cross-80 E heat transports are as sociated with the equatorial waves, and strong interannual variability exists in both 136

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these heat transports. However t her e i s not an obvious correlation between the the heat transports across equator and 80 E. Positive anomalies for the cross-80 E heat transport indicate that more heat gain in the Arabian Sea i s carried eastward across the cross-80 -section into the Bay of Bengal and then transported southward back the the southern basin across the easte rn portion of the eq uatorial section. The model in its present form gives r easona ble r es ults to explain both the annual a nd in te rannual variability in the circul atio n and heat budget of the upper Indian Ocean. Some shortcomings, howev er, still exist in t he current version of our thermo d ynamic model. The simplified formulations for the compl i cated mixed-layer physics n eeds further improvement specificaly to include the effects of sa linit y and of verti cal s hear The Indonesian throughflow needs to be quantitativ e ly controlled at the easte rn open boundary. The long-t e rm r e duction trend of the second layer thickness in the northern basin suggests that circulation in the deeper layers also may con tribute to the meridional overturning, which r e quires further study. Finally, we ne e d to inv est igate the effects of precipitation on surface heat flux in our model. 137

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REFERENCES Anderson L. T. D., D. J. Carrin gton, R. Corry, a nd C. Gordo n Modeling the Va ri abilit y of the Somali Current, J. Mar. Re s 49, 659-696, 1991. Anders o n L. T. D. and P. B. Rowlands The Somali Current Response to the Mon soon: The R e lative Importance of Local and R emote Forcing, J. Mar. R es., 395 417, 1976. Barnier B. B. L. Hua, and C. L. Provost O n the Catal ytic Role of High Baroclinic Modes in Eddy-dr i ven Large Scale Circu lation s, J Phys. Oceanogr., 21, 976 997 1991 Breid e nbach J. EOFs of Pseudo-Stress ove r the Indian Ocean ( 1977-85), Bul. Arne. M et. Soc. 71(10), 1448 1 454 1 990 Brown 0. B. J G. Bruce, and R. H. Evan, Evo lu tion o f Sea Surface Temperature in the Somal i Basin Dring the Southwest Monsoo n of 1979 S cience, 209(8), 595 597, 1980. Bruce, J. G., Edd i es Off the So m al i Coast During the Southwest Mo n soo n J. Geophys. Res., 84(C12), 7742 7748, 1979. Bunke r A. F Computations o f Surfac e Energy flux and Annual A i r-Sea Inte racti on Cycle of t h e North Atlantic Ocean, Monthly Weath. Rev 104 1123 1141 197 6 C l emens, S., vV. Prell D. Mur ray, G Shimmield, and F. Weedon Forcing Mechanisms of the Indian Ocean Monsoon, Nature, 353 720 725 1991. Cox M. D., A Mathematical Mode l of the Indian Ocean D eep Sea Res. 17, 1970. Cox, M. D., Equatorially Trape d \ "''aves and the Generati on of the Somali Curre n t D eep Sea Res. 23, 1139 1152 1976. Cox, M. D., A N um erica l Study of Somali Curr ent Eddies, J Phys. Oceanogr. 9 311 326, 1979 Cutler, A. N. and J. C. Swallow Surfac e Currents i n Indian Ocean( to 25 S, 100 E): Compiled From Hi s to rical Data Archived by the Meteorological Office, Brackn e ll UK, Inst. of Oceanogr. Sci., \Vor mley, E ngland 1984. D avis, R. E., Predictability o f Sea Surface Temperature and Sea l eve l Press ur e Anomalies over the North Pacific Ocean J. Phy s Oceanogr. 6 249-266, 1976. Di.iin g, vV., The Somali Curre n t: Past a nd Recent Observation s Pres ented at the F I E-Workshop, SCRIPPS Institution, La Jolla California 1979. Di.iing vV. and A. Leetmaa, Arabian Sea Cooling : A Preliminary Heat Bud get. J. Phys. Oc eanogr., 10, 307 312, 1 980. 138

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Evans, R. H. and 0. B. Brown, Prpagation of thermal fronts in the Somali Current System, Deep Sea Res. 28, 7521-527, 1981. Findlater, J., Mean Monthly Airflow at Low Levels Over the Western Indian Ocean, Geophys Mem. 115, 53, 1971. Gent, P. R. a nd J C. McWilliams Isop y cnal Mixing in Ocean Circulation, J. Phys. Oceanogr., 20, 150-155, 1990 Gent P. R., K. O 'N eill, and M. A. Cane A Model of the Semiannual Oscillation in the Equatorial Indian Ocean, J. Phyt-. Oceanogr., 13, 2148-2160, 1983. Gill, A. E. and J S. Turner, A comparison of Seasonal Thermocline Models With Observation, dsr, 23, 391-401, 1976 Godfrey, J. S., A. Alexiou, A G. Ilahude D. M. Legler M. E Luther, J. P. M. Jr., K Mizuno R. R. Rao, S. R. J. H. Toole, and S. Wacongne, The Role of the Indoan Ocean in the Global Climate System: Recommendations regarding the Global Ocean Observing syste m Tech. rep., Texas A&M University, College Station, Texas Ocean Observing System Development Pan e l Rep. 1995 Hardy, D. M and J J. Walton, Principal Components analysis of Vector Wind Mea surements, J Appl. Met., 17, 1153 1162, 1978 Hastenrath S. and L. Greischar, The Monsoonal Current Regimes of the Topical Indian Ocean: Observed Surface Flow Fields and Their Geotrophic and Wind driven Components J Geophys Res., 96(C7), 12,619 12,633 1991. Hastenrath S. and L. Greischar, The Monsoon Heat Budget of Hydrosphere Atmosphere System in the Indian Ocean, J. Geophys. R es., 98(C4), 6869-6881, 1993. Hastenrath S. and P. J. Lamb Climatic Atlas of the Indian Ocean Part I: Surface Cli mate and Atmospheric circulation, University of Wisconsin Press, Madison, 1979a. Hastenrath S. and P. J. Lamb, Climatic Atlas of the Indian Ocean Part II: The Oceanic Heat Budget University of Wisconsin Press Madison, 1979b. Hsiung J., R. E. Newell, and T. Houghtby The Annual Cycle of Oceanic Heat Storage and Oceanic Meridional heat Q. J R Meteorol. Soc., 115(485), 1-28 1989 Hurlburt H E. and J D Thomson A Numerical Model of the Somali Current, J Phys. Oceanogr., 6, 646-664, 1976. Jensen T. G. A Numerical Study of the Seasonal Variability of the Somali Current, Ph.D. thesis, Florida State University, 1990. Jensen, T. G., Modeling the Seasonal Un d e rcurrents in t he Somali Curent System, J. Geophys Res. 96(22), 22,151-22,167 1991. Jensen T. G., Equatorial Variability and Resonance in a Wind-Driven Incian Ocean Model, J. Geophys. Res., 98 22,533 -22,552, 1993. Jones C. S., D. M Leg ler, and J J. O'brien, Varibility of Surface Fluxes over the Indian Ocean; 1960-1989 Glob. Atm. Oce. Sys. 3, 249 -272, 1995. 139

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Kindle, J C. and J. D. Thompson The 26-and 50-day Oscillations in the Western Indian Ocean:Model Results, J. Geophys. Res. 94(C4) 4 ,7214 ,736, 1989. Knox, R. A., The Indian Ocean: Interaction With Monsoon, in Monsoons edited by Fein J. S. and P. L. Stephens, pp. 365-397, John Wiley New York 1987. Kraus, E. B. and J. S Turner A One-Dimensional Model of the Seasonal Thermocline. II: The General Theory and Its Consequences, Tellus 119, 89-106 1967 Kutzbach, J. E. Empirical Eigenvectors of Sea-Level Pressure, Surface Temporature and Precipitation Complexes over North America, J. Appl. Met. 6 791801, 1967. Lee, T and J. Marotzke, Seasonal Cycles of Meridional Overturning and Heat Transport of the Indian Ocean Tech. rep., MIT, Center for Global Change Science, Cambridge, Mass., Rept. No. 47, 1997 Legler, D. :\1., Empirical Orthogonal Function analysis of Wind Vectors over the Tropical Pacific Region Bul. Ame. Met. Soc. 64(3) 234-241 1983. Legler D. :YI., I. M. Navon and J. J. O Brien, Objective Analysis of Pseudostress Over the Indian Ocean Using a Direct-Minimization Approach Mon. Weath. Rev., 117 709-720, 1989. Lighthill M. J. Dynamic Response of the Indian Ocean to Onset of the Southwest Monsoon, Phil. Trans. Roy. Soc. London, A265, 45-92 1969. Lin, L. B and H E Hurlburt, Maximum Simplification of nonlin ear Somali Current Dynamics in Monsoon Dynamics, edited by Lighthill, M. J. and R. P. Pearce, Cambridge University Press, Cambridge, 1981. Lorenz, E. N., Empirical Orthogonal Functions and Statistical Weather Prediction Tech. rep. MIT Dept. of Meteorology, Cambridge Mass., Science Rept. No. 1, Statistical Forecasting Project, 1956. Luther, M. E., Interannual variability in the Somali Current, 1954-1976, Nonlinear World, to appear, 1997. Luther M. E. and J. J. O'Brien, A Model of the Seasonal Circulation in the Arabian Sea Forced by Observed Winds, Prog. Oceanogr., 14, 353 385, 1985. Luther, M. E. and J. J. O'Brien A ModModelling the Variability in the Somali Current, in MedoscalejSynoptic Coherent Structures in Geophysical Turbulence, edited by Nihoul, J C. J. and B. M. Jamart, pp. 373 386 1989. Luther, M. E. J. J O'Brien, and A. H. Meng, Morphology of the Somali Current Sys tem During the Southwest Monsoon, in Coupled Ocean-Atmosphere Models, edited by Nihoul J. C. J., pp 405-437, Elsevier Science Publishers B.V Amsterdam Netherlands, 1985. Luyten, J R. and D. H Roemmich Equatorial Currents at Semi-Annual Period in the Indian Ocean, J. Phys. Oceanogr., 12, 406 413, 1982. McBean, G. A., Estimation of the Pacific Ocean Meridional Heat Flux at 35 N, Atmosphere-Ocean, 29(3), 576-595, 1991. 140

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McCreary J. and P. K Kundu, A Numerica l Investigation of Somali Current During the Southwest Monsoon, jmr, 46, 406-413 1988. McCreary, J. and P. K Kundu, A Numerical Investigation o f Sea Surface Temperatur e Variability in the Arabian Sea J. Geophys. Res., 94(Cll), 16, 097-16,114, 1989. McCreary, J. P K. Kundu and R. L. Molinari A Mumerical Investigation of Dy namics Thermodynamics and Mixed-Layer Processes in the Indian Ocean, po, 31, 181-244, 1993. Molinari R. L., J. Swallow, and J. F. Festa, Evolution of the N ear Surface Thermal Structure in the Western Indian O c ean During FGGE, 1979 J. Mar. Res. 44(4) 739762, 1986. North, G R., T L. Bell R. F Cahalan and F. G. Moeng Sampling Errors in the Estimation of Epirical Orthogonal Functions Monthly Weather Review, 110 699706, 1982. Philander S. G. H., W. J. Hurlin and A D. Seigel Simulation of the Seasonal Cycle of the Tropical Pacific Ocean J. Phys. Oce anogr. 17 1 986-2 ,002, 1987. Philander, S. G. H. and R. Pacanowski A Model of the Seasonal Cycle in the Tropical Atlantic Ocean, J Geophys. Res., 91, 14, 192 14,220 1986. Potemra J T., M. E. Luther and J. J. O Brien The Seasonal Circulation of the Upper Ocean in the Bay of Bengal, J. Geophys Res. 96(C7), 12,667-12,683 1991. Preisendorfer R. W. Principal Component Analysis in Meteorology and Oceanogra phy Elsevier Science Publishers B V., New York Developments in Atmospheric Science 17 Compiled and edited by Curtis D. Mobley 1988. Price, J. F., Upper Ocean Response to a Hurricane, J Phys Oceanogr., 11, 153-175, 1981. Rago, T. A. and H. T. Heat Transport into the North Atlantic Ocean North of 32 N Latitude J. Phys. Oceanogr., 17, 854 871 1987. Rao R. R. R. L. Molinari and J. F. Festa, Evaluation of the Climatological Near Surface Thermal Structure of the Tropical Indian Ocean !.Description of Mean Monthly Mixed Layer Depth, and Seas Surface Temperature Surface Current and Surface Meteorological fields J. Geophys. Res. 84(C8) 10,801-10, 815, 1989. Rao R. R. R. L. Molinari, and J. F. Festa Surface Meteorological and Near Sur face Oceanographic Atlas, Tech. rep. Atlantic Oceanographic and Meteorological Laboratory Miami Florida NOAA Technical Memorandum ERL AOML-69 1991. Schopf, P. S. and M. A Cane, On Equatorial Dynamics Mixed La y er Physics and Sea Surface Temperature, J Phys Oceanogr., 13, 357 381 1983 Schott, F Monsoon R e sponse of the Somali Current and Associated U pwelling, Prog. Oceanogr., 12, 357-381 1983. Schott, F Seasonal Variation of Cross-Equatorial Flow in the Somali Current J. Geophys. Res. 91, 10,581 -10, 584, 1986. 141

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Schott F., J. C. Swallow, and M. Fieux The Somali Current at the Equator: An nual Cycle of Currents and Transports in the Upper 1000 m and Connection to Neighboring Latitudes Deep Sea Res. 37(12) 18251848 1990. Semtner, A. J. and R. M. Chervin, Ocean General Circulation From a Global Eddy Resolving Model J. Geophys. Res., 97(C4), 5,493 5 550, 1992. Slutz, R. J. T. J. Lubker S D. Woodruff R. L. Jenne D. H. Joseph, P. M. Steurer, and J. D. Elms GOADS Comprehensive Ocean-Atmosphere Data Set Release 1 CIRES University of Colorado, 1985. Swallow J. C. and J. G. Bruce Current Measur e ments Off the Somali Coast During the Southwest Monsoon of 1964 Deep Sea Res., 13(8) 861 928 1966. Tennekes, H. and J. L Lumley A First Course in Tutbulence The MIT Press Cam bridge, Massachusetts and London England 1972. Toole, J. M. and M. E. Raymer Heat and Fresh Water Budgets of the Indian Ocean Revisited D e ep S e a Res., 32(8) 917 -928, 1985. Tsai, P. T. H., K. J. O'Brien and M. E. Luther The 26-Day Oscillation Observed in the Satellite Sea Surface Temperature Measurements in the Equatorial Western Indian Ocean J. Geophys. Res., 97(C6) 9605 9618, 1992. Valenti, M G. M. E. Luther and Z. Ji, Interannual variability in the wind-driven Indian Ocean circulation 1977-1992, Journal of Climate submitted, 1997. Wacongne, S. and R. Pacanowski Seasonal Heat Transport in a Primitive Equations Model of the Tropical Indian Ocean, J. Phys. Oceanogr 26, 2 666-2 699 1996 Woodbury, S. E. M. E. Luther, and J. J. O'Brien The \iVind-Driven Seasonal Cir culation in the Soutern Tropical Idian Ocean J. Geophys. Res., 94, 17 ,98518,002 1989. Wylie D. P. and B B. Hinton, The \iVind Stress Patterns over the Indian Ocean During the Summer Monsoon of 1979 J. Phys. Oc e anogr., 12, 186-199 1982. Wyrtki, K., Oceanographic ATLAS of the International Indian Ocean Expedition published for the National Science Foundation Washington D.C. by Amerind Publishing Co. Pvt. Lit. New Dehli with the assistance of E. B. Bennett and D. J Rochford 1971. Wyrtki, K., An Equatorial Jet in the Indian O c ean, Science 181, 262-264 1973. 142

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VITA Zaihua Ji received a Bachelor 's Deuee in Phys ic s from East China Nor mal Uni ver s ity in 1982 in Shanghai C hin a. H e r ece i ved a M.S. Degree in Coastal D y namics from Ocean University o f Qingdao in Q ingdao C hina. After his mast e r degree h e started teaching as a lectu r e r in D epart m e n t of Oce an E ngineering Ocean University of Qingdao. Zaihua Ji e ntered hi s Ph.D. program in D epa rtment of Mar ine Scien ce, University o f South Florida in 1990 in Tampa. H e worked as a research associate during his Ph.D. pro g ram. Started in 1995, h e enrolled another M.S. Degr ee in Comput e r Scienc e in U niv ersity o f Sout h Florida as a dua l degree stud ent H e s u ccessf ull y defended hi s M.S. D eg ree in comput e r sc i ence a nd Ph.D. in m a rin e science in September and October 1997 respectively.


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